objective bayes model selection in probit models we describe a new variable selection procedure for categorical responses where the candidate models are all probit regression models the procedure uses objective intrinsic priors for the model parameters which do not depend on tuning parameters and ranks the models for the different subsets of covariates according to their model posterior probabilities when the number of covariates is moderate or large the number of potential models can be very large and for those cases we derive a new stochastic search algorithm that explores the potential sets of models driven by their model posterior probabilities the algorithm allows the user to control the dimension of the candidate models and thus can handle situations when the number of covariates exceed the number of observations we assess through simulations the performance of the procedure and apply the vari able selector to a gene expression data set where the response is whether a patient exhibits pneumonia software needed to run the procedures is available in the r package varselectip copyright 2011 john wiley sons ltd categorical responses often appear in the analysis of the effect of a medical treatment which is applied to a collection of patients these patients are typically characterized by a set of p potential covariates and a first important statistical problem in the presence of covariates is to reduce the dimension of the model by retaining from the original p covariates those that have some influence in the observed responses thus we have a model selection problem in the class of 2 p models in this paper we describe a new variable selection procedure applicable to dichotomous responses that are modeled with a probit regression although under the 0 1 loss function an optimal solution is the model having the highest posterior probability the 0 1 loss function might not be realistic for many applications one potential shortcoming is that submodels different from the true one are assigned the same loss regardless of how far or close to the true one they are therefore it seems appropriate to not choose a single optimal model but a subset of them having posterior probabilities over a given threshold thus the output of our model selection procedure will be a ranking of the models according to their posterior probabilities the literature on variable selection in logistic or probit models is not large researchers have car ried out variable selection in logistic regression with lasso type procedures for instance meier et al 1 used a group lasso for logistic regression whereas kyung et al 2 used the latent variable probit model for bayesian lasso variable selection the bayesian approaches tend to dominate and researchers typically solve the main difficulties in its formulation the choice of the prior for the models involved and for the model parameters by using subjective priors swartz and shete 3 did a simulation study of the five types of variable selection in case control logistic regression and found that a bayesian stochastic search based on a spike and slab prior was the best performer chen and dey 4 also used a bayesian approach and were particularly concerned with correlated binary responses in multivariate logistic regression in their study the researchers developed subjective priors and selected models on the

identifiability improper priors and gibbs sampling for generalized linear models markov chain monte carlo algorithms are widely used in the fitting of generalized linear models glms such model fitting is somewhat of an art form requiring suitable trickery and tuning to obtain results in which one can have confidence a wide range of practical issues arise the focus here is on parameter identifiability and posterior propriety in particular we clarify that nonidentifiability arises for usual glms and discuss its implications for simulation based model fitting because often some part of the prior specification is vague we consider whether the resulting posterior is proper providing rather general and easily checked results for glms we also show that if a gibbs sampler is run with an improper posterior then it may be possible to use the output to obtain meaningful inference for certain model unknowns

a new heterogeneous multidimensional unfolding procedure a variety of joint space multidimensional scaling mds methods have been utilized for the spatial analysis of two or three way dominance data involving subjects preferences choices considerations intentions etc so as to provide a parsimonious spatial depiction of the underlying relevant dimensions attributes stimuli and or subjects utility structures in the same joint space representation we demonstrate that care must be taken with respect to a key assumption in existent joint space mds models such that all estimated dimensions are utilized by each and every subject in the sample as this assumption can lead to serious distortions with respect to the derived joint spaces we develop a new bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three way dominance data a consumer psychology application regarding the preference for over the counter otc analgesics is provided we conclude by discussing the practical implications of the results as well as directions for future research

the variable selection problem abstract the problem of variable selection is one of the most pervasive model selection problems in statistical applications often referred to as the problem of subset selection it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors but there is uncertainty about which subset to use this vignette reviews some of the key developments that have led to the wide variety of approaches for this problem

classification of partially occluded objects using 3 point matching and distance transformation abstract recognition of partially occluded objects has been recently made possible by describing an object boundary with a sequence of local feature segments localized with control or dominant points and then matching the representations with those of a set of known reference shapes when part of the object boundary is being occluded contiguous intact feature segments will be used for identifying the object and distorted elements will be rejected in the matching process the main problem associated with this method is that the nature of occlusion may separate the object contour into discrete regions resulting in the degeneration of an individual representation into small isolated clusters reflecting only weak evidence on the object identity in this paper a new scheme capable of combining the isolated clusters for object classification is presented in essence curvature guided polygonal approximation is employed for detecting the dominant points of the boundaries a 3 point matching technique is developed for extracting cluster s of dominant points on an unknown boundary which matched against reference objects and to link up the scattered clusters to form a complete representation the chamfer 3 4 distance transform together with a quantitative measurement on the boundary covered by the matched dominant points is employed for calculating the similarity between the unknown and the reference contours the scheme has been successfully applied for recognizing multiple overlapped handtools in different sizes and orientations

