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16
On the Relationship Between Markov Chain Monte Carlo Methods for Model Uncertainty
 JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
, 2001
"... This article considers Markov chain computational methods for incorporating uncertainty about the dimension of a parameter when performing inference within a Bayesian setting. A general class of methods is proposed for performing such computations, based upon a product space representation of the ..."
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Cited by 32 (3 self)
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This article considers Markov chain computational methods for incorporating uncertainty about the dimension of a parameter when performing inference within a Bayesian setting. A general class of methods is proposed for performing such computations, based upon a product space representation of the problem which is similar to that of Carlin and Chib. It is shown that all of the existing algorithms for incorporation of model uncertainty into Markov chain Monte Carlo (MCMC) can be derived as special cases of this general class of methods. In particular, we show that the popular reversible jump method is obtained when a special form of MetropolisHastings (MH) algorithm is applied to the product space. Furthermore, the Gibbs sampling method and the variable selection method are shown to derive straightforwardly from the general framework. We believe that these new relationships between methods, which were until now seen as diverse procedures, are an important aid to the understanding of MCMC model selection procedures and may assist in the future development of improved procedures. Our discussion also sheds some light upon the important issues of "pseudoprior" selection in the case of the Carlin and Chib sampler and choice of proposal distribution in the case of reversible jump. Finally, we propose efficient reversible jump proposal schemes that take advantage of any analytic structure that may be present in the model. These proposal schemes are compared with a standard reversible jump scheme for the problem of model order uncertainty in autoregressive time series, demonstrating the improvements which can be achieved through careful choice of proposals
Inferring spatial phylogenetic variation along nucleotide sequences: A multiple changepoint model
 J Am StatAssoc
, 2003
"... We develop a Bayesian multiple changepoint model to infer spatial phylogenetic variation (SPV) along aligned molecular sequence data. SPV occurs in sequences from organisms that have undergone biological recombination or when evolutionary rates and selective pressures vary along the sequences. This ..."
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Cited by 25 (10 self)
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We develop a Bayesian multiple changepoint model to infer spatial phylogenetic variation (SPV) along aligned molecular sequence data. SPV occurs in sequences from organisms that have undergone biological recombination or when evolutionary rates and selective pressures vary along the sequences. This Bayesian approach permits estimation of uncertainty regarding recombination, the crossingover locations, and all other model parameters. The model assumes that the sites along the data separate into an unknown number of contiguous segments, each with possibly different evolutionary relationships between organisms, evolutionary rates, and transition: transversion ratios. We develop a transition kernel, use reversiblejump Markov chain Monte Carlo to t our model, and draw inference from both simulated and real data. Through simulation, we examine the minimal length recombinant segment that our model can detect for several levels of evolutionary divergence. We examine the entire genome of a reported human immunode ciency virus (HIV)1 isolate, related to a purported recombinant virus thought to be the causative agent of an epidemic outbreak of HIV1 infection among intravenous drug users in Russia. We nd that regions of the genome differ in their evolutionary history and selective pressures. There is strong evidence for multiple crossovers along the genome and frequent shifts in selective pressure changes throughout the vif through env genes.
Oh Brother, Where Art Thou? A Bayes Factor Test for Recombination with Uncertain Heritage
, 2002
"... Current methods to identify recombination between subtypes of human immunodeficiency virus 1 (HIV1) fall into a sequential testing trap, in which significance is assessed conditional on parental representative sequences and crossover points (COPs) that maximize the same test statistic. We overcame ..."
