variable selection in bayesian smoothing spline anova models a bayesian nonparametric regression model for curve fitting and variable selection is proposed for analyzing complex computer model output the smoothing splines anova framework is used to separate the regression function into main effects and interacti

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

correlated random measures abstractwe develop correlated random measures random measures where the atom weights can exhibit a flexible pattern of dependence and use them to develop powerful hierarchical bayesian nonparametric models hierarchical bayesian nonparametric models are usually built from completely random measures a poisson process based construction in which the atom weights are independent completely random measures imply strong independence assumptions in the corresponding hierarchical model and these assumptions are often misplaced in real world settings correlated random measures address this limitation they model correlation within the measure by using a gaussian process in concert with the poisson process with correlated random measures for example we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern we develop several other examples as well we study a correlated random measure model of pairwise count data we derive an eff

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

operator algebras and the conjugacy of transformations abstract a family of algebras is associated with each continuous map on a compact hausdorff space these algebras are called conjugacy algebras it is shown that two continuous maps are conjugate if and only if some conjugacy algebra of one is isomorphic to some conjugacy for the other numerous examples of conjugacy algebras are provided

nonparametric bayesian estimators for counting processes this paper is concerned with nonparametric bayesian inference of the aalen s multiplicative counting process model for a desired nonparametric prior distribution of the cumulative intensity function a class of l6vy processes is considered and it is shown that the class of l6vy processes is conjugate for the multiplicative counting process model and formulas for obtaining a posterior process are derived finally our results are applied to several practically important models such as one point processes for right censored data poisson processes and markov processes

analysis of hybrid selection maximal ratio combining in correlated nakagami fading we present an analysis of a hybrid selection maximal ratio combining diversity system over an evenly correlated slow frequency nonselective nakagami fading channel where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same and all average branch signal to noise ratios snrs are equal in this system the l branches with the largest instantaneous snr out of n available branches are selected and combined using maximal ratio combining from the joint characteristic function cf of the instantaneous branch snrs we obtain an expression for the cf of the combiner output snr as a series of elementary cfs the expression can be conveniently used to obtain the symbol error probability of coherent detection of different m ary modulation schemes we illustrate our methodology using m ary phase shift keying as an example

bayesian poisson process partition calculus with an application to bayesian levy moving averages this article develops and describes how to use results concerning disintegrations of poisson random measures these results are fashioned as simple tools that can be tailor made to address inferential questions arising in a wide range of bayesian nonparametric and spatial statistical models the poisson disintegration method is based on the formal statement of two results concerning a laplace functional change of measure and a poisson palm fubini calculus in terms of random partitions of the integers 1 n the techniques are analogous to but much more general than techniques for the dirichlet process and weighted gamma process developed in ann statist 12 1984 351 3571 and ann inst statist math 41 1989 227 245 in order to illustrate the flexibility of the approach large classes of random probability measures and random hazards or intensities which can be expressed as functionals of poisson random measures are described we describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models the analysis circumvents many of the difficult issues involved in bayesian nonparametric calculus including a combinatorial component this allows one to focus on the unique features of each process which are characterized via real valued functions h the applicability of the technique is further illustrated by obtaining explicit posterior expressions for levy cox moving average processes within the general setting of multiplicative intensity models in addition novel computational procedures similar to efficient procedures developed for the dirichlet process are briefly discussed for these models

latent space approaches to social network analysis network models are widely used to represent relational information among interacting units in studies of social networks recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors we develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved social space we make inference for the social space within maximum likelihood and bayesian frameworks and propose markov chain monte carlo procedures for making inference on latent positions and the effects of observed covariates we present analyses of three standard datasets from the social networks literature and compare the method to an alternative stochastic blockmodeling approach in addition to improving on model fit for these datasets our method provides a visual and interpretable model based spatial representation of social relationships and improv

on the distributional properties of model selection criteria abstract it is commonly accepted that statistical modeling should follow the parsimony principle namely that simple models should be given priority whenever possible but little quantitative knowledge is known concerning the amount of penalty for complexity regarded as allowable we try to understand the parsimony principle in the context of model selection in particular the generalized final prediction error criterion is considered and we argue that the penalty term should be chosen between 1 5 and 5 for most practical situations applying our results to the cross validation criterion we obtain insights into how the partition of data should be done we also discuss the small sample performance of our methods

