a unified treatment of integer parameter models abstract it is shown that there is an analog to the score function the derivative of the log likelihood with respect to the parameter here called the difference score which plays an important theoretical role in integer parameter models a unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score lds it is established that many of the exact results available for exponential family models also hold for lds models in particular we find an information lower bound show the uniqueness of the maximum likelihood estimator establish monotone likelihood ratio and establish optimality properties in two sided tests it is also shown that if one has a multiparameter likelihood in which there is a conditional likelihood depending on n alone then these exact results apply there as well it is also established when and why the usual likelihood methodology will apply to a class of nonstandard models in which the natural approxima

functional clustering by bayesian wavelet methods summary we propose a nonparametric bayes wavelet model for clustering of functional data the wavelet based methodology is aimed at the resolution of generic global and local features during clustering and is suitable for clustering high dimensional data based on the dirichlet process the nonparametric bayes model extends the scope of traditional bayes wavelet methods to functional clustering and allows the elicitation of prior belief about the regularity of the functions and the number of clusters by suitably mixing the dirichlet processes posterior inference is carried out by gibbs sampling with conjugate priors which makes the computation straightforward we use simulated as well as real data sets to illustrate the suitability of the approach over other alternatives

species sampling models consistency for the number of species this paper considers species sampling models using constructions that arise from bayesian nonparametric prior distributions a discrete random measure used to generate a species sampling model can have either a countable infinite number of atoms which has been the emphasis in the recent literature or a finite number of atoms k while allowing k to be assigned a prior probability distribution on the positive integers it is the latter class of model we consider here due to the interpretation of k as the number of species we demonstrate the consistency of the posterior distribution of k as the sample size increases copyright 2013 oxford university press

full predictivistic modeling of stock market data application to change point problems in change point problems in general we should answer three questions how many changes are there where are they and what is the distribution of the data within the blocks in this paper we develop a new full predictivistic approach for modeling observations within the same block of observation and consider the product partition model ppm for treating the change point problem the ppm brings more flexibility into the change point problem because it considers the number of changes and the instants when the changes occurred as random variables a full predictivistic characterization of the model can provide a more tractable way to elicit the prior distribution of the parameters of interest once prior opinions will be required only about observable quantities we also present an application to the problem of identifying multiple change points in the mean and variance of a stock market return time series

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

product partition models for normal means abstract i consider probability models for the estimation of normal means that allow for some of the means to be equal these probability models called product partition models specify prior probabilities for a random partition the posterior probability of the partition given the observations has the same form the resulting estimate of the means the product estimate is obtained by conditioning on the partition and summing over all possible partitions the large number of computations involved leads to the use of markov sampling to compute the product estimate i compare the product estimate to other estimates of normal means both in a simulation study and in the prediction of baseball batting averages

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

mixture models with a prior on the number of components abstracta natural bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric dirichlet weights and put a prior on the number of components that is to use a mixture of finite mixtures mfm the most commonly used method of inference for mfms is reversible jump markov chain monte carlo but it can be nontrivial to design good reversible jump moves especially in high dimensional spaces meanwhile there are samplers for dirichlet process mixture dpm models that are relatively simple and are easily adapted to new applications it turns out that in fact many of the essential properties of dpms are also exhibited by mfms an exchangeable partition distribution restaurant process random measure representation and stick breaking representation and crucially the mfm analogues are simple enough that they can be used much like the corresponding dpm properties consequently many of the powerful methods developed for inference in dpms

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

separation measures and the geometry of bayes factor selection for classification conjugacy assumptions are often used in bayesian selection over a partition because they allow the otherwise unfeasibly large model space to be searched very quickly the implications of such models can be analysed algebraically we use the explicit forms of the associated bayes factors to demonstrate that such methods can be unstable under common settings of the associated hyperparameters we then prove that the regions of instability can be removed by setting the hyperparameters in an unconventional way under this family of assignments we prove that model selection is determined by an implicit separation measure a function of the hyperparameters and the sufficient statistics of clusters in a given partition we show that this family of separation measures has plausible properties the methodology proposed is illustrated through the selection of clusters of longitudinal gene expression profiles

