introduction to matrix analytic methods in stochastic modeling preface part i quasi birth and death processes 1 examples part ii the method of phases 2 ph distributions 3 markovian point processes part iii the matrix geometric distribution 4 birth and death processes 5 processes under a taboo 6 homogeneous qbds 7 stability condition part iv algorithms 8 algorithms for the rate matrix 9 spectral analysis 10 finite qbds 11 first passage times part v beyond simple qbds 12 nonhomogeneous qbds 13 processes skip free in one direction 14 tree processes 15 product form networks 16 nondenumerable states bibliography index

comparing the performance of two indices for spatial model selection application to two mortality data the statistical analysis of spatially correlated data has become an important scientific research topic lately the analysis of the mortality or morbidity rates observed at different areas may help to decide if people living in certain locations are considered at higher risk than others once the statistical model for the data of interest has been chosen further effort can be devoted to identifying the areas under higher risks many scientists including statisticians have tried the conditional autoregressive car model to describe the spatial autocorrelation among the observed data this model has greater smoothing effect than the exchangeable models such as the poisson gamma model for spatial data this paper focuses on comparing the two types of models using the index lg the ratio of local to global variability two applications taiwan asthma mortality and scotland lip cancer are considered and the use of lg is illustrated the estimated values for both data sets are small implying a poisson gamma model may be favoured over the car model we discuss the implications for the two applications respectively to evaluate the performance of the index lg we also compute the bayes factor a bayesian model selection criterion to see which model is preferred for the two applications and simulation data to derive the value of lg we estimate its posterior mode based on samples derived from the bugs program while for bayes factor we use the double laplace metropolis method schwarz criterion and a modified harmonic mean for approximations the results of lg and bayes factor are consistent we conclude that lg is fairly accurate as an index for selection between poisson gamma and car model when easy and fast computation is of concern we recommend using lg as the first and less costly index

limit distribution of maximal non aligned two sequence segmental score consider two independent sequences x 1 x n and y 1 y n suppose that x 1 x n are i i d x and y 1 y n are i i d y where x and y are distributions on finite alphabets x and y respectively a score f x x y r is assigned to each pair x i y j and the maximal nonaligned segment score is m n maxo 0 i j n 0 k 1 f x i k y j k the limit distribution of m n is derived here when x and y are not too far apart and f is slightly constrained

bayesian hybrid generative discriminative learning based on finite liouville mixture models recently hybrid generative discriminative approaches have emerged as an efficient knowledge representation and data classification engine however little attention has been devoted to the modeling and classification of non gaussian and especially proportional vectors our main goal in this paper is to discover the true structure of this kind of data by building probabilistic kernels from generative mixture models based on liouville family from which we develop the beta liouville distribution and which includes the well known dirichlet as a special case the beta liouville has a more general covariance structure than the dirichlet which makes it more practical and useful our learning technique is based on a principled purely bayesian approach which resulted models are used to generate support vector machine svm probabilistic kernels based on information divergence in particular we show the existence of closed form expressions of the kullback leibler and renyi divergences between two beta liouville distributions and then between two dirichlet distributions as a special case through extensive simulations and a number of experiments involving synthetic data visual scenes and texture images classification we demonstrate the effectiveness of the proposed approaches

model comparison of nonlinear structural equation models with fixed covariates recently it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory a new nonlinear structural equation model with fixed covariates is proposed in this article a procedure which utilizes the powerful path sampling for computing the bayes factor is developed for model comparison in the implementation the required random observations are simulated via a hybrid algorithm that combines the gibbs sampler and the metropolis hastings algorithm it is shown that the proposed procedure is efficient and flexible and it produces bayesian estimates of the parameters latent variables and their highest posterior density intervals as by products empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example

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

sworn testimony of the model evidence gaussian mixture importance game sampling what is the best model the answer to this question lies in part in the eyes of the beholder nevertheless a good model must blend rigorous theory with redeeming qualities such as parsimony and quality of fit model selection is used to make inferences via weighted averaging from a set of k candidate models formula presented and help identify which model is most supported by the observed data formula presented here we introduce a new and robust estimator of the model evidence formula presented which acts as normalizing constant in the denominator of bayes theorem and provides a single quantitative measure of relative support for each hypothesis that integrates model accuracy uncertainty and complexity however formula presented is analytically intractable for most practical modeling problems our method coined gaussian mixture importance game sampling uses bridge sampling of a mixture distribution fitted to samples of the posterior model parameter distribution derived from mcmc simulation we benchmark the accuracy and reliability of game sampling by application to a diverse set of multivariate target distributions up to 100 dimensions with known values of formula presented and to hypothesis testing using numerical modeling of the rainfall runoff transformation of the leaf river watershed in mississippi usa these case studies demonstrate that game sampling provides robust and unbiased estimates of the evidence at a relatively small computational cost outperforming commonly used estimators the game sampler is implemented in the matlab package of dream and simplifies considerably scientific inquiry through hypothesis testing and model selection

