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190
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 203 (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.
Making the most of statistical analyses: Improving interpretation and presentation
 American Journal of Political Science
, 2000
"... Social scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. ..."
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Cited by 164 (18 self)
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Social scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a readerfriendly manner. Using this technique requires some expertise,
Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation
 American Political Science Review
, 2000
"... We propose a remedy for the discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. Methodologists and statisticians agree that "multiple imputation" is a superior approach to the problem of missing data scattered through ..."
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Cited by 141 (40 self)
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We propose a remedy for the discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. Methodologists and statisticians agree that "multiple imputation" is a superior approach to the problem of missing data scattered through one's explanatory and dependent variables than the methods currently used in applied data analysis. The reason for this discrepancy lies with the fact that the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise. In this paper, we adapt an existing algorithm, and use it to implement a generalpurpose, multiple imputation model for missing data. This algorithm is considerably faster and easier to use than the leading method recommended in the statistics literature. We also quantify the risks of current missing data practices, ...
General state space Markov chains and MCMC algorithm
 PROBABILITY SURVEYS
, 2004
"... This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform e ..."
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Cited by 114 (27 self)
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This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for MetropolisHastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.
People Tracking Using Hybrid Monte Carlo Filtering
, 2001
"... Particle filters are used for hidden state estimation with nonlinear dynamical systems. The inference of 3d human motion is a natural application, given the nonlinear dynamics of the body and the nonlinear relation between states and image observations. However, the application of particle filters ..."
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Cited by 102 (6 self)
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Particle filters are used for hidden state estimation with nonlinear dynamical systems. The inference of 3d human motion is a natural application, given the nonlinear dynamics of the body and the nonlinear relation between states and image observations. However, the application of particle filters has been limited to cases where the number of state variables is relatively small, because the number of samples needed with high dimensional problems can be prohibitive. We describe a filter that uses hybrid Monte Carlo (HMC) to obtain samples in high dimensional spaces. It uses multiple Markov chains that use posterior gradients to rapidly explore the state space, yielding fair samples from the posterior. We find that the HMC filter is several thousand times faster than a conventional particle filter on a 28D people tracking problem.
Modelbased Geostatistics
 Applied Statistics
, 1998
"... Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random v ..."
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Cited by 96 (4 self)
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Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The first concerns the assessment of residual contamination from nuclear weapons testing on a South Pacific island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity; we conclude that a coventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of North Lancashire and South C...
Gascuel O. Approximate LikelihoodRatio Test for Branches: A
 Fast, Accurate, and Powerful Alternative. Systematic Biology
"... Abstract.—We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihoodratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLR ..."
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Cited by 86 (4 self)
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Abstract.—We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihoodratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the 1 2 1 2 χ 2 0 + χ
Bayesian Methods for Hidden Markov Models  Recursive Computing in the 21st Century
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2002
"... Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) use ..."
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Cited by 86 (8 self)
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Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) used in practice can be improved by incorporating established recursive algorithms. The most important is a set of forwardbackward recursions calculating conditional distributions of the hidden states given observed data and model parameters. We show how to use the recursive algorithms in an MCMC context and demonstrate mathematical and empirical results showing a Gibbs sampler using the forwardbackward recursions mixes more rapidly than another sampler often used for HMM's. We introduce an augmented variables technique for obtaining unique state labels in HMM's and finite mixture models. We show how recursive computing allows statistically efficient use of MCMC output when estimating the hidden states. We directly calculate the posterior distribution of the hidden chain's state space size by MCMC, circumventing asymptotic arguments underlying the Bayesian information criterion, which is shown to be inappropriate for a frequently analyzed data set in the HMM literature. The use of loglikelihood for assessing MCMC convergence is illustrated, and posterior predictive checks are used to investigate application specific questions of model adequacy.
Bayesian phylogenetic inference via Markov chain Monte Carlo methods
 Biometrics
, 1999
"... SUMMARY. We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cop ..."
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Cited by 85 (3 self)
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SUMMARY. We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain. We illustrate the algorithm with restriction site data on 9 plant species, then extend to DNA sequences from 32 species of fish. The algorithm mixes well in both examples from random starting trees, generating reproducible estimates and credible sets for the path of evolution.
CODA: Convergence Diagnosis and Output Analysis Software for Gibbs sampling output Version 0.30
, 1995
"... ing beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values Reading Data file... Abstracting beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values 10 Next, you will be prompted to specify which (if any ..."
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Cited by 85 (5 self)
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ing beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values Reading Data file... Abstracting beta ... 200 valid values Abstracting alpha ... 200 valid values Abstracting sigma ... 200 valid values 10 Next, you will be prompted to specify which (if any) variables take values restricted to either the range (0, 1) or to the positive real line. CODA requires this information in order to correctly compute Gelman and Rubin (1992)'s convergence diagnostic for nonnormal variables (see x4.2), and to produce kernel density estimates within the appropriate range (see x3.1). Are any variables restricted to values between 0 and 1 (y/n) ? 1: For the line example, you should respond n to this question. The next prompt to appear is as follows: Are any variables restricted to all positive values (y/n) ? 1: For the line example, you should respond y to this question, which causes the following display to appear: Available variables: ++...