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

bayesian inference on changes in response densities over predictor clusters in epidemiology it often is of interest to assess how individuals with different trajectories over time in an environmental exposure or biomarker differ with respect to a continuous response for ease in interpretation and presentation of results epidemiologists typically categorize predictors before analysis to extend this approach to time varying predictors individuals can be clustered by their predictor trajectory with the cluster index included as a predictor in a regression model for the response this article develops a semiparametric bayes approach that avoids assuming a prespecified number of clusters and allows the response to vary nonparametrically over predictor clusters this methodology is motivated by interest in relating trajectories in weight gain during pregnancy to the distribution of birth weight adjusted for gestational age at delivery in this setting the proposed approach allows the tails of the birth weight density to vary flexibly over weight gain clusters

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

a parameter optimized adi fdtd method based on the 2 4 stencil this paper presents a parameter optimized alternating direction implicit adi finite difference time domain fdtd method based on the 2 4 stencil denoted as 2 4 parameter optimized po adi fdtd method to achieve better dispersion performance with different optimization schemes the method can be applied to satisfy various requirements such as zero numerical dispersion error znde in the axes direction znde in the diagonal direction zero anisotropy dispersion znde for two arbitrary angles and minimum average dispersion error through the stability analysis for the 2 4 po adi fdtd method it can be proved that all the schemes proposed here are unconditionally stable the variation of the performance of the 2 4 po adi fdtd method for different frequencies is also studied one can find that the desired performance of the 2 4 po adi fdtd method can be basically preserved within a frequency band without deterioration through comparison it can be concluded that the 2 4 po adi fdtd method outperforms the previous parameter optimized adi fdtd method based on the 2 2 stencil in several aspects

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

set partitioning via inclusion exclusion given a set n with n elements and a family mathcal f of subsets we show how to partition n into k such subsets in 2 n n o 1 time we also consider variations of this problem where the subsets may overlap or are weighted and we solve the decision counting summation and optimization versions of these problems our algorithms are based on the principle of inclusion exclusion and the zeta transform in effect we get exact algorithms in 2 n n o 1 time for several well studied partition problems including domatic number chromatic number maximum k cut bin packing list coloring and the chromatic polynomial we also have applications to bayesian learning with decision graphs and to model based data clustering if only polynomial space is available our algorithms run in time 3 n n o 1 if membership in mathcal f can be decided in polynomial time we solve chromatic number in o 2 2461 n time and domatic number in o 2 8718 n time finally we present a family of polynomial space approximation algorithms that find a number between chi g and lceil 1 epsilon chi g rceil in time o 1 2209 n 2 2461 e epsilon n

clustering and variable selection in the presence of mixed variable types and missing data we consider the problem of model based clustering in the presence of many correlated mixed continuous and discrete variables some of which may have missing values discrete variables are treated with a latent continuous variable approach and the dirichlet process is used to construct a mixture model with an unknown number of components variable selection is also performed to identify the variables that are most influential for determining cluster membership the work is motivated by the need to cluster patients thought to potentially have autism spectrum disorder on the basis of many cognitive and or behavioral test scores there are a modest number of patients 486 in the data set along with many 55 test score variables many of which are discrete valued and or missing the goal of the work is to 1 cluster these patients into similar groups to help identify those with similar clinical presentation and 2 identify a sparse subset of tests that inform the clusters in order to eliminate unnecessary testing the proposed approach compares very favorably with other methods via simulation of problems of this type the results of the autism spectrum disorder analysis suggested 3 clusters to be most likely while only 4 test scores had high 0 5 posterior probability of being informative this will result in much more efficient and informative testing the need to cluster observations on the basis of many correlated continuous discrete variables with missing values is a common problem in the health sciences as well as in many other disciplines

parameter based asymptotics in certain cases statistical methods based on standard maximum likelihood asymptotics become valid as the true parameter value approaches a boundary of the parameter space examples are given which motivate a general parameter based asymptotic theory and a result is obtained which covers such situations of particular interest are applications to stochastic process models