bayesian inference for finite mixtures of generalized linear models with random effects we present an hierarchical bayes approach to modeling parameter heterogeneity in generalized linear models the model assumes that there are relevant subpopulations and that within each subpopulation the individual level regression coefficients have a multivariate normal distribution however class membership is not known a priori so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions this approach combines the flexibility of semiparametric latent class models that assume common parameters for each sub population and the parsimony of random effects models that assume normal distributions for the regression parameters the number of subpopulations is selected to maximize the posterior probability of the model being true simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub populations an application is presented concerning preferences for various aspects of personal computers

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

sampling rare events statistics of local sequence alignments a method to calculate probability distributions in regions where the events are very unlikely e g p approximately 10 40 is presented the basic idea is to map the underlying model on a physical system the system is simulated at a low temperature such that preferably configurations with originally low probabilities are generated since the distribution of such a physical system is known the original unbiased distribution can be obtained as an application local alignment of protein sequences is studied the deviation of the distribution p s of optimum scores from the extreme value distribution is quantified this deviation decreases with growing sequence length

score statistics of global sequence alignment from the energy distribution of a modified directed polymer and directed percolation problem sequence alignment is one of the most important bioinformatics tools for modern molecular biology the statistical characterization of gapped alignment scores has been a long standing problem in sequence alignment research using a variant of the directed path in random media model we investigate the score statistics of global sequence alignment taking into account in particular the compositional bias of the sequences compared such statistics are used to distinguish accidental similarity due to compositional similarity from biologically significant similarity to accommodate the compositional bias we introduce an extra parameter p indicating the probability for positive matching scores to occur when p is small a high scoring alignment obviously cannot come from compositional similarity when p is large the highest scoring point within a global alignment tends to be close to the end of both sequences in which case we say the system percolates by applying finite size scaling theory on percolating probability functions of various sizes sequence lengths the critical p at infinite size is obtained for alignment of length t the fact that the score fluctuation grows as chi t 1 3 is confirmed upon investigating the scaling form of the alignment score using the kolmogorov smirnov statistics test we show that the random variable if properly scaled follows the tracy widom distributions gaussian orthogonal ensemble for p slightly larger than pc and gaussian unitary ensemble for larger p although these results deepen our understanding of the distribution of alignment scores the use of these results in practical applications remains somewhat heuristic and needs to be further developed nevertheless the possibility of characterizing score statistics for modest system size sequence lengths via proper reparametrization of alignment scores is illustrated

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

finite temperature local protein sequence alignment percolation and free energy distribution sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases it can be mapped on the physical model of directed polymers in random media we consider the finite temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase where the free energy grows linearly or logarithmically with the sequence length by means of numerical simulations and finite size scaling analysis we determine the phase diagram in the plane that is spanned by the gap costs and the temperature we use the most frequently used parameter set for protein alignment the critical exponents that describe the parameter driven transition are found to be explicitly temperature dependent furthermore we study the shape of the free energy distribution close to the transition by rare event simulations down to probabilities on the order 10 ensuremath 64 it is well known that in the logarithmic region the optimal score distribution t 0 is described by a modified gumbel distribution we confirm that this also applies for the free energy distribution tg0 however in the linear phase the distribution crosses over to a modified gaussian distribution

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

asymmetric exclusion process and extremal statistics of random sequences a mapping is established between sequence alignment one of the most commonly used tools of computational biology at a certain choice of scoring parameters and the asymmetric exclusion process one of the few exactly solvable models of nonequilibrium physics the statistical significance of sequence alignments is characterized through studying the total hopping current of the discrete time and space version of the asymmetric exclusion process

the maximal smoothing principle in density estimation abstract we propose a widely applicable method for choosing the smoothing parameters for nonparametric density estimators it has come to be realized in recent years e g see hall and marron 1987 scott and terrell 1987 that cross validation methods for finding reasonable smoothing parameters from raw data are of very limited practical value their sampling variability is simply too large the alternative discussed here the maximal smoothing principle suggests that we consider using the most smoothing that is consistent with the estimated scale of our data this greatly generalizes and exploits a phenomenon noted in terrell and scott 1985 that measures of scale tend to place upper bounds on the smoothing parameters that minimize asymptotic mean integrated squared error of density estimates such as histograms and frequency polygons the method avoids the extreme sampling variability of cross validation by using ordinary scale estimators such as the standard deviation and interquartile range which

