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147
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 598 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
General methods for monitoring convergence of iterative simulations
 J. Comput. Graph. Statist
, 1998
"... We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develo ..."
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Cited by 270 (8 self)
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We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develop convergencemonitoring summaries that are relevant for the purposes for which the simulations are used. We recommend applying a battery of tests for mixing based on the comparison of inferences from individual sequences and from the mixture of sequences. Finally, we discuss multivariate analogues, for assessing convergence of several parameters simultaneously.
Simulating Normalized Constants: From Importance Sampling to Bridge Sampling to Path Sampling
 Statistical Science, 13, 163–185. COMPARISON OF METHODS FOR COMPUTING BAYES FACTORS 435
, 1998
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 153 (4 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Computational and Inferential Difficulties With Mixture Posterior Distributions
 Journal of the American Statistical Association
, 1999
"... This paper deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo techniques usually have difficult ..."
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Cited by 118 (12 self)
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This paper deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo techniques usually have difficulties with wellseparated modes such as occur here; the Markov chain Monte Carlo sampler stays within a neighbourhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed on the Markov chain Monte Carlo sampler using tempered transitions based on Langevin algorithms. However, as the prior distribution does not distinguish between the different components, the posterior mixture distribution is symmetric and thus standard estimators such as posterior means cannot be used. Since this is also true for most nonsymmetric priors, we propose alternatives for Bayesian inference for permutation invariant posteriors, including a cluster...
Optimal Scaling for Various MetropolisHastings Algorithms
, 2001
"... We review and extend results related to optimal scaling of MetropolisHastings algorithms. We present various theoretical results for the highdimensional limit. We also present simulation studies which confirm the theoretical results in finite dimensional contexts. ..."
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Cited by 97 (23 self)
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We review and extend results related to optimal scaling of MetropolisHastings algorithms. We present various theoretical results for the highdimensional limit. We also present simulation studies which confirm the theoretical results in finite dimensional contexts.
Optimal scaling of discrete approximations to Langevin diffusions
 J. R. Statist. Soc. B
, 1997
"... . We consider the optimal scaling problem for proposal distributions in HastingsMetropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate, independ ..."
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Cited by 76 (25 self)
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. We consider the optimal scaling problem for proposal distributions in HastingsMetropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0:574. We show that as a function of dimension n, the complexity of the algorithm is O(n 1=3 ), which compares favourably with the O(n) complexity of randomwalk Metropolis algorithms. We illustrate this comparison with a number of example simulations. Keywords. Langevin algorithm, HastingsMetropolis, Markov chain Monte Carlo, weak convergence. * Statistical Laboratory, University of Cambridge, Cambridge CB2 1SB, U.K. Internet: G.O.Roberts@statslab.cam.ac.uk. ** Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 1A1. Internet: jeff@utstat.toronto.edu. Supported in part by NSERC o...
Adaptive Markov Chain Monte Carlo through Regeneration
, 1998
"... this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the ..."
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Cited by 70 (4 self)
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this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the proofs from Sections 2 and 3 are placed in the Appendix. 2 Regeneration: A Framework for Adaptation
Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach
, 2002
"... This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically ..."
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Cited by 69 (12 self)
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This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically, the parameter point estimates converge to their pseudotrue values, and the best model under the KullbackLeibler distance will have the highest posterior probability. Second, we illustrate the strong small sample behavior of the approach using a wellknown application: the U.S. cattle cycle. Bayesian estimates outperform maximum likelihood results, and the proposed model is easily compared with a set of BVARs.
Hierarchical SpatioTemporal Mapping of Disease Rates
 Journal of the American Statistical Association
, 1996
"... Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or oth ..."
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Cited by 63 (7 self)
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Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in lowpopulation areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatiotemporal interactions. Fitting the resulting highlyparametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of countyspecific lung cancer rates in the state of Ohio during the period 19681988...
On the ergodicity properties of some adaptive MCMC algorithms
 Annals of Applied Probability
"... In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a socalled adaptive MCMC sampler conver ..."
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Cited by 59 (8 self)
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In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a socalled adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the Independent MetropolisHastings algorithm and the Random Walk Metropolis algorithm with symmetric increments. Finally we propose an application of these results to the case where the proposal distribution of the MetropolisHastings update is a mixture of distributions from a curved exponential family.