the choice of variables in multivariate regression a non conjugate bayesian decision theory approach we consider the choice of explanatory variables in multivariate linear regression our approach balances prediction accuracy against costs attached to variables in a multivariate version of a decision theory approach pioneered by lindley 1968 we also employ a non conjugate proper prior distribution for the parameters of the regression model extending the standard normal inverse wishart by adding a component of error which is unexplainable by any number of predictor variables thus avoiding the determinism identified by dawid 1988 simulated annealing and fast updating algorithms are used to search for good subsets when there are very many regressors the technique is illustrated on a near infrared spectroscopy example involving 39 observations and 300 explanatory variables this demonstrates the effectiveness of multivariate regression as opposed to separate univariate regressions it also emphasises that within a bayesian framework more variables than observations can be utilised

a parallel algorithm for detecting dominant points on multiple digital curves abstract a new parallel algorithm is proposed for detecting corners of multiple planar curves or shapes this algorithm is based on an analysis of morphological residues and corner characteristics the method is different from traditional chain code based corner detection algorithms which associate with a chain coding and floating point computation for multiple objects in an image the proposed algorithm treats them uniformly and applies simultaneously on curves and shapes of multiple objects the experiments demonstrate that the algorithm can be effectively executed on an simd parallel computer a boundary constrained morphological method is presented for filling closed curves into shapes which are subsequently used for corner detection

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

parallel maximum likelihood estimator for multiple linear regression models consistency and run time are important questions in performing multiple linear regression models in response we introduce a new parallel maximum likelihood estimator for multiple linear models we first provide an equivalent condition between the method and the generalized least squares estimator we also consider the rank of projections and the eigenvalue we then present consistency when a stable solution exists in this paper we describe several consistency theorems and perform experiments on consistency outlier and scalability finally we fit the proposed method onto bankruptcy data

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

nonparametric regression using bayesian variable selection abstract this paper estimates an additive model semiparametrically while automatically selecting the significant independent variables and the appropriate power transformation of the dependent variable the nonlinear variables are modeled as regression splines with significant knots selected from a large number of candidate knots the estimation is made robust by modeling the errors as a mixture of normals a bayesian approach is used to select the significant knots the power transformation and to identify outliers using the gibbs sampler to carry out the computation empirical evidence is given that the sampler works well on both simulated and real examples and that in the univariate case it compares favorably with a kernel weighted local linear smoother the variable selection algorithm in the paper is substantially faster than previous bayesian variable selection algorithms

the influence of variable selection a bayesian diagnostic perspective abstract variable selection is ubiquitous in statistical practice forward selection backwards elimination or a combination thereof are among the most popular techniques statistical texts teach direct interpretation of coefficients after variable selection for scientific purposes the desired interpretation is unconditional on the variable selection in this article an influence analysis of variable selection is performed from a bayesian viewpoint variable selection is shown to be surprisingly influential a new statistic is recommended for routine examination during variable selection

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

lindley s paradox 1982 lindley s paradox journal of the american statistical association vol 77 no 378 pp 325 334

on detecting dominant points abstract detecting dominant points is a crucial preprocessing step for shape recognition and point based motion estimation polygonal approximation has been a commonly used approach in detecting dominant points this paper presents two alternatives which detect stable dominant points in the first method we find a set of positive maximum and negative minimum curvature points along the gaussian smoothed boundary followed by a split and merge polygonal approximation algorithm the resulting break points vertices of the approximated polygon are the dominant points experimental results show that dominant points obtained by this method are less sensitive to the orientation of the boundary than other polygonal approximation algorithms in the sense that the number and the location of the dominant points along the contour remain relatively unchanged in the second method we smooth a boundary by a gaussian filter using various widths until the extreme curvature points remain relatively unchanged for a range of filter widths the resulting extreme curvature points which are stable to orientation and a reasonable range of scaling are the dominant points

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

bayesian identification selection and estimation of semiparametric functions in high dimensional additive models in this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions each function is written as a linear combination of basis terms with coefficients regularized by a proper linearly constrained gaussian prior given any potentially rank deficient prior precision matrix we show how to derive linear constraints so that the corresponding effect is identified in the additive model this allows for the use of a wide range of bases and precision matrices in priors for regularization by introducing indicator variables each constrained gaussian prior is augmented with a point mass at zero thus allowing for function selection posterior inference is calculated using markov chain monte carlo and the smoothness in the functions is both the result of shrinkage through the constrained gaussian prior and model averaging we show how using non degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case we show the favourable performance of our approach when compared to two contemporary alternative bayesian methods to highlight the potential of our approach in high dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra day electricity load both models feature a variety of different univariate and bivariate functions which require different levels of smoothing and where component selection is meaningful priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right

model averaging and dimension selection for the singular value decomposition many multivariate data analysis techniques for an m n matrix y are related to the model y m e where y is an m n matrix of full rank and m is an unobserved mean matrix of rank k m n typically the rank of m is estimated in a heuristic way and then the least squares estimate of m is obtained via the singular value decomposition of y yielding an estimate that can have a very high variance in this article we suggest a model based alternative to the preceding approach by providing prior distributions and posterior estimation for the rank of m and the components of its singular value decomposition in addition to providing more accurate inference such an approach has the advantage of being extendable to more general data analysis situations such as inference in the presence of missing data and estimation in a generalized linear modeling framework