general solution of the poisson equation for quasi birth and death processes we consider the poisson equation i p u g where p is the transition matrix of a quasi birth and death process with infinitely many levels g is a given infinite dimensional vector and u is the unknown our main result is to provide the general solution of this equation to this purpose we use the block tridiagonal and block toeplitz structure of the matrix p to obtain a set of matrix difference equations which are solved by constructing suitable resolvent triples

bayesian analysis of the error correction model this paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model a second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space this prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in bayesian cointegration analysis using this new prior and laplace approximation an estimator for the posterior probability of the rank is given the approach performs well compared with information criteria in monte carlo experiments

estimating bayes factors via posterior simulation with the laplace metropolis estimator abstract the key quantity needed for bayesian hypothesis testing and model selection is the integrated or marginal likelihood of a model we describe a way to use posterior simulation output to estimate integrated likelihoods we describe the basic laplace metropolis estimator for models without random effects for models with random effects we introduce the compound laplace metropolis estimator we apply this estimator to data from the world fertility survey and show it to give accurate results batching of simulation output is used to assess the uncertainty involved in using the compound laplace metropolis estimator the method allows us to test for the effects of independent variables in a random effects model and also to test for the presence of the random effects

on the connection between directed percolation and directed polymers we consider the scaling behaviour of the directed paths of minimum energy on a lattice to each bond of which energy 0 or 1 is randomly assigned in 1 1 dimensions it is shown by numerical transfer matrix calculations that in all the regions below the directed percolation threshold these paths still scale with the directed percolation exponent at the same time degeneracy of these paths at and below the threshold is found to be very different the problem of stability of the directed percolation ground state and the case when the energy on each bond can take randomly q 2 different values are also considered

approximate marginal densities of nonlinear functions this paper presents an asymptotic approximation for the marginal density of a nonlinear function g 0 that is applicable when the joint density of 0 is dominated by a single mode and the jacobian of g is of full rank near that mode the approximation is based on laplace s method and its asymptotic properties are similar to those of the saddlepoint approximation the approximation is applied to the computation of a marginal posterior density a marginal sampling density and a marginal density based on a multivariate saddlepoint approximation to a joint density

a robust bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete weibull distribution this article proposes a bayesian mixed effects zero inflated discrete weibull zidw regression model for zero inflated and highly skewed longitudinal count data as an alternative to mixed effects regression models that are based on the negative binomial zero inflated negative binomial and conventional discrete weibull dw distributions the mixed effects zidw regression model is an extension of a recently introduced model based on the dw distribution and uses the log link function to specify the relationship between the linear predictors and the median counts the zidw approach offers a more robust characteristic of central tendency compared to the mean count when there is skewness in the data a matrix generalized half t mgh t prior distribution is specified for the random effects covariance matrix as an alternative to the widely used wishart prior distribution the methodology is applied to a longitudinal dataset from an epilepsy clinical trial in a data contamination simulation study we show that the mixed effect zidw regression model is more robust than the competing mixed effects regression models when the data contain excess zeros or outliers the performance of the zidw regression model is also assessed in a simulation study under the specification of respectively the mgh t and wishart prior distributions for the random effects covariance matrix it turns out that the highest posterior density intervals under the mgh t prior for the fixed effects maintain nominal coverage when the true variability between random slopes over time is small whereas those under the wishart prior are generally conservative

a unified perturbation analysis framework for countable markov chains abstract in this paper we are devoted to singular perturbation analysis for discrete time or continuous time markov chains we modify and extend the drift condition method well known for regular perturbation to develop a new framework for singular perturbation analysis our results extend and improve the corresponding ones in 2 for singularly perturbed markov chains by allowing a general perturbation form less restrictive conditions and more computable bounds our analysis covers the regular perturbation analysis and hence unifies singular and regular perturbation analysis furthermore our results are illustrated by two two dimensional markov chains including a discrete time queue and a continuous time level dependent quasi birth death process