bnp seq bayesian nonparametric differential expression analysis of sequencing count data abstractwe perform differential expression analysis of high throughput sequencing count data under a bayesian nonparametric framework removing sophisticated ad hoc pre processing steps commonly required in existing algorithms we propose to use the gamma beta negative binomial process which takes into account different sequencing depths using sample specific negative binomial probability dispersion parameters to detect differentially expressed genes by comparing the posterior distributions of gene specific negative binomial dispersion probability parameters these model parameters are inferred by borrowing statistical strength across both the genes and samples extensive experiments on both simulated and real world rna sequencing count data show that the proposed differential expression analysis algorithms clearly outperform previously proposed ones in terms of the areas under both the receiver operating characteristic and precision recall curves supplementary materials for this article are avai

prediction via orthogonalized model mixing abstract we introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors we focus on the choice of predictors in linear models and mix over possible subsets of candidate predictors our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix advantages are both statistical and computational statistically orthogonalization often leads to a reduction in the number of competing models by eliminating correlations computationally large model spaces cannot be enumerated recent approaches are based on sampling models with high posterior probability via markov chains based on orthogonalization of the space of candidate predictors we can approximate the posterior probabilities of models by products of predictor specific terms this leads to an importance sampling function for sampling directly from the joint distribution over the model space without resorting to markov chains compared to the latter ortho

posterior simulation and bayes factors in panel count data models abstract this paper is concerned with the problems of posterior simulation and model choice for poisson panel data models with multiple random effects efficient algorithms based on markov chain monte carlo methods for sampling the posterior distribution are developed a new parameterization of the random effects and fixed effects is proposed and compared with a parameterization in common use and computation of marginal likelihoods and bayes factors via chib s 1995 method is also considered the methods are illustrated with two real data applications involving large samples and multiple random effects

an mdl framework for sparse coding and dictionary learning the power of sparse signal modeling with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields from signal processing to statistical inference and machine learning however the statistical properties of these models such as underfitting or overfitting given sets of data are still not well characterized in the literature as a result the success of sparse modeling depends on hand tuning critical parameters for each data and application this work aims at addressing this by providing a practical and objective characterization of sparse models by means of the minimum description length mdl principle a well established information theoretic approach to model selection in statistical inference the resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which by virtue of the mdl principle are completely parameter free furthermore such framework allows to incorporate additional prior information to existing models such as markovian dependencies or to define completely new problem formulations including in the matrix analysis area in a natural way these virtues will be demonstrated with parameter free algorithms for the classic image denoising and classification problems and for low rank matrix recovery in video applications however the framework is not limited to this imaging data and can be applied to a wide range of signal and data types and tasks

combinatorial clustering and the beta negative binomial process we develop a bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual we introduce a combinatorial stochastic process known as the negative binomial process rm nbp as an infinite dimensional prior appropriate for such problems we show that the rm nbp is conjugate to the beta process and we characterize the posterior distribution under the beta negative binomial process rm bnbp and hierarchical models based on the rm bnbp the rm hbnbp we study the asymptotic properties of the rm bnbp and develop a three parameter extension of the rm bnbp that exhibits power law behavior we derive mcmc algorithms for posterior inference under the rm hbnbp and we present experiments using these algorithms in the domains of image segmentation object recognition and document analysis

semicrossed products of operator algebras and their c envelopes abstract let a be a unital operator algebra and let be an automorphism of a that extends to a automorphism of its c envelope c env a we introduce the isometric semicrossed product a is z and we show that c env a is z c env a z in contrast the c envelope of the familiar contractive semicrossed product a z may not equal c env a z our main tool for calculating c envelopes for semicrossed products is a new concept the relative semicrossed product of an operator algebra by an endomorphism as an application of our theory we show that if t x is the tensor algebra of a c correspondence x a and is a extendible automorphism of t x that fixes the diagonal elementwise then the contractive semicrossed product satisfies c env t x z o x z where o x denotes the cuntz pimsner algebra of x a this extends the main result of davidson and katsoulis 2010 6