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

regressions by leaps and bounds this paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic less than six floating point operations per regression and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets the result is a reduction of several orders of magnitude in the number of operations required to find the best subsets

variational inference for latent variables and uncertain inputs in gaussian processes the gaussian process latent variable model gp lvm provides a flexible approach for non linear dimensionality reduction that has been widely applied however the current approach for training gp lvms is based on maximum likelihood where the latent projection variables are maximised over rather than integrated out in this paper we present a bayesian method for training gp lvms by introducing a non standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a gp lvm by maximising an analytic lower bound on the exact marginal likelihood we apply this method for learning a gp lvm from i i d observations and for learning non linear dynamical systems where the observations are temporally correlated we show that a benefit of the variational bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non linear latent space the resulting framework is generic flexible and easy to extend for other purposes such as gaussian process regression with uncertain or partially missing inputs we demonstrate our method on synthetic data and standard machine learning benchmarks as well as challenging real world datasets including high resolution video data

optimal predictive model selection often the goal of model selection is to choose a model for future prediction and it is natural to measure the accuracy of a future prediction by squared error loss under the bayesian approach it is commonly perceived that the optimal predictive model is the model with highest posterior probability but this is not necessarily the case in this paper we show that for selection among normal linear models the optimal predictive model is often the median probability model which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1 2 of being in a model the median probability model often differs from the highest probability model

a control point matching algorithm abstract a general procedure for point matching is outlined which deals effectively with the dual problems of finding matches between two point sets and correctly identifying missing or spurious points

variable selection and functional form uncertainty in cross country growth regressions regression analyses of cross country economic growth data are complicated by two main forms of model uncertainty the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function most discussions in the literature address these problems independently yet a joint treatment is essential we present a new framework that makes such a joint treatment possible using flexible nonlinear models specified by gaussian process priors and addressing the variable selection problem by means of bayesian model averaging using this framework we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory while taking into account the uncertainty in selecting explanatory variables controlling for variable selection uncertainty we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies however controlling for functional form uncertainty we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections

the horseshoe estimator for sparse signals this paper proposes a new approach to sparsity called the horseshoe estimator the horseshoe is a close cousin of other widely used bayes rules arising from for example double exponential and cauchy priors in that it is a member of the same family of multivariate scale mixtures of normals but the horseshoe enjoys a number of advantages over existing approaches including its robustness its adaptivity to dierent sparsity patterns and its analytical tractability we prove two theorems that formally characterize both the horseshoe s adeptness at large outlying signals and its super ecient rate of convergence to the correct estimate of the sampling density in sparse situations finally using a combination of real and simulated data we show that the horseshoe estimator corresponds quite closely to the answers one would get by pursuing a full bayesian model averaging approach using a discrete mixture prior to model signals and noise

model based partial shape recognition using contour curvature and affine transformation abstract the problem of recognizing partially occluded parts is of considerable interest in the field of manufacturing automation in this paper we describe a technique of recognizing partially obscured and overlapping two dimensional objects by using the contour curvature and affine transformation in a model base this technique is based on the invariant attribute of an object called footprint for the purpose of hashing by such a recognition method we could identify an object by matching all model objects against a period of the partial contour of composite objects and by voting one of the best matches from the pre established model base the technique is divided into the following procedures digitization from camera thresholding into binary object labeling border operator chain coding footprint extraction building the model base and hashing table finding breakpoints building the segment table affine transformation and matching process

object representation and recognition in shape spaces in this paper we describe a shape space based approach for invariant object representation and recognition in this approach an object and all its similarity transformed versions are identified with a single point in a high dimensional manifold called the shape space object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space this approach produced promising results in 2d object recognition experiments it is invariant to similarity transformations and is relatively insensitive to noise and occlusion potentially it can also be used for 3d object recognition

minors of the moore penrose inverse abstract let q k n 1 k 1 1 k n denote the strictly increasing sequences of k elements from 1 n for q k n we denote by a the submatrix of a with rows indexed by columns by the submatrix obtained by deleting the rows and columns is denoted by a lsqb rsqb for nonsingular a r n n the jacobi identity relates the minors of the inverse a 1 to those of a det a 1 lsqb rsqb 1 k i 1 i k i 1 i det a lsqb rsqb det a for any q k n we generalize the jacobi identity to matrices a r m n r expressing the minors of the moore penrose inverse a in terms of the minors of the maximal nonsingular submatrices a ij of a in our notation det a lsqb rsqb 1 vol 2 a i j n det a ij a a ij for any q k m q k n 1 k r where vol 2 a denotes the sum of squares of determinants of r r submatrices of a we apply our results to questions concerning the nonnegativity of principal minors of the moore penrose inverse