bayesian inference and model comparison for metallic fatigue data abstract in this work we present a statistical treatment of stress life s n data drawn from a collection of records of fatigue experiments that were performed on 75s t6 aluminum alloys our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration model selection and model ranking with reference to s n data to this purpose we consider fatigue limit models and random fatigue limit models that are specially designed to allow the treatment of the run outs right censored data we first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen to assess the robustness of the estimation of the quantile functions we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio we then compare and rank the models by classical measures of fit based on information criteria we also consider a bayesian approach that provides under the prior distribution of the model parameters selected by the user their simulation based posterior distributions we implement and apply bayesian model comparison methods such as bayes factor ranking and predictive information criteria based on cross validation techniques under various a priori scenarios

the time dependent expected reward and deviation matrix of a finite qbd process abstract deriving the time dependent expected reward function associated with a continuous time markov chain involves the computation of its transient deviation matrix in this paper we focus on the special case of a finite quasi birth and death qbd process motivated by the desire to compute the expected revenue lost in a map ph 1 c queue we use two different approaches in this context the first is based on the solution of a finite system of matrix difference equations it provides an expression for the blocks of the expected reward vector the deviation matrix and the mean first passage time matrix the second approach based on some results in the perturbation theory of markov chains leads to a recursive method to compute the full deviation matrix of a finite qbd process we compare the two approaches using some numerical examples

exact asymptotic results for the bernoulli matching model of sequence alignment finding analytically the statistics of the longest common subsequence lcs of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology we present exact asymptotic results for the distribution of the lcs in a simpler yet nontrivial variant of the original model called the bernoulli matching bm model we show that in the bm model for all c the distribution of the asymptotic length of the lcs suitably scaled is identical to the tracy widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a gaussian unitary ensemble

a bivariate bayes method for improving the estimates of mortality rates with a twofold conditional autoregressive model a bivariate bayes method is proposed for estimating the mortality rates of a single disease for a given population using additional information from a second disease the information on the two diseases is assumed to be from the same population groups or areas the joint frequencies of deaths for the two diseases for given populations are assumed to have a bivariate poisson distribution with joint means proportional to the population sizes the relationship between the mortality rates of the two different diseases if formulated through the twofold conditional autoregressive car model where spatial effects as well as indexes of spatial dependence are introduced to capture the structured clusterings among areas this procedure is compared to a univariate hierarchical bayes procedure that uses information from one disease only comparisons of two procedures are made by the optimal property a monte carlo study real data and the bayes factor all of the methods that we consider demonstrate a substantial

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

variational learning for finite dirichlet mixture models and applications in this paper we focus on the variational learning of finite dirichlet mixture models compared to other algorithms that are commonly used for mixture models such as expectation maximization our approach has several advantages first the problem of over fitting is prevented furthermore the complexity of the mixture model i e the number of components can be determined automatically and simultaneously with the parameters estimation as part of the bayesian inference procedure finally since the whole inference process is analytically tractable with closed form solutions it may scale well to large applications both synthetic and real data generated from real life challenging applications namely image databases categorization and anomaly intrusion detection are experimented to verify the effectiveness of the proposed approach

replica model for an unusual directed polymer in 1 1 dimensions and prediction of the extremal parameter of gapped sequence alignment statistics sequence alignment is one of the most important bioinformatics tools for modern molecular biology the statistical characterization of gapped alignment scores has been a long standing problem in sequence alignment research in this paper we provide a self contained exposition of sequence alignment a short review about how this problem is related to the directed polymer problem in statistical physics and some analytical results that can be used for predicting alignment score statistics basically we present two classes of solutions for the gapped alignment statistics by explicitly calculating the evolution of the few replica partition function in 1 1 dimensions we have obtained the conditions under which the more important extremal parameter lambda characterizing the alignment score statistics becomes predictable

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

behavior in a dynamic decision problem an analysis of experimental evidence using a bayesian type classification algorithm different people may use different strategies or decision rules when solving complex decision problems we provide a new bayesian procedure for drawing inferences about the nature and number of decision rules present in a population and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem subjects practiced before playing for money based on money round decisions our procedure classifies subjects into three types which we label near rational fatalist and confused there is clear evidence of continuity in subjects behaviors between the practice and money rounds types who performed best in practice also tended to perform best when playing for money however the agreement between practice and money play is far from perfect the divergences appear to be well explained by a combination of type switching due to learning and or increased effort in money play and errors in our probabilistic type assignments