optimized 2 4 stencil runge kutta ade adi fdtd with application to plasma this paper discusses the improvement of the numerical dispersion characteristics of alternating direction implicit adi finite difference time domain fdtd aimed at acquiring more accurate electromagnetic information of plasma through adding the optimization method which is based on the optimization of spatial derivative to the 2 4 stencil adi fdtd the optimized 2 4 stencil adi fdtd is proposed and its unconditional stability is proved theoretically the phase velocity error of the optimized 2 4 stencil adi fdtd versus propagation angle and grid density is investigated in addition the runge kutta auxiliary differential equation rkade scheme for tackling the constitutive relation equation of plasma is deduced which is without additional storage occupation and computational burden compared with ade scheme its numerical conductivity error is analyzed under different incident frequencies and electron collision frequencies through incorporating the rkade scheme into the optimized 2 4 stencil adi fdtd the optimized 2 4 stencil rkade adi fdtd is presented the accuracy and relatively wideband capability of the proposed method is validated by two numerical experiments

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

bayes and empirical bayes multiplicity adjustment in the variable selection problem this paper studies the multiplicity correction effect of standard bayesian variable selection priors in linear regression our first goal is to clarify when and how multiplicity correction happens automatically in bayesian analysis and to distinguish this correction from the bayesian ockham s razor effect our second goal is to contrast empirical bayes and fully bayesian approaches to variable selection through examples theoretical results and simulations considerable differences between the two approaches are found in particular we prove a theorem that characterizes a surprising aymptotic discrepancy between fully bayes and empirical bayes this discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical bayes estimate indeed even at the extreme when the empirical bayes estimate converges asymptotically to the true variable inclusion probability the potential for a serious difference remains

optimal consumption in a growth model with the cobb douglas production function an optimal consumption problem is studied in a growth model for the cobb douglas production function in a finite horizon the problem is transferred into a stochastic ramsey problem so as to reduce the dimension of the state space the corresponding state equation is a stochastic differential equation with inherently non lipschitz coefficients whose unique solvability is established the unique existence of the classical solution of the hamilton jacobi bellman equation associated with the original problem is proved and a synthesis of the optimal consumption policy is presented in the feedback form

exact bayesian curve fitting and signal segmentation we consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments we present an algorithm for perfect simulation from the posterior distribution of such a model even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment the algorithm is simple can scale well to large data sets and avoids the problem of diagnosing convergence that is present with monte carlo markov chain mcmc approaches to this problem we demonstrate our algorithm on standard denoising problems on a piecewise constant ar model and on a speech segmentation problem

estimation in dirichlet random effects models we develop a new gibbs sampler for a linear mixed model with a dirich let process random effect term which is easily extended to a generalized linear mixed model with a probit link function our gibbs sampler exploits the properties of the multinomial and dirichlet distributions and is shown to be an improvement in terms of operator norm and efficiency over other commonly used mcmc algorithms we also investigate methods for the estimation of the precision parameter of the dirichlet process finding that maximum likelihood may not be desirable but a posterior mode is a reasonable approach examples are given to show how these models perform on real data our results complement both the theoretical basis of the dirichlet process nonparametric prior and the computational work that has been done to date

bayesian multiple change points and segmentation application to homogenization of climatic series 1 in this paper we describe a new multiple change point detection technique based on segmenting the time series under study into subsequences these segments correspond to the episodes that are likely to contain a unique jump they are found by applying bayesian decision theory through the minimization of simple cost functions all calculations can be performed explicitly without falling back on markov chain monte carlo methods and resulting in particularly light implementation through prior distributions derived from a stochastic renewal process description of jump occurrences expert knowledge of jump amplitude and return period is also introduced in our decision process comparison to several multiple change point methods on simulated series lead to similar or better performance achieved at lower computational cost

clustering using objective functions and stochastic search summary a new approach to clustering multivariate data based on a multilevel linear mixed model is proposed a key feature of the model is that observations from the same cluster are correlated because they share cluster specific random effects the inclusion of cluster specific random effects allows parsimonious departure from an assumed base model for cluster mean profiles this departure is captured statistically via the posterior expectation or best linear unbiased predictor one of the parameters in the model is the true underlying partition of the data and the posterior distribution of this parameter which is known up to a normalizing constant is used to cluster the data the problem of finding partitions with high posterior probability is not amenable to deterministic methods such as the em algorithm thus we propose a stochastic search algorithm that is driven by a markov chain that is a mixture of two metropolis hastings algorithms one that makes small scale changes to individual objects and another that performs large scale moves involving entire clusters the methodology proposed is fundamentally different from the well known finite mixture model approach to clustering which does not explicitly include the partition as a parameter and involves an independent and identically distributed structure