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

consistent variable selection in linear models abstract a method of estimating linear model dimension and variable selection is proposed this new criterion which generalizes the cp criterion the akaike information criterion aic the bayes information criterion and the phiv criterion and is consistent under certain conditions is based on a new class of penalty functions and a procedure of sorting covariates based on t statistics in the course of introducing this method we discuss the important role of the penalty function in the consistency of model dimension estimation and in variable selection the proposed method requires less computation than resampling based methods that search over all subsets of covariates for the true model simulation results show that the new method is superior to the cp criterion and aic in finite sample situations as well

on posterior consistency of survival models ghosh and ramamoorthi studied posterior consistency for survival models and showed that the posterior was consistent when the prior on the distribution of survival times was the dirichlet process prior in this paper we study posterior consistency of survival models with neutral to the right process priors which include dirichlet process priors a set of sufficient conditions for posterior consistency with neutral to the right process priors are given interestingly not all the neutral to the right process priors have consistent posteriors but most of the popular priors such as dirichlet processes beta processes and gamma processes have consistent posteriors with a class of priors which includes beta processes a necessary and sufficient condition for the consistency is also established an interesting counter intuitive phenomenon is found suppose there are two priors centered at the true parameter value with finite variances surprisingly the posterior with smaller prior variance can be inconsistent while that with larger prior variance is consistent

bayesian analysis of multistate event history data beta dirichlet process prior bayesian analysis of a finite state markov process which is popularly used to model multistate event history data is considered a new prior process called a beta dirichlet process is introduced for the cumulative intensity functions and is proved to be conjugate in addition the beta dirichlet prior is applied to a bayesian semiparametric regression model to illustrate the application of the proposed model we analyse a dataset of credit histories copyright 2012 oxford university press

the little bootstrap and other methods for dimensionality selection in regression x fixed prediction error abstract when a regression problem contains many predictor variables it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables usually a regression equation based on a few variables will be more accurate and certainly simpler there are various methods for picking good subsets of variables and programs that do such procedures are part of every widely used statistical package the most common methods are based on stepwise addition or deletion of variables and on best subsets the latter refers to a search method that given the number of variables to be in the equation say five locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations all of these procedures generate a sequence of regression equations the first based on one variable the next based on two variables and so on each member of this sequence is called a submodel and the number of variables in the e

error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers this paper discusses the performance of communication systems using binary coherent and differential phase shift keyed psk modulation in correlated rician fading channels with diversity reception the presence of multiple rician faded cochannel users which may have arbitrary and nonidentical parameters is modeled exactly exact bit error probability bep expressions are derived via the moment generating functions mgfs of the relevant decision statistics which are obtained through coherent detection with maximum ratio combining for coherent psk modulation and differential detection with equal gain combining egc for differential modulation evaluating the exact expressions requires a complexity that is exponential in the number of interferers to avoid this potentially time consuming operation we derive two low complexity approximate methods each for coherent and differential modulation formats which are more accurate than the traditional gaussian approximation approach two new and interesting results of this analysis are 1 unlike in the case of rayleigh fading channels increasing correlation between diversity branches may lead to better performance in rician fading channels and 2 the phase distribution of the line of sight or static fading components of the desired user has a significant influence on the bep performance in correlated diversity channels

c envelopes of semicrossed products by lattice ordered abelian semigroups abstract a semicrossed product is a non selfadjoint operator algebra encoding the action of a semigroup on an operator or c algebra we prove that when the positive cone of a discrete lattice ordered abelian group acts on a c algebra the c envelope of the associated semicrossed product is a full corner of a crossed product by the whole group by constructing a c cover that itself is a full corner of a crossed product and computing the shilov ideal we obtain an explicit description of the c envelope this generalizes a result of davidson fuller and kakariadis from z n to the class of all discrete lattice ordered abelian groups

regenerative composition structures a new class of random composition structures the ordered analog of kingman s partition structures is defined by a regenerative description of component sizes each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline and separating the points into clusters by an independent regenerative random set examples are composition structures derived from residual allocation models including one associated with the ewens sampling formula and composition structures derived from the zero set of a brownian motion or bessel process we provide characterisation results and formulas relating the distribution of the regenerative

computational methods for multiplicative intensity models using weighted gamma processes proportional hazards marked point processes and panel count data we develop computational procedures for a class of bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures a key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of bayesian hierarchical models using the dirichlet process using this fact along with an approximation for the weighted gamma process we show that with some care one can adapt efficient algorithms used for the dirichlet process to this setting we discuss blocked gibbs sampling procedures and polya urn gibbs samplers we illustrate our methods with applications to proportional hazard models poisson spatial regression models recurrent events and panel count data

poisson calculus for spatial neutral to the right processes neutral to the right ntr processes were introduced by doksum in 1974 as bayesian priors on the class of distributions on the real line since that time there have been numerous applications to models that arise in survival analysis subject to possible right censoring however unlike the dirichlet process the larger class of ntr processes has not been used in a wider range of more complex statistical applications here to circumvent some of these limitations we describe a natural extension of ntr processes to arbitrary polish spaces which we call spatial neutral to the right processes our construction also leads to a new rich class of random probability measures which we call ntr species sampling models we show that this class contains the important two parameter extension of the dirichlet process we provide a posterior analysis which yields tractable ntr analogues of the blackwell macqueen distribution our analysis turns out to be closely related to the study of regenerative composition structures a new computational scheme which is an ordered variant of the general chinese restaurant processes is developed this can be used to approximate complex posterior quantities we also discuss some relationships to results that appear outside of bayesian nonparametrics

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

priors for random count matrices derived from a family of negative binomial processes abstractwe define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns the three distributions we consider are derived from the gamma poisson gamma negative binomial and beta negative binomial processes which we refer to generically as a family of negative binomial processes because the models lead to closed form update equations within the context of a gibbs sampler they are natural candidates for nonparametric bayesian priors over count matrices a key aspect of our analysis is the recognition that although the random count matrices within the family are defined by a row wise construction their columns can be shown to be independent and identically distributed iid this fact is used to derive explicit formulas for drawing all the columns at once moreover by analyzing these matrices combinatorial structure we describe how to sequentially construct a column iid random count matrix one row at a time and derive the predictive d

spike and slab gene selection for multigroup microarray data dna microarrays can provide insight into genetic changes that characterize different stages of a disease process accurate identification of these changes has significant therapeutic and diagnostic implications statistical analysis for multistage multigroup data is challenging however anova based extensions of two sample z tests a popular method for detecting differentially expressed genes in two groups do not work well in multigroup settings false detection rates are high because of variability of the ordinary least squares estimators and because of regression to the mean induced by correlated parameter estimates we develop a bayesian rescaled spike and slab hierarchical model specifically designed for the multigroup gene detection problem data preprocessing steps are introduced to deal with unique features of microarray data and to enhance selection performance we show theoretically that spike and slab models naturally encourage sparse solutions through a process called selective shrinkage t

explicit analytical expressions for outage and error rate of diversity cellular systems in the presence of multiple interferers and correlated rayleigh fading the outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience rayleigh fading and have the same correlation matrix two special cases when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues are considered for both the equal power cochannel interference case and the unequal power cochannel interference case further the average bit error rate of a coherent binary phase shift keying bpsk modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated rayleigh fading is derived the effects of the average signal to noise ratio snr and the average signal power to interference power ratio on the system performance are examined

spike and slab variable selection frequentist and bayesian strategies variable selection in the linear regression model takes many apparent faces from both frequentist and bayesian standpoints in this paper we introduce a variable selection method referred to as a rescaled spike and slab model we study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation specifically we study the usefulness of continuous bimodal priors to model hypervariance parameters and the effect scaling has on the posterior mean through its relationship to penalization several model selection strategies some frequentist and some bayesian in nature are developed and studied theoretically we demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification and show this is achieved using the posterior from a rescaled spike and slab model we also show how to verify a procedure s ability to reduce model uncertainty in finite samples using a specialized forward selection strategy using this tool we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty

medlda maximum margin supervised topic models a supervised topic model can use side information such as ratings or labels associated with documents or images to discover more predictive low dimensional topical representations of the data however existing supervised topic models predominantly employ likelihood driven objective functions for learning and inference leaving the popular and potentially powerful max margin principle unexploited for seeking predictive representations of data and more discriminative topic bases for the corpus in this paper we propose the maximum entropy discrimination latent dirichlet allocation medlda model which integrates the mechanism behind the max margin prediction models e g svms with the mechanism behind the hierarchical bayesian topic models e g lda under a unified constrained optimization framework and yields latent topical representations that are more discriminative and more suitable for prediction tasks such as document classification or regression the principle underlying the medlda formalism is quite general and can be applied for jointly max margin and maximum likelihood learning of directed or undirected topic models when supervising side information is available efficient variational methods for posterior inference and parameter estimation are derived and extensive empirical studies on several real data sets are also provided our experimental results demonstrate qualitatively and quantitatively that medlda could 1 discover sparse and highly discriminative topical representations 2 achieve state of the art prediction performance and 3 be more efficient than existing supervised topic models especially for classification

bootstrap model selection abstract in a regression problem typically there are p explanatory variables possibly related to a response variable and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response a bootstrap variable model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error where the bootstrap estimates are constructed based on a data set of size n although the bootstrap estimates have good properties this bootstrap selection procedure is inconsistent in the sense that the probability of selecting the optimal subset of variables does not converge to 1 as n this inconsistency can be rectified by modifying the sampling method used in drawing bootstrap observations for bootstrapping pairs response explanatory variable it is found that instead of drawing n bootstrap observations a customary bootstrap sampling plan much less bootstrap observations should be sampled the bootstrap selection p

negative binomial process count and mixture modeling the seemingly disjoint problems of count and mixture modeling are united under the negative binomial nb process a gamma process is employed to model the rate measure of a poisson process whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an nb process for count modeling a draw from the nb process consists of a poisson distributed finite number of distinct atoms each of which is associated with a logarithmic distributed number of data samples we reveal relationships between various count and mixture modeling distributions and construct a poisson logarithmic bivariate distribution that connects the nb and chinese restaurant table distributions fundamental properties of the models are developed and we derive efficient bayesian inference it is shown that with augmentation and normalization the nb process and gamma nb process can be reduced to the dirichlet process and hierarchical dirichlet process respectively these relationships highlight theoretical structural and computational advantages of the nb process a variety of nb processes including the beta geometric beta nb marked beta nb marked gamma nb and zero inflated nb processes with distinct sharing mechanisms are also constructed these models are applied to topic modeling with connections made to existing algorithms under poisson factor analysis example results show the importance of inferring both the nb dispersion and probability parameters

on the outage probability of optimum combining and maximal ratio combining schemes in an interference limited rice fading channel in this letter we study the performance of optimum combining oc and maximal ratio combining mrc diversity schemes in wireless digital communication systems with rice fading and cochannel interference new simplified closed form expressions are derived for the probability density function pdf as well as the outage probability for oc and mrc when the desired signal has a line of sight and the interferers are assumed to be scattered and further away from the receiver it is assumed that the interferers have equal powers and their number l is larger than the diversity order m i e l m

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

variable selection in nonparametric regression with categorical covariates abstract this article extends the problem of variable selection to a nonparametric regression model with categorical covariates two selection criteria are considered the cross validation cv criterion and the accumulated prediction error ape criterion we find that asymptotically the cv criterion performs well only when the true model is infinite dimensional while the ape criterion is appropriate when the true model is finite dimensional this is very similar to the case of linear regression model a simulation study reveals some interesting small sample properties of these criteria to be more specific suppose that we have observations x 1 y 1 xn yn that are iid random vectors and x x 1 x 2 where the x i s are categorical we allow y to be of any type now a new observation x has arrived and we want to predict the corresponding y such a framework is more appropriate than regressions with fixed covariates in situations where the covariates are observational rather than bei

multiple shrinkage and subset selection in wavelets this paper discusses bayesian methods for multiple shrinkage estimation in wavelets wavelets are used in applications for data denoising via shrinkage of the coefficients towards zero and for data compression by shrinkage and setting small coefficients to zero we approach wavelet shrinkage by using bayesian hierarchical models assigning a positive prior probability to the wavelet coefficients being zero the resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns we discuss fast computational implementations with a focus on easy to compute analytic approximations as well as importance sampling and markov chain monte carlo methods multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions we demonstrate this in simulated test examples comparing various implementations of multiple shrinkage to commonly used shrinkage rules finally we illustrate our approach with an application to the so called glint data

a strongly consistent procedure for model selection in a regression problem summary we consider the multiple regression model yn xn en where yn and en are n vector random variables xn is an n x m matrix and 83 is an m vector of unknown regression parameters each component of 3 may be zero or nonzero which gives rise to 2 possible models for multiple regression we provide a decision rule for the choice of a model which is strongly consistent for the true model as n oo the result is proved under certain mild conditions for instance without assuming normality of the distribution of the components of en