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

robust fit of bayesian mixed effects regression models with application to colony forming unit count in tuberculosis research early bactericidal activity of tuberculosis drugs is conventionally assessed using statistical regression modeling of colony forming unit cfu counts over time typically most cfu counts deviate little from the regression curve but gross outliers due to erroneous sputum sampling are occasionally present and can markedly influence estimates of the rate of change in cfu count which is the parameter of interest a recently introduced bayesian nonlinear mixed effects regression model was adapted to offer a robust approach that accommodates both outliers and potential skewness in the data at its most general the proposed regression model fits the skew student t distribution to residuals and random coefficients deviance information criterion statistics and compound laplace metropolis marginal likelihoods were used to discriminate between alternative bayesian nonlinear mixed effects regression models we present a relatively easy method to calculate the marginal likelihoods required to determine compound laplace metropolis marginal likelihoods by adapting methods available in currently available statistical software the robust methodology proposed in this paper was applied to data from 6 clinical trials the results provide strong evidence that the distribution of cfu count is often heavy tailed and negatively skewed suggesting the presence of outliers therefore we recommend that robust regression models such as those proposed here should be fitted to cfu count

bayesian tests of extra binomial variability a simple model for extra binomial variability is the beta binomial a complication in testing the binomial against the beta binomial alternative is that the binomial lies on the boundary of the beta binomial which forces modifications to the usual asymptotic arguments in this paper we propose a bayesian test using a pair of approximate bayes factors one for the case in which the maximum likelihood estimator mle of the extra binomial variability is zero and one for the case in which it is positive these approximate bayes factors are easy to compute we evaluate the operating characteristics of the bayes factors and find them to be more powerful than the likelihood ratio test we then apply the method to three data sets including one in which the issue is whether a logistic regression intercept should be considered a random effect in each case our approximate bayes factors are close to the exact bayes factors which may also be computed with additional effort copyright 2004 john wiley sons ltd

objective method for estimating asymptotic parameters with an application to sequence alignment sequence alignment is an indispensable computational tool in modern molecular biology the model underlying biological sequence alignment is of interest to physicists because it approximates the statistical mechanics of dna and protein annealing while bearing an intimate relationship to models of directed polymers in random media recent methods for determining the statistics of random sequence alignments have reduced the computation time to less than 1 s opening up some interesting possibilities for online computation with biological search engines before implementation however the methods required an objective technique for computing regression coefficients pertinent to an asymptotic regime typically physicists estimate parameters pertinent to an asymptotic regime subjectively they eyeball their data estimate the asymptotic regime where the regression model holds with reasonable accuracy and then regress data only within the estimated asymptotic regime our publicly available computer program arrp replaces the subjective assessment of the asymptotic regime with an objective change point detection method increasing confidence in the scientific objectivity of the parameter estimates asymptotic regression has potential applications across most of physics

the computation of key properties of markov chains via perturbations abstract computational procedures for the stationary probability distribution the group inverse of the markovian kernel and the mean first passage times of a finite irreducible markov chain are developed using perturbations the derivation of these expressions involves the solution of systems of linear equations and structurally inevitably the inverses of matrices by using a perturbation technique starting from a simple base where no such derivations are formally required we update a sequence of matrices formed by linking the solution procedures via generalised matrix inverses and utilising matrix and vector multiplications four different algorithms are given some modifications are discussed and numerical comparisons are made using a test example the derivations are based upon the ideas outlined by hunter 14

time series of continuous proportions summary a vector of continuous proportions consists of the proportions of some total accounted for by its constituent components an example is the proportions of world motor vehicle production by japan the usa and all other countries we consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts reasons for analysing such times series include estimation of the underlying trend estimation of the effect of covariates and interventions and forecasting we develop a state space model for time series of continuous proportions conditionally on the unobserved state the observations are assumed to follow the dirichlet distribution often considered to be the most natural distribution on the simplex the state follows the dirichlet conjugate distribution which is introduced here thus the model although based on the dirichlet distribution does not have its restrictive independence properties covariates trends seasonality and interventions may be incorporated in a natural way the model has worked well when applied to several examples and we illustrate with components of world motor vehicle production

bayesian model choice asymptotics and exact calculations abstract model determination is a fundamental data analytic task here we consider the problem of choosing amongst a finite with loss of generality we assume two set of models after briefly reviewing classical and bayesian model choice strategies we present a general predictive density which includes all proposed bayesian approaches we are aware of using laplace approximations we can conveniently assess and compare asymptotic behavior of these approaches concern regarding the accuracy of these approximation for small to moderate sample sizes encourages the use of monte carlo techniques to carry out exact calculations a data set fit with nested non linear models enables comparison between proposals and between exact and asymptotic values

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

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

unmasking multivariate outliers and leverage points comment detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers to avoid this masking effect we propose to compute distances based on very robust estimates of location and covariance in the case of regression data the outliers also may be unmasked by using a highly robust regression method a new display is proposed in which the robust regression residuals are plotted versus the robust distances

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea