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256
Markov chain monte carlo convergence diagnostics
 JASA
, 1996
"... A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise ..."
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Cited by 371 (6 self)
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A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including applying diagnostic procedures to a small number of parallel chains, monitoring autocorrelations and crosscorrelations, and modifying parameterizations or sampling algorithms appropriately. We emphasize, however, that it is not possible to say with certainty that a finite sample from an MCMC algorithm is representative of an underlying stationary distribution. 1
JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling
, 2003
"... JAGS is a program for Bayesian Graphical modelling which aims for compatibility with Classic BUGS. The program could eventually be developed as an R package. This article explains the motivations for this program, briefly describes the architecture and then discusses some ideas for a vectorized form ..."
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Cited by 197 (0 self)
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JAGS is a program for Bayesian Graphical modelling which aims for compatibility with Classic BUGS. The program could eventually be developed as an R package. This article explains the motivations for this program, briefly describes the architecture and then discusses some ideas for a vectorized form of the BUGS language.
BUGS: Bayesian inference using Gibbs sampling. Version 1.4.1, Medical Research council BiostatisticsUnit, CambridgeUniversity,
, 2004
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Bayesian Inference on Network Traffic Using Link Count Data
 J. Amer. Statist. Assoc
, 1996
"... We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article, and of interest in both ..."
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Cited by 98 (1 self)
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We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article, and of interest in both communication and transportation network studies. The current paper develops the theoretical framework of variants of the origindestination flow problem, and introduces Bayesian approaches to analysis and inference. In the first, the socalled fixed routing problem, traffic or messages pass between nodes in a network, with each message originating at a specific source node, and ultimately moving through the network to a predetermined destination node. All nodes are candidate origin and destination points. The framework assumes no travel time complications, considering only the number of messages passing between pairs of nodes in a specified time interval. The route count, or route flow, pro...
An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants
 Biometrika
, 2006
"... Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method i ..."
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Cited by 89 (4 self)
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Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.
Quantifying uncertainty in projections of regional climate change: a Bayesian approach to the analysis of multimodel ensembles
 Journal of Climate
, 2005
"... A Bayesian statistical model is proposed that combines information from a multimodel ensemble of atmosphereocean general circulation models and observations to determine probability distributions of future temperature change on a regional scale. The posterior distributions derived from the statist ..."
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Cited by 59 (6 self)
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A Bayesian statistical model is proposed that combines information from a multimodel ensemble of atmosphereocean general circulation models and observations to determine probability distributions of future temperature change on a regional scale. The posterior distributions derived from the statistical assumptions incorporate the criteria of bias and convergence in the relative weights implicitly assigned to the ensemble members. This approach can be considered an extension and elaboration of the Reliability Ensemble Averaging method. For illustration, we consider output of mean surface temperature from 9 AOGCMs, run under the A2 SRES scenario, for Boreal winter and summer, aggregated over 22 land regions. The shapes of the final probability density functions of temperature change vary widely, from unimodal curves for regions where model results agree, or outlying projections are discounted due to bias, to multimodal curves where models that cannot be discounted on the basis of bias give diverging projections. Besides the basic statistical model, we consider including correlation between present and future temperature responses, and test alternative forms of probability distributions for the model error terms. We suggest that a probabilistic approach, particularly in the form of a Bayesian model, is a useful platform from which to synthesize the information from an ensemble of simulations, at regional scales. The probability distributions of temperature change reveal features such as multimodality and long tails that could not otherwise be easily discerned. Furthermore, the Bayesian model can serve as an interdisciplinary tool through which climate modelers, climatologists, and statisticians can work more closely. For example, climate modelers, through their expert judgment, could contribute to the formulations of prior distributions in the statistical model. 1
Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo
, 2011
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Deviance Information Criterion for Comparing Stochastic Volatility Models
 Journal of Business and Economic Statistics
, 2002
"... Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed d ..."
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Cited by 52 (11 self)
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Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this paper is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measureoffit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the S&P100 index.
A Bayesian model to forecast new product performance in domestic and international markets. Marketing Science 115–136
, 1999
"... This paper attempts to shed light on the following research questions: When a firm introduces a new product (or service) how can it effectively use the different information sources available to generate reliable new product performance forecasts? How can the firm account for varying information ava ..."
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Cited by 48 (1 self)
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This paper attempts to shed light on the following research questions: When a firm introduces a new product (or service) how can it effectively use the different information sources available to generate reliable new product performance forecasts? How can the firm account for varying information availability at different stages of the new product launch and generate forecasts at each stage? We address these questions in the context of the sequential launches of motion pictures in international markets. Players in the motion picture industry require forecasts at different stages of the movie launch process to aid decisionmaking, and the information sets available to generate such forecasts vary at different stages. Despite the importance of such forecasts, the industry struggles to understand and predict
HIGHERORDER LATENT TRAIT MODELS FOR COGNITIVE DIAGNOSIS
, 2004
"... Higherorder latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a highdimensional attribute vector that is natural in many situations when specific cogni ..."
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Cited by 43 (2 self)
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Higherorder latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a highdimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative item response model would be a reasonable alternative. This approach stems from viewing the attributes as the specific knowledge required for examination performance, and modeling these attributes as arising from a broadlydefined latent trait resembling the 0 of item response models. In this way a relatively simple model for the joint distribution of the attributes results, which is based on a plausible model for the relationship between general aptitude and specific knowledge. Maxkov chain Monte Carlo algorithms for parameter estimation axe given for selected response distributions, and simulation results axe presented to examine the performance of the algorithm as well as the sensitivity of classification to model misspecification. An analysis of fraction subtraction data is provided as an example.