finding factors influencing risk comparing bayesian stochastic search and standard variable selection methods applied to logistic regression models of cases and controls when modeling the risk of a disease the very act of selecting the factors to be included can heavily impact the results this study compares the performance of several variable selection techniques applied to logistic regression we performed realistic simulation studies to compare five methods of variable selection 1 a confidence interval ci approach for significant coefficients 2 backward selection 3 forward selection 4 stepwise selection and 5 bayesian stochastic search variable selection ssvs using both informed and uniformed priors we defined our simulated diseases mimicking odds ratios for cancer risk found in the literature for environmental factors such as smoking dietary risk factors such as fiber genetic risk factors such as xpd and interactions we modeled the distribution of our covariates including correlation after the reported empirical distributions of these risk factors we also used a null data set to calibrate the priors of the bayesian method and evaluate its sensitivity of the standard methods 95 per cent ci backward forward and stepwise selection the ci approach resulted in the highest average per cent of correct associations and the lowest average per cent of incorrect associations ssvs with an informed prior had a higher average per cent of correct associations and a lower average per cent of incorrect associations than the ci approach this study shows that the bayesian methods offer a way to use prior information to both increase power and decrease false positive results when selecting factors to model complex disease risk

identifiability and convergence issues for markov chain monte carlo fitting of spatial models the marked increase in popularity of bayesian methods in statistical practice over the last decade owes much to the simultaneous development of markov chain monte carlo mcmc methods for the evaluation of requisite posterior distributions however along with this increase in computing power has come the temptation to fit models larger than the data can readily support meaning that often the propriety of the posterior distributions for certain parameters depends on the propriety of the associated prior distributions an important example arises in spatial modelling wherein separate random effects for capturing unstructured heterogeneity and spatial clustering are of substantive interest even though only their sum is well identified by the data increasing the informative content of the associated prior distributions offers an obvious remedy but one that hampers parameter interpretability and may also significantly slow the convergence of the mcmc algorithm in this paper we investigate the relationship among identifiability bayesian learning and mcmc convergence rates for a common class of spatial models in order to provide guidance for prior selection and algorithm tuning we are able to elucidate the key issues with relatively simple examples and also illustrate the varying impacts of covariates outliers and algorithm starting values on the resulting algorithms and posterior distributions

bayes model averaging with selection of regressors when a number of distinct models contend for use in prediction the choice of a single model can offer rather unstable predictions in regression stochastic search variable selection with bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors here we look at bayes model averaging incorporating variable selection for prediction this offers similar mean square errors of prediction but with a vastly reduced predictor space this can greatly aid the interpretation of the model it also reduces the cost if measured variables have costs the development here uses decision theory in the context of the multivariate general linear model in passing this reduced predictor space bayes model averaging is contrasted with single model approximations a fast algorithm for updating regressions in the markov chain monte carlo searches for posterior inference is developed allowing many more variables than observations to be contemplated we discuss the merits of absolute rather than proportionate shrinkage in regression especially when there are more variables than observations the methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution

bayesian model selection using test statistics existing bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set in practice this requirement limits the application of bayesian model selection methodology to overcome this limitation we propose a new approach towards bayesian model selection that uses classical test statistics to compute bayes factors between possible models in several test cases our approach produces results that are similar to previously proposed bayesian model selection and model averaging techniques in which prior distributions were carefully chosen in addition to eliminating the requirement to specify complicated prior distributions this method offers important computational and algorithmic advantages over existing simulation based methods because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates our method facilitates the selection of hyperparameter values through prior predictive simulation

predictive specification of prior model probabilities in variable selection summary we examine the problem of specifying prior probabilities for all possible subset models in the context of variable selection in normal linear models a solution is proposed that uses a prior prediction for the observable an associated weight and prior opinion regarding error precision as the only required input numerical examples are given to illustrate the method

imputation and variable selection in linear regression models with missing covariates across multiply imputed data sets variable selection methods such as stepwise regression and other criterion based strategies that include or exclude particular variables typically result in models with different selected predictors thus presenting a problem for combining the results from separate complete data analyses here drawing on a bayesian framework we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates one approach which we call impute then select its involves initially performing multiple imputation and then applying bayesian variable selection to the multiply imputed data sets a second strategy is to conduct bayesian variable selection and missing data imputation simultaneously within one gibbs sampling process which we call simultaneously impute and select sias the methods are implemented and evaluated using the bayesian procedure known as stochastic search variable selection for multivariate normal data sets but both strategies offer general frameworks within which different bayesian variable selection algorithms could be used for other types of data sets a study of mental health services utilization among children in foster care programs is used to illustrate the techniques simulation studies show that both its and sias outperform complete case analysis with stepwise variable selection and that sias slightly outperforms its

bayesian variable selection in structured high dimensional covariate spaces with applications in genomics we consider the problem of variable selection in regression modeling in high dimensional spaces where there is known structure among the covariates this is an unconventional variable selection problem for two reasons 1 the dimension of the covariate space is comparable and often much larger than the number of subjects in the study and 2 the covariate space is highly structured and in some cases it is desirable to incorporate this structural information in to the model building process we approach this problem through the bayesian variable selection framework where we assume that the covariates lie on an undirected graph and formulate an ising prior on the model space for incorporating structural information certain computational and statistical problems arise that are unique to such high dimensional structured settings the most interesting being the phenomenon of phase transitions we propose theoretical and computational schemes to mitigate these problems we illustrate our methods on two