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

the jacobson radical for analytic crossed products we characterise the jacobson radical of an analytic crossed product c0 x z answering a question first raised by arveson and josephson in 1969 in fact we characterise the jacobson radical of analytic crossed products c0 x zd this consists of all elements whose fourier coefficients vanish on the recurrent points of the dynamical system and the first one is zero the multidimensional version requires a variation of the notion of recurrence taking into account the various degrees of freedom

minimax multiple shrinkage estimation on presente des nouveaux estimateurs qui incorporent l information partielle a priori en utilisant les donnees comme emulation du comportement et du risque des estimateurs consideres les plus efficaces

model selection via multifold cross validation a natural extension of the simple leave one out cross validation cv method is to allow the deletion of more than one observations in this article several notions of the multifold cross validation mcv method have been discussed in the context of variable selection under a linear regression model we show that the delete d mcv criterion is asymptotically equivalent to the well known fpe criterion two computationally more feasible methods the r fold cross validation and the repeated learning testing criterion are also studied the performance of these criteria are compared with the simple leave one out cross validation method simulation results are obtained to gain some understanding on the small sample properties of these methods

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

bayesian nonparametric statistical inference for poisson point processes a random measure is said to be selected by a weighted gamma prior probability if the values it assigns to disjoint sets are independent gamma random variables with positive multipliers if the intensity measure of a nonhomogeneous poisson point process is selected by a weighted gamma prior probability and if a sample is drawn from the poisson point process having this intensity measure then the posterior random intensity measure given the observations is also selected by a weighted gamma prior probability if the measure space is euclidean and if the true intensity measure is continuous and finite the centered posterior process rescaled by the square root of the sample size will converge weakly in skorohod topology to a wiener process subject to a change of time scale

dual branch mrc receivers under spatial interference correlation and nakagami fading despite being ubiquitous in practice the performance of maximal ratio combining mrc in the presence of interference is not well understood because the interference received at each antenna originates from the same set of interferers but partially decorrelates over the fading channel it possesses a complex correlation structure this paper develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry modeling interference by a poisson shot noise process with independent nakagami fading we derive the link success probability for dual branch interference aware mrc using this result we show that the common assumption that all receive antennas experience equal interference power underestimates the true performance although this gap rapidly decays with increasing the nakagami parameter m rm i of the interfering links in contrast ignoring interference correlation leads to a highly optimistic performance estimate for mrc especially for large m rm i in the low outage probability regime our success probability expression can be considerably simplified observations based from the analysis include the following 1 for small path loss exponents mrc and minimum mean square error combining exhibit similar performance and 2 the gains of mrc over selection combining are smaller in the interference limited case than in the well studied noise limited case

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

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

semicrossed products of simple c algebras let mathcal a alpha and mathcal b beta be c dynamical systems and assume that mathcal a is a separable simple c algebra and that and are automorphisms then the semicrossed products mathcal a times alpha mathbb z and mathcal b times beta mathbb z are isometrically isomorphic if and only if the dynamical systems mathcal a alpha and mathcal b beta are outer conjugate

novel representations for the equicorrelated multivariate non central chi square distribution and applications to mimo systems in correlated rician fading novel representations for the multivariate probability density function and cumulative distribution function of the non central chi square distribution are derived the solutions are expressed in terms of well known functions which are available in common mathematical software when the number of degrees of freedom m is even the new representation has the advantage that only a single integral computation is needed to compute a n dimensional distribution the new representations are used to numerically evaluate the outage probability of multiple input multiple output systems with receiver antenna selection operating in correlated rician fading the well known equal correlation model which is considered to be a useful model for a closely placed set of antennas is used for the analysis

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results