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

simulation run length control in the presence of an initial transient this paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation it considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present it explores a procedure based on schruben s brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean the procedure is evaluated empirically for a variety of output sequences the performance measures considered are bias confidence interval coverage mean confidence interval width mean run length and mean amount of deleted data if the output sequence contains a strong transient then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias narrower confidence intervals and shorter run lengths than when no check for stationarity is performed if the output sequence contains no initial transient then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test if the run length is short relative to the extent of the initial transient the stationarity tests may not be powerful enough to detect the transient resulting in a procedure with unreliable point and interval estimates

did shakespeare write a newly discovered poem summary the consistency of the word usage in a previously unknown nine stanza poem attributed to shakespeare with that of the shakespearean canon is examined using a nonparametric empirical bayes model we consider also poems by jonson marlowe and donne as well as four poems definitely attributed to shakespeare on balance the poem is found to fit previous shakespearean usage reasonably well

minimally informative prior distributions for non parametric bayesian analysis summary we address the problem of how to conduct a minimally informative non parametric bayesian analysis the central question is how to devise a model so that the posterior distribution satisfies a few basic properties the concept of local mass provides the key to the development of the limiting dirichlet process model this model is then used to provide an engine for inference in the compound decision problem and for multiple comparisons inference in a one way analysis of variance setting our analysis in this setting may be viewed as a limit of the analyses that were developed by escobar and by gopalan and berry computations for the analysis are described and the predictive performance of the model is compared with that of mixture of dirichlet processes models

a model selection approach to analysis of variance and covariance an alternative to analysis of variance is a model selection approach where every partition of the treatment means into clusters with equal value is treated as a separate model the null hypothesis that all treatments are equal corresponds to the partition with all means in a single cluster the alternative hypothesis correspond to the set of all other partitions of treatment means a model selection approach can also be used for a treatment by covariate interaction where the null hypothesis and each alternative correspond to a partition of treatments into clusters with equal covariate effects we extend the partition as model approach to simultaneous inference for both treatment main effect and treatment interaction with a continuous covariate with separate partitions for the intercepts and treatment specific slopes the model space is the cartesian product of the intercept partition and the slope partition and we develop five joint priors for this model space in four of these priors the intercept and slope partition are dependent we advise on setting priors over models and we use the model to analyze an orthodontic data set that compares the frictional resistance created by orthodontic fixtures

bayesian non parametric hidden markov models with applications in genomics we consider the development of bayesian nonparametric methods for product partition models such as hidden markov models and change point models our approach uses a mixture of dirichlet process mdp model for the unknown sampling distribution likelihood for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference the method uses novel mcmc methodology which combines recent retrospective sampling methods with the use of slice sampler variables the methodology is computationally efficient both in terms of mcmc mixing properties and robustness to the length of the time series being investigated moreover the method is easy to implement requiring little or no user interaction we apply our methodology to the analysis of genomic copy number variation

kernel stick breaking processes we propose a class of kernel stick breaking processes for uncountable collections of dependent random probability measures the process is constructed by first introducing an infinite sequence of random locations independent random probability measures and beta distributed random weights are assigned to each location predictor dependent random probability measures are then constructed by mixing over the locations with stick breaking probabilities expressed as a kernel multiplied by the beta weights some theoretical properties of the process are described including a covariate dependent prediction rule a retrospective markov chain monte carlo algorithm is developed for posterior computation and the methods are illustrated using a simulated example and an epidemiological application