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

invariant representation matching and pose estimation of 3d space curves under similarity transformations this paper presents a system for matching and pose estimation of 3d space curves under the similarity transformation composed of rotation translation and uniform scaling the system makes use of constraints not only on the feature points but also on curve segments a representation called the similarity invariant coordinate system sics is presented for deriving semi local invariants of 3d curves the sics also enables an efficient exploration of constraints on the shape of the entire curve model based curve matching is performed in the principle of maximum a posteriori map probability in which markov random fields mrfs are used to model the prior probability results are given to demonstrate the matching with missing and extra feature points the extensive exploration of the curve shape constraints in both the matching and the pose estimation stages are shown to significantly improve the quality of the recognition and pose estimation

detecting differentially expressed genes in microarrays using bayesian model selection dna microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease the high throughput nature of these arrays where differential expression for thousands of genes can be measured simultaneously creates an enormous wealth of information but also poses a challenge for data analysis because of the large multiple testing problem involved the solution has generally been to focus on optimizing false discovery rates while sacrificing power the drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold we introduce a new method for detecting differentially expressed genes based on a high dimensional model selection technique bayesian anova for microarrays bam which strikes a balance between false rejections and false nonrejections the basis of the new approach involves a weighted average of generalized ridge

small sample bias of point estimators of the odds ratio from matched sets the bias of several point estimators of the odds ratio arising from matched pair data is investigated for small samples simple alternatives to the traditional maximum likelihood estimator are suggested on both the original scale and the logarithm scale in each case the suggested estimators possess a superior performance in terms of mean square error generalizations are given for 1 r matched data sets

partial factor modeling predictor dependent shrinkage for linear regression we develop a modified gaussian factor model for the purpose of inducing predictor dependent shrinkage for linear regression the new model predicts well across a wide range of covariance structures on real and simulated data furthermore the new model facilitates variable selection in the case of correlated predictor variables which often stymies other methods

on the pitman yor process with spike and slab base measure summaryfor the most popular discrete nonparametric models beyond the dirichlet process the prior guess at the shape of the data generating distribution also known as the base measure is assumed to be diffuse such a specification greatly simplifies the derivation of analytical results allowing for a straightforward implementation of bayesian nonparametric inferential procedures however in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure and then the dirichlet process is essentially the only tractable choice for the prior in this paper we fill this gap by considering the pitman yor process with an atom in its base measure we derive computable expressions for the distribution of the induced random partitions and for the predictive distributions these findings allow us to devise an effective generalized polya urn gibbs sampler applications to density estimation clustering and curve estimation with both simulated and real data serve as an illustration of our results and allow comparisons with existing methodology in particular we tackle a functional data analysis problem concerning basal body temperature curves

error analysis in stereo determination of 3 d point positions the relationship between the geometry of a stereo camera setup and the accuracy in obtaining three dimensional position information is of great practical importance in many imaging applications assuming a point in a scene has been correctly identified in each image its three dimensional position can be recovered via a simple geometrical method known as triangulation the probability that position estimates from triangulation are within some specified error tolerance is derived an ideal pinhole camera model is used and the error is modeled as known spatial image plane quantization a point s measured position maps to a small volume in 3 d determined by the finite resolution of the stereo setup with the assumption that the point s actual position is uniformly distributed inside this volume closed form expressions for the probability distribution of error in position along each coordinate direction horizontal vertical and range are derived following this the probability that range error dominates over errors in the point s horizontal or vertical position is determined it is hoped that the results presented will have an impact upon both sensor design and error modeling of position measuring systems for computer vision and related applications

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

nonnegativity of principal minors of generalized inverses of p0 matrices abstract the result of principal interest established in this paper is that if a is an n n singular irreducible m matrix then a large class of generalized inverses of a possesses the property that each of its elements has all its principal minors nonnegative the class contains both the group and the moore penrose generalized inverses of a in an application of our results it is shown that the fundamental matrix of a continuous in time ergodic markov chain on a finite state space has all its principal minors nonnegative

an alternative to the standard bayesian procedure for discrimination between normal linear models summary we consider the standard bayesian procedure for discrimination focusing on its tendency to give low posterior probabilities to some correct models even in conditions of moderate to large sampling sizes furthermore in some situations that could well occur in practice the standard procedure is even asymptotically inconsistent we claim that the explanation is that the standard procedure inflates the posterior probability of the model that has the smallest expected increase in information about its parameters we then propose to modify it by an amount related to the expected gain in information and show that the lindley paradox does not occur finally we obtain the limiting alternative criterion that results by letting the prior densities become noninformative which enables us to measure how sensitive the discrimation is to the informative prior densities used