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Cited by 15 (6 self)
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Current methods to identify recombination between subtypes of human immunodeficiency virus 1 (HIV1) fall into a sequential testing trap, in which significance is assessed conditional on parental representative sequences and crossover points (COPs) that maximize the same test statistic. We overcame this shortfall by testing for recombination while inferring parental heritage and COPs using an extended Bayesian multiple changepoint model. The model assumes that aligned molecular sequence data consist of an unknown number of contiguous segments that may support alternative topologies or varying evolutionary pressures. We allowed for heterogeneity in the substitution process and specifically tested for intersubtype recombination using Bayes factors. We also developed a new class of priors to assess significance across a wide range of support for recombination in the data. We applied our method to three putative gag gene recombinants. HIV1 isolate RW024 decisively supported recombination with an inferred parental heritage of AD and a COP 95 % Bayesian credible interval of (1152, 1178) using the HXB2 numbering scheme. HIV1 isolate VI557 barely supported recombination. HIV1 isolate RF decisively rejected recombination as expected, given that the sequence is commonly used as a reference sequence for subtype B. We employed scaled regeneration quantile plots to assess convergence and found this approach convenient to use even for our
Bayesian Input Variable Selection Using Posterior Probabilities and Expected Utilities
, 2002
"... We consider the input variable selection in complex Bayesian hierarchical models. Our goal is to find a model with the smallest number of input variables having statistically or practically at least the same expected utility as the full model with all the available inputs. A good estimate for the ..."
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Cited by 6 (1 self)
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We consider the input variable selection in complex Bayesian hierarchical models. Our goal is to find a model with the smallest number of input variables having statistically or practically at least the same expected utility as the full model with all the available inputs. A good estimate for the expected utility can be computed using crossvalidation predictive densities. In the case of input selection and a large number of input combinations, the computation of the crossvalidation predictive densities for each model easily becomes computationally prohibitive. We propose to use the posterior probabilities obtained via variable dimension MCMC methods to find out potentially useful input combinations, for which the final model choice and assessment is done using the expected utilities.
A samplingbased approach to nonparametric dynamic system identification and estimation
 In Proc. of the American Control Conference
, 2004
"... Abstract — We propose a new probabilistic framework for nonparametric identification and estimation of dynamic systems. Under the parametric paradigm, a model of the system and a set of observations are given and the parameter space of the model is searched to optimize an objective function. However ..."
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Cited by 4 (2 self)
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Abstract — We propose a new probabilistic framework for nonparametric identification and estimation of dynamic systems. Under the parametric paradigm, a model of the system and a set of observations are given and the parameter space of the model is searched to optimize an objective function. However, if we are uncertain about the model, the parametric approach can easily overfit data and lead to risky decisions. In nonparametric estimation, the model uncertainty is introduced in a systematic manner to find both the model and associated parameters of the system. In this paper, we consider a dynamic system consisting of a varying number of subsystems with noisy observations. The objective is to identify the subsystems at each time step and estimate the associated parameters such that the observations are explained the best. We develop an efficient algorithm based on Markov chain Monte Carlo methods and apply our approach to multiple target tracking problems. We address the issues with the subsystem initiation and termination and initial state estimation. In simulation our algorithm shows excellent performance for tracking a varying number of maneuvering targets with nonlinear dynamics. In some cases our algorithm outperforms any linear filtering algorithm with perfect associations. I.
Bayesian Modeling of Continuously Marked Spatial Point Patterns
"... Many analyses of continuously marked spatial point patterns assume that the density of points, with differing marks, is identical. However, as noted in the originative paper of Goulard et al. (1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many ..."
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Cited by 3 (2 self)
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Many analyses of continuously marked spatial point patterns assume that the density of points, with differing marks, is identical. However, as noted in the originative paper of Goulard et al. (1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many more small trees than large, hence the model should allow for a higher density of points with small marks. In addition, as suggested by Ogata & Tanemura (1985), the interaction between points should be a function of their mark, allowing, for example, the range of interaction for large trees to exceed that of smaller trees. The aforementioned articles use frequentist inferential techniques, but interval estimation presents difficulties due to the complex distributional properties of the estimates. We suggest the use of Bayesian inferential techniques. Although a Bayesian approach requires a complex, computational implementation of (reversible jump) MCMC methodology, it enables a wide variety of inferences (including interval estimation). We demonstrate our approach by analyzing the well known Norway spruce dataset. Keywords: Markov chain Monte Carlo (MCMC), reversible jump MCMC, pairwise interacting point process, mark chemical activity function 1 Figure 1: Location of n = 134 Norway spruce trees in a 56 × 38 meter field.
Generic reversible jump MCMC using graphical models
, 2005
"... field of Bayesian statistics. Their enormous power and their generalizability have rendered them the method of choice for statistical inference in many scientific disciplines. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is ..."
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Cited by 3 (1 self)
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field of Bayesian statistics. Their enormous power and their generalizability have rendered them the method of choice for statistical inference in many scientific disciplines. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis of such “transdimensional ” models is not easy, with several significant technical and practical difficulties to overcome. In this paper we present a class of graphical models that allow relatively straightforward analysis of a subset of these transdimensional problems. We also present a ‘guided tour ’ of the reversible jump methodology underlying our approach and discuss how each of the various difficulties has been circumvented. Our approach has been implemented using the WinBUGS framework as a GibbsMetropolis sampling ‘engine’. The main advantage of this is that it affords the analyst much modelling flexibility: transdimensional subgraphs may be used as generic components within an arbitrarily wide range of Bayesian graphical models. We present three example analyses to illustrate our approach.
A New Strategy for Simulating From Mixture Distributions With Applications to Bayesian Model Selection
"... We present a method of generating random vectors from a distribution having an absolutely continuous component and a discrete component. The method is then extended to more general mixture distributions that arise quite naturally when dealing with nested models within a Bayesian framework. The main ..."
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Cited by 1 (1 self)
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We present a method of generating random vectors from a distribution having an absolutely continuous component and a discrete component. The method is then extended to more general mixture distributions that arise quite naturally when dealing with nested models within a Bayesian framework. The main idea is to transform the mixture distribution of interest into an absolutely continuous one, in a way that does not require the explicit calculation of the relative weights of the various components of the mixture. For nested models, the proposed method represents a simple alternative to Reversible Jump MCMC schemes. Its distinguishing features are the absence of a proposal step to reduce/increase the dimension of the current space and the fact that in order to assess the convergence of the chain, one can use all the standard tools available for MCMC on a space of fixed dimension.
Model Selection for Dags via RJMCMC for the Discrete and Mixed Case
"... Based on a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm which was developed by Fronk and Giudici (2000) to deal with model selection for Gaussian dags, we propose a new approach for the pure discrete case. Here, the main idea is to introduce latent variables which then allow to fall b ..."
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Cited by 1 (0 self)
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Based on a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm which was developed by Fronk and Giudici (2000) to deal with model selection for Gaussian dags, we propose a new approach for the pure discrete case. Here, the main idea is to introduce latent variables which then allow to fall back on the already treated continuous case. This makes it also straightforward to tackle the mixed case, i.e. to deal simultaneously with continuous and discrete variables. The performance of the approach isinvestigated by means of a simulation study for di erent standard situations. In addition, a real data application is provided. Keywords: Bayesian model selection � dag models � reversible jump Markov Chain Monte Carlo. 1
ASSESSING FINGERPRINT INDIVIDUALITY USING EPIC: A CASE STUDY IN THE ANALYSIS OF SPATIALLY DEPENDENT MARKED PROCESSES
"... Fingerprint individuality refers to the extent of uniqueness of fingerprints and is governed by the distribution of fingerprint features, termed minutiae, in a population. This paper develops a flexible class of marked point processes for minutiae and associated methodology for assessing fingerprint ..."
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Fingerprint individuality refers to the extent of uniqueness of fingerprints and is governed by the distribution of fingerprint features, termed minutiae, in a population. This paper develops a flexible class of marked point processes for minutiae and associated methodology for assessing fingerprint individuality. Inference is carried out in a Bayesian MCMC framework. The flexibility of the model fit to different kinds of minutiae patterns is demonstrated using real fingerprints. Evidence of a Paired Impostor Correspondence (EPIC) is developed as a measure of fingerprint individuality and its value is obtained using a simulation procedure based on the fitted models.