bayesian analysis of isochores statistical identification of isochore structure the variation in large scale gc composition proportion of dna bases that are g or c as opposed to a or t of mammalian genomes is a necessary requirement for understanding both the evolution of base composition and the many genomic features such as mutation and recombination rates which covary with base composition we have developed a bayesian method for isochore analysis that we demonstrate to be more accurate than the commonly used binary segmentation approach implemented within the program isofinder the method accounts for both fine scale and large scale structure we adapt direct simulation methods to allow for iid samples from the posterior distribution of our model and provide an accurate approximation to this that can analyze data from a chromosome in a matter of seconds we apply our method to human chromosome 1 the resulting estimate of how gc content varies across this region is shown to be a better predictor of local recombination rates t

bayesian capture recapture methods for error detection and estimation of population size heterogeneity and dependence summary this paper considers estimation of the unknown size n of a population based on multiple capture recapture samples we extend the bayesian multiple recapture model to accommodate possible heterogeneity and dependence among the samples and possible heterogeneity within the samples in the dependent model we show that posterior inference for n is independent of almost all the nuisance parameters we develop a flexible bayesian model for heterogeneity within samples and demonstrate how gibbs sampling can be used to calculate the bayesian estimator for n and other quantities of interest the performance of the proposed estimators is evaluated by simulation under both correct and incorrect model specifications and we illustrate our methods in two examples about software review and estimation of a cottontail rabbit population

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

generalized ewens pitman model for bayesian clustering we propose a bayesian method for clustering from discrete data structures that commonly arise in genetics and other applications this method is equivariant with respect to relabelling units unsampled units do not interfere with sampled data and missing data do not hinder inference cluster inference using the posterior mode performs well on simulated and real datasets and the posterior predictive distribution enables supervised learning based on a partial clustering of the sample

are gibbs type priors the most natural generalization of the dirichlet process discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in bayesian inference here we focus on the family of gibbs type priors a recent elegant generalization of the dirichlet and the pitman yor process priors these random probability measures share properties that are appealing both from a theoretical and an applied point of view i they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism ii they stand out in terms of mathematical tractability iii they include several interesting special cases besides the dirichlet and the pitman yor processes the goal of our paper is to provide a systematic and unified treatment of gibbs type priors and highlight their implications for bayesian nonparametric inference we deal with their distributional properties the resulting estimators frequentist asymptotic validation and the construction of time dependent versions applications mainly concerning mixture models and species sampling serve to convey the main ideas the intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the dirichlet process

an objective approach to prior mass functions for discrete parameter spaces we present a novel approach to constructing objective prior distributions for discrete parameter spaces these types of parameter spaces are particularly problematic as it appears that common objective procedures to design prior distributions are problem specific we propose an objective criterion based on loss functions instead of trying to define objective probabilities directly we systematically apply this criterion to a series of discrete scenarios previously considered in the literature and compare the priors the proposed approach applies to any discrete parameter space making it appealing as it does not involve different concepts according to the model supplementary materials for this article are available online

the formal definition of reference priors reference analysis produces objective bayesian inference in the sense that inferential statements depend only on the assumed model and the available data and the prior distribution used to make an inference is least informative in a certain information theoretic sense reference priors have been rigorously defined in specific contexts and heuristically defined in general but a rigorous general definition has been lacking we produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions the explicit expression can be used to derive new reference priors both analytically and numerically

clustering from categorical data sequences the three parameter cluster model is a combinatorial stochastic process that generates categorical response sequences by randomly perturbing a fixed clustering parameter this clear relationship between the observed data and the underlying clustering is particularly attractive in cluster analysis in which supervised learning is a common goal and missing data is a familiar issue the model is well equipped for this task as it can handle missing data perform out of sample inference and accommodate both independent and dependent data sequences moreover its clustering parameter lies in the unrestricted space of partitions so that the number of clusters need not be specified beforehand we establish these and other theoretical properties and also demonstrate the model on datasets from epidemiology genetics political science and legal studies

what is a statistical model this paper addresses two closely related questions what is a statistical model and what is a parameter the notions that a model must make sense and that a parameter must have a well defined meaning are deeply ingrained in applied statistical work reasonably well understood at an instinctive level but absent from most formal theories of modelling and inference in this paper these concepts are defined in algebraic terms using morphisms functors and natural transformations it is argued that inference on the basis of a model is not possible unless the model admits a natural extension that includes the domain for which inference is required for example prediction requires that the domain include all future units subjects or time points although it is usually not made explicit every sensible statistical model admits such an extension examples are given to show why such an extension is necessary and why a formal theory is required in the definition of a subparameter it is shown that certain parameter functions are natural and others are not inference is meaningful only for natural parameters this distinction has important consequences for the construction of prior distributions and also helps to resolve a controversy concerning the box cox model

optimized three dimensional fdtd discretizations of maxwell s equations on cartesian grids in this paper novel finite difference time domain fdtd schemes are introduced for the numerical solution of maxwell s equations on dual staggered cartesian three dimensional lattices the proposed techniques are designed to accomplish optimized performance according to certain features and requirements dictated by the investigated problems thus making efficient use of the available computational resources starting from only few initial assumptions a construction process based on the minimization of specific error formulae is developed which is later exploited to derive the final form of the finite difference operators previously an elaborate analysis of the proposed indicators is provided targeting at global error control over all propagation angles our methodology guarantees upgraded flexibility as accuracy can be maximized within either narrow or wider frequency bands without practically inducing significant computational overhead attractive qualities such as high convergence rates are now the natural consequence of the effective design process rather than the minimization of the truncation errors of the difference expressions in fact the proposed fdtd approaches verify the possibility to attain improved levels of accuracy without resorting to the traditional taylor based forms of the individual operators a theoretical analysis of the inherent dispersion artifacts reveals the full potential of the new algorithms while numerical tests and comparisons unveil their unquestionable merits in practical applications

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

discontinuous hamiltonian monte carlo for discrete parameters and discontinuous likelihoods hamiltonian monte carlo has emerged as a standard tool for posterior computation in this article we present an extension that can efficiently explore target distributions with discontinuous densities our extension in particular enables efficient sampling from ordinal parameters though embedding of probability mass functions into continuous spaces we motivate our approach through a theory of discontinuous hamiltonian dynamics and develop a corresponding numerical solver the proposed solver is the first of its kind with a remarkable ability to exactly preserve the hamiltonian we apply our algorithm to challenging posterior inference problems to demonstrate its wide applicability and competitive performance

optimal consumption models in economic growth abstract we study the optimal consumption problem in the one sector model of economic growth under uncertainty we show the existence of a classical solution of the hamilton jacobi bellman equation associated with the stochastic optimization problem and then give an optimal consumption policy in terms of its solution

initial size estimation for the linear pure death process summary consider a linear pure death process in which the common death rate and the initial size n of the population are both unknown an estimate of n is required based on the observed times of the firstj deaths i e with censored sampling it is shown that the only reliable non bayesian method is to use interval estimates for all the standard point estimation techniques are liable to fail appropriate interval estimators are derived and discussed the corresponding truncated sampling model is briefly considered the linear pure death process may be characterized as representing a dying population in which the lifetimes are independently and identically distributed each with probability density ae t t 0 for some a 0 we assume that both the initial population size n and the rate parameter a are unknown and our aim is to estimate n for many years work on the estimation of population size such as by johnson 1962 hoel 1968 and marcus blumenthal 1974 assumed a lifetime distribution which was general but completely specified recently interest has been shown in lifetime distributions with unknown parameters in particular in papers by sanathanan 1977 who gives asymptotic results for maximum likelihood estimation and blumenthal marcus 1975 who consider precisely the above problem we consider mainly the censored sampling model under which an estimate of n is required immediately after the jth death where j is a preassigned integer known not to exceed n in 2 we derive an invariantly sufficient statistic and its distribution in 3 we discuss point estimation of n unbiased estimators do not exist while the methods of moments and of maximum likelihood are both liable to fail in that there is positive probability sometimes close to 2 that the equation for the estimator has no finite solution in 4 we derive an interval estimator and discuss its properties while an interval estimate is always available it is in some circumstances quite vague this brings out clearly that for the present problem it is more than usually inadvisable to rely on point

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

bayesian disease mapping using product partition models our objective is to develop a model to estimate the relative risk of disease in each area a i i 1 n of a region and to identify areas of unusually high or low risk we use a product partition model ppm in which we assume that the true relative risks can be partitioned into a number of components or sets of areas where the relative risks are equal the ppm allows the data to weight those partitions likely to hold and inference about particular parameters may be made by first conditioning on the partition and then averaging over all partitions we develop markov chain monte carlo mcmc techniques to approximate the posterior distributions of the partitions and the parameters we first test the method in a simulation study and then apply it to data for two separate groups of different types of cancer in the mid western health board region in ireland the results are compared with those obtained using the standardized mortality ratio method an empirical bayes method a spatial scan method and a nonparametric bayesian method

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

emulation of numerical models with over specified basis functions abstractmathematical models are frequently used to explore physical systems but can be computationally expensive to evaluate in such settings an emulator is used as a surrogate in this work we propose a basis function approach for computer model emulation to combine field observations with a collection of runs from the numerical model we use the proposed emulator within the kennedy o hagan framework of model calibration a novel feature of the approach is the use of an over specified set of basis functions where number of bases used and their inclusion probabilities are treated as unknown quantities the new approach is found to have smaller predictive uncertainty and computational efficiency than the standard gaussian process approach to emulation and calibration along with several simulation examples focusing on different model characteristics we also use the method to analyze a dataset on laboratory experiments related to astrophysics

objective priors for discrete parameter spaces this article considers the development of objective prior distributions for discrete parameter spaces formal approaches to such development such as the reference prior approach often result in a constant prior for a discrete parameter which is questionable for problems that exhibit certain types of structure to take advantage of structure this article proposes embedding the original problem in a continuous problem that preserves the structure and then using standard reference prior theory to determine the appropriate objective prior four different possibilities for this embedding are explored and applied to a population size model the hypergeometric distribution the multivariate hypergeometric distribution the binomial beta distribution and the binomial distribution the recommended objective priors for the first third and fourth problems are new

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

bayesian clustering and product partition models summary we present a decision theoretic formulation of product partition models ppms that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously a key observation in our construction is the fact that ppms can be formulated in the context of model selection the underlying partition structure in these models is closely related to that arising in connection with dirichlet processes this allows a straightforward adaptation of some computational strategies originally devised for nonparametric bayesian problems to our framework the resulting algorithms are more flexible than other competing alternatives that are used for problems involving ppms we propose an algorithm that yields bayes estimates of the quantities of interest and the groups of experimental units we explore the application of our methods to the detection of outliers in normal and student t regression models with clustering structure equivalent to that induced by a dirichlet process prior we also discuss the sensitivity of the results considering different prior distributions for the partitions

classification based on a permanental process with cyclic approximation we introduce a doubly stochastic marked point process model for supervised classification problems regardless of the number of classes or the dimension of the feature space the model requires only 2 3 parameters for the covariance function the classification criterion involves a permanental ratio for which an approximation using a polynomial time cyclic expansion is proposed the approximation is effective even if the feature region occupie d by one class is a patchwork interlaced with regions occupied by other classes an application to dna microarray analysis indicates that the cyclic approximation is effective even for high dimensional data it can employ feature variables in an efficient way to reduce the prediction error signi ficantly this is critical when the true classification relies on non reducible high dimensional f eatures

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

product partition models for change point problems product partition models assume that observations in different components of a random partition of the data are independent if the probability distribution of random partitions is in a certain product form prior to making the observations it is also in product form given the observations the product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions these models apply with special computational simplicity to change point problems where the partitions divide the sequence of observations into components within which different regimes hold we show with appropriate selection of prior product models that the observations can eventually determine approximately the true partition

nonparametric hierarchical bayes via sequential imputations we consider the empirical bayes estimation of a distribution using binary data via the dirichlet process let d denote a dirichlet process with being a finite measure on 0 1 instead of having direct samples from an unknown random distribution f from d we assume that only indirect binomial data are observable this paper presents a new interpretation of lo s formula and thereby relates the predictive density of the observations based on a dirichlet process model to likelihoods of much simpler models as a consequence the log likelihood surface as well as the maximum likelihood estimate of c 0 1 is found when the shape of is assumed known together with a formula for the fisher information evaluated at the estimate the sequential imputation method of kong liu and wong is recommended for overcoming computational difficulties commonly encountered in this area the related approximation formulas are provided an analysis of the tack data of beckett and diaconis which motivated this study is supplemented to illustrate our methods