estimation of the false negative fraction of a diagnostic kit through bayesian regression model averaging in modelling we usually endeavour to find a single best model that explains the relationship between independent and dependent variables selection of a single model fails to take into account the prior uncertainty in the model space the bayesian model averaging bma approach tackles this problem by considering the set of all possible models we apply bma approach to the estimation of the false negative fraction fnf in a particular case of a two stage multiple screening test for bowel cancer we find that after taking model uncertainty into consideration the estimate of the fnf obtained is largely dependent on the covariance structure of the priors results obtained when the zellner g prior for the prior variance is used is largely influenced by the magnitude of g

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

mixtures of g priors for bayesian variable selection zellner s g prior remains a popular conventional prior for use in bayesian variable selection despite several undesirable consistency issues in this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular we present theoretical properties of the mixture g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors empirical bayes approaches and other default procedures please see arnold zellner s letter and the author s response

on some classes of linear complementarity problems with matrices of order n and rank n 1 in this paper we generalize a fundamental result observed by b c eaves on the nature of solutions constructed by lemke s algorithm applied to solve the linear complementarity problem q m initiating it with the positive vector d rn we use this generalization and identify two subclasses of the class of n n matrices m of rank n 1 for which the set of q rn such that the lcp q m has a solution is convex we also present algorithms to compute a solution to q m if one exists for these classes of matrices

generalized inverses with nonnegative principal minors abstract conditions for a g inverse to be a p0 matrix are obtained in terms of bordered matrices some results are derived as corollary in the case of matrices of order n and rank n 1 a sufficient condition is given for the moore penrose inverse of i t to be a p0 matrix where t is the transition probability matrix of a markov chain

incorporating spatial dependence into bayesian multiple testing of statistical parametric maps in functional neuroimaging abstract the analysis of functional neuroimaging data often involves the simultaneous testing for activation at thousands of voxels leading to a massive multiple testing problem this is true whether the data analyzed are time courses observed at each voxel or a collection of summary statistics such as statistical parametric maps spms it is known that classical multiplicity corrections become strongly conservative in the presence of a massive number of tests some more popular approaches for thresholding imaging data such as the benjamini hochberg step up procedure for false discovery rate control tend to lose precision or power when the assumption of independence of the data does not hold bayesian approaches to large scale simultaneous inference also often rely on the assumption of independence we introduce a spatial dependence structure into a bayesian testing model for the analysis of spms by using spms rather than the voxel time courses much of the computational burden of bayesian analysis is mitigated increased power is demonstrated by using the dependence model to draw inference on a real dataset collected in a fmri study of cognitive control the model also is shown to lead to improved identification of neural activation patterns known to be associated with eye movement tasks

using polygons to recognize and locate partially occluded objects we present computer vision algorithms that recognize and locate partially occluded objects the scene may contain unknown objects that may touch or overlap giving rise to partial occlusion the algorithms revolve around a generate test paradigm the paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects polygon representations of the object s boundary guide the hypothesis generation scheme choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification special vertices of the polygon called corners help detect and locate the model in the scene polygon moment calculations lead to estimates of the dissimilarity between scene and model corners and determine the model corner location in the scene an association graph represents the matches and compatibility constraints extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis using a coordinate transform that maps the model onto the scene the hypothesis gives the proposed model s location and orientation hypothesis verification requires checking for region consistency the union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene experimental results give examples of all phases of recognizing and locating the objects

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

decoupling shrinkage and selection in bayesian linear models a posterior summary perspective selecting a subset of variables for linear models remains an active area of research this article reviews many of the recent contributions to the bayesian model selection and shrinkage prior literature a posterior variable selection summary is proposed which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors

robust multidimensional matched subspace classifiers based on weighted least squares we propose and design two classes of robust subspace classifiers for classification of multidimensional signals our classifiers are based on robust m estimators and the least median of squares principle and we show that they may be unified as iterated reweighted oblique subspace classifiers the performance of the proposed classifiers are demonstrated by two examples noncoherent detection of space time frequency shift keying signals and shape classification of partially occluded two dimensional 2 d objects in both cases the proposed robust subspace classifiers outperform the conventional subspace classifiers

bayesian wavelet regression on curves with application to a spectroscopic calibration problem motivated by calibration problems in near infrared nir spectroscopy we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands we tackle this regression problem by calculating the wavelet transforms of the discretized curves then applying a bayesian variable selection method using mixture priors to the multivariate regression of predictands on wavelet coefficients for prediction purposes we average over a set of likely models applied to a particular problem in nir spectroscopy this approach was able to find subsets of the wavelet coefficients with overall better predictive performance than the more usual approaches in the application the available predictors are measurements of the nir reflectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths the aim is to predict the composition i e the fat flour sugar and water content of the doug

partially occluded object recognition using statistical models in this paper we present a new bayesian framework for partially occluded object recognition based on matching extracted local features on a one to one basis with object features we introduce two different statistical models for occlusion one model assumes that each feature in the model can be occluded independent of whether any other features are occluded whereas the second model uses spatially correlated occlusion to represent the extent of occlusion using these models the object recognition problem reduces to finding the object hypothesis with largest generalized likelihood we develop fast algorithms for finding the optimal one to one correspondence between scene features and object features to compute the generalized likelihoods under both models we conduct experiments illustrating the differences between the two occlusion models using different quantitative metrics we also evaluate the recognition performance of our algorithms using examples extracted from object silhouettes and synthetic aperture radar imagery and illustrate the performance advantages of our approach over alternative algorithms

mixtures of g priors for bayesian model averaging with economic application this paper examines the issue of variable selection in linear regression modeling where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset in this context bayesian model averaging presents a formal bayesian solution to dealing with model uncertainty the main interest here is the effect of the prior on the results such as posterior inclusion probabilities of regressors and predictive performance the authors combine a binomial beta prior on model size with a g prior on the coefficients of each model in addition they assign a hyperprior to g as the choice of g has been found to have a large impact on the results for the prior on g they examine the zellner siow prior and a class of beta shrinkage priors which covers most choices in the recent literature the authors propose a benchmark beta prior inspired by earlier findings with fixed g and show it leads to consistent model selection inference is conducted through a markov chain monte carlo sampler over model space and g the authors examine the performance of the various priors in the context of simulated and real data for the latter they consider two important applications in economics namely cross country growth regression and returns to schooling recommendations for applied users are provided

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

performance of variable and function selection methods for estimating the nonlinear health effects of correlated chemical mixtures a simulation study statistical methods for identifying harmful chemicals in a correlated mixture often assume linearity in exposure response relationships nonmonotonic relationships are increasingly recognized eg for endocrine disrupting chemicals however the impact of nonmonotonicity on exposure selection has not been evaluated in a simulation study we assessed the performance of bayesian kernel machine regression bkmr bayesian additive regression trees bart bayesian structured additive regression with spike slab priors bstarss generalized additive models with double penalty gamdp and thin plate shrinkage smoothers gamts multivariate adaptive regression splines mars and lasso penalized regression we simulated realistic exposure data based on pregnancy exposure to 17 phthalates and phenols in the us national health and nutrition examination survey using a multivariate copula we simulated data sets of size n 250 and compared methods across 32 scenarios varying by model size and sparsity signal to noise ratio correlation structure and exposure response relationship shapes we compared methods in terms of their sensitivity specificity and estimation accuracy in most scenarios bkmr bstarss gamdp and gamts achieved moderate to high sensitivity 0 52 0 98 and specificity 0 21 0 99 bart and mars achieved high specificity 0 90 but low sensitivity in low signal to noise ratio scenarios 0 20 0 51 lasso was highly sensitive 0 71 0 99 except for quadratic relationships 0 27 penalized regression methods that assume linearity such as lasso may not be suitable for studies of environmental chemicals hypothesized to have nonmonotonic relationships with outcomes instead bkmr bstarss gamdp and gamts are attractive methods for flexibly estimating the shapes of exposure response relationships and selecting among correlated exposures

a truncated em approach for spike and slab sparse coding we study inference and learning based on a sparse coding model with spike and slab prior as in standard sparse coding the model used assumes independent latent sources that linearly combine to generate data points however instead of using a standard sparse prior such as a laplace distribution we study the application of a more flexible spike and slab distribution which models the absence or presence of a source s contribution independently of its strength if it contributes we investigate two approaches to optimize the parameters of spike and slab sparse coding a novel truncated em approach and for comparison an approach based on standard factored variational distributions the truncated approach can be regarded as a variational approach with truncated posteriors as variational distributions in applications to source separation we find that both approaches improve the state of the art in a number of standard benchmarks which argues for the use of spike and slab priors for the corresponding data domains furthermore we find that the truncated em approach improves on the standard factored approach in source separation tasks which hints to biases introduced by assuming posterior independence in the factored variational approach likewise on a standard benchmark for image denoising we find that the truncated em approach improves on the factored variational approach while the performance of the factored approach saturates with increasing numbers of hidden dimensions the performance of the truncated approach improves the state of the art for higher noise levels

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

global description of edge patterns using moments abstract shape recognition has traditionally been accomplished using well bounded segmented regions or their closed contours in this way the internal edge details of the objects are ignored there are cases such as in character recognition and in object recognition when patterns are not closed contours in this paper such patterns are defined as edge patterns and edge standard moments esm are developed which are invariant to location scale and rotation results of patterns matching with character recognition and polyhedral object recognition are presented

on bayesian calculations for mixture likelihoods and priors we present methodology for calculating bayes factors between models as well as posterior probabilities of the models when the indicator variables of the models are integrated out of the posterior before markov chain monte carlo mcmc computations standard methodology would include the indicator functions as part of the mcmc computations we demonstrate that our methodology can give substantially greater accuracy than the traditional approach we illustrate the methodology using the model selection prior of george and mcculloch applied to logistic regression and to a mixture model for observations in a hierarchical random effects model

on the distribution of a deforming triangle this paper presents the mathematical treatment of a new measure sphericity which is used to quantify the similarity between two triangles various properties of sphericity such as maximal invariance and its probability density function are derived

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

occluded objects recognition using multiscale features and hopfield neural network abstract a new method to recognize partially visible two dimensional objects by means of multiscale features and hopfield neural network was proposed the hopfield network was employed to perform global feature matching since the network only guarantees to converge to a local optimal state the matching results heavily depend on the initial network state determined by the extracted features to acquire more satisfactory initial matching results a new feature vector was developed which consists of the multiscale evolution of the extremal position and magnitude of the wavelet transformed contour orientation these features can even be used to discriminate dominant points hence good initial states can be obtained the good initiation enables our proposed method to recognize objects even heavily occluded that cannot be achieved by using the nasrabadi li s method in addition to make the matching results more insensitive to the threshold value selection of the network we replace the step like thresholding function by a ramp like one experimental results have shown that our method is effective even for noisy occluded objects

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

variable selection and bayesian model averaging in case control studies covariate and confounder selection in case control studies is often carried out using a statistical variable selection method such as a two step method or a stepwise method in logistic regression inference is then carried out conditionally on the selected model but this ignores the model uncertainty implicit in the variable selection process and so may underestimate uncertainty about relative risks we report on a simulation study designed to be similar to actual case control studies this shows that p values computed after variable selection can greatly overstate the strength of conclusions for example for our simulated case control studies with 1000 subjects of variables declared to be significant with p values between 0 01 and 0 05 only 49 per cent actually were risk factors when stepwise variable selection was used we propose bayesian model averaging as a formal way of taking account of model uncertainty in case control studies this yields an easily interpreted summary the posterior probability that a variable is a risk factor and our simulation study indicates this to be reasonably well calibrated in the situations simulated the methods are applied and compared in the context of a case control study of cervical cancer

a bayesian approach to nonparametric bivariate regression abstract this article outlines a general bayesian approach to estimating a bivariate regression function in a nonparametric manner it models the function using a bivariate regression spline basis with many terms binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression the regression function is estimated using an estimate of its posterior mean smoothing over the distribution of these binary indicator variables to make the computations tractable all estimates are obtained using markov chain monte carlo sampling extensive simulated comparisons are provided that demonstrate the competitive performance of this approach against other data driven bivariate surface estimators prominent in the literature it is then shown how the procedure can be extended to provide a general approach to nonparametric bivariate surface estimation in two difficult regression settings the first

recognition of occluded objects a cluster structure algorithm clustering techniques have been used to perform image segmentation to detect lines and curves in images and to solve several other problems in pattern recognition and image analysis in this paper we apply clustering methods to a new problem domain and present a new method based on a cluster structure approach for the recognition of 2 d partially occluded objects basically the technique consists of three steps clustering of border segment transformations finding continuous sequences of segments in appropriately chosen clusters and clustering of sequence average transformation values as compared to some of the earlier methods which identify an object based on only one sequence of matched segments the new approach allows the identification of all parts of the model which match in the occluded scene we also discuss the application of the clustering techniques to 3 d scene analysis in both cases the cluster structure algorithm entails the application of clustering concepts in a hierarchical manner resulting in a decrease in the computational effort as the recognition algorithm progresses the implementation of the techniques discussed for the 2 d case has been completed and the algorithm has been evaluated with respect to a large number of examples where several objects partially occlude one another the method is able to tolerate a moderate change in scale and a significant amount of shape distortion arising as a result of segmentation and or the polygonal approximation of the boundary of the object a summary of the results is presented

partial shape recognition a landmark based approach a method of recognizing partially occluded objects is presented in which each object is represented by a set of landmarks given a scene consisting of partially occluded objects a model object in the scene is hypothesized by matching the landmarks of the model with those in the scene a measure of similarity between two landmarks is needed to perform this matching a local shape measure sphericity is introduced it is shown that any invariant function under a similarity transformation is a function of the sphericity to match landmarks between the model and the scene a table of compatibility is constructed a technique known as hopping dynamic programming is described to guide the landmark matching through the compatibility table the location of the model in the scene is estimated with a least squares fit among the matched landmarks a heuristic measure is then computed to decide if the model is in the scene

a two stage bayesian model selection strategy for supersaturated designs in early stages of experimentation one often has many candidate factors of which only few have significant influence on the response supersaturated designs can offer important advantages however standard regression techniques of fitting a prediction line using all candidate variables fail to analyze data from such designs stepwise regression may be used but has drawbacks as reported in the literature a two stage bayesian model selection strategy able to keep all possible models under consideration while providing a level of robustness akin to bayesian analyses incorporating noninformative priors is proposed the strategy is demonstrated on a well known dataset and compared to competing methods via simulation