Analyzing Markov chain Monte Carlo output

Vats, Dootika; Robertson, Nathan; Flegal, James M.; Jones, Galin L.

doi:10.1002/wics.1501

Cited by 13 publications

(8 citation statements)

References 63 publications

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“…Samples from the posterior distribution are generated by MCMC, and to tell whether these samples are adequately near to the posterior to be applied for inference is part of the objectives. Model's Markov chains convergence can be monitored through estimated Monte Carlo (MC) error for the posterior means [22,23]. MC error measures the variableness of each estimate produced by Markov chain simulation [13,24].…”

Section: Methodsmentioning

confidence: 99%

Bayesian MCMC Approach in Prognostic Modelling of Cardiovascular Disease in Malaysia: A Convergence Diagnostic

Juhan¹,

Zubairi²,

Zuhdi³

et al. 2022

Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022)

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Most studies that considered the Bayesian Markov Chain Monte Carlo (MCMC) approach in prognostic modelling of cardiovascular disease were only focused on the application of the Bayesian approach in variable selection, model, and prior distribution choice. Yet rarely of these studies have explored the convergence of Markov chains in the model. In this study, convergence diagnostics were performed using both visual inspection and other diagnostic to assess the convergence of Markov chains. This study analysed 7180 male patients with ST-Elevation Myocardial Infarction (STEMI) from the National Cardiovascular Disease Database-Acute Coronary Syndrome (NCVD-ACS) registry from 2006 to 2013. Six significant variables were identified in the multivariate Bayesian model, namely diabetes mellitus, family history of cardiovascular disease, chronic lung disease, renal disease, Killip class and age group. Based on these significant variables, the trace plots showed no particular patterns, and the model's MCMC mixing is generally good. As for the Gelman plots, almost all the parameters stabilise around a value of 1.0 for chain segments containing the 100,000 iterations and the chains are converging near the end of the sampling period. Also, the Gelman-Rubin diagnostic showed model convergence where all variables with estimated potential scale reduction factors (PSRF) were equal to 1.0. Concerning generic use of the MCMC approach, the application of a variety of plots and other diagnostic tool in this study indicated that the Markov chains have reached convergence.

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Section: Methodsmentioning

confidence: 99%

Bayesian MCMC Approach in Prognostic Modelling of Cardiovascular Disease in Malaysia: A Convergence Diagnostic

Juhan¹,

Zubairi²,

Zuhdi³

et al. 2022

Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022)

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“…, where Λ n denotes the sample covariance and Σ n denotes the multivariate batch mean estimator of the covariance matrix in the Markov chain central limit theorem (Roy, 2020;Vats et al, 2020). The sample size n is chosen to be the minimum n such that mESS ≥ 260 which ensures a confidence level of δ = 0.1 and a tolerance level of = 0.25 for the expectation in the three parameter (C, α, p)-space (Vats et al, 2019).…”

Section: Prediction and Uncertaintymentioning

confidence: 99%

Probabilistic predictions of SIS epidemics on networks based on population-level observations

Zerenner¹,

Lauro²,

Dashti³

et al. 2021

Preprint

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We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erdős-Rényi and Barabási-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.

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“…The goal in output analysis for MCMC is to estimate Σ in order to assess variability in Ȳ (Flegal et al, 2008;Roy, 2019;Vats et al, 2020). There is a rich literature on estimating Σ for singlechain MCMC implementations.…”

Section: Long-run Variance Estimatorsmentioning

confidence: 99%

Globally-centered autocovariances in MCMC

Agarwal¹,

Vats²

2020

Preprint

Self Cite

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Autocovariances are a fundamental quantity of interest in Markov chain Monte Carlo (MCMC) simulations with autocorrelation function (ACF) plots being an integral visualization tool for performance assessment. Unfortunately, for slow mixing Markov chains, the empirical autocovariance can highly underestimate the truth. For multiple-chain MCMC sampling, we propose a globally-centered estimator of the autocovariance function (G-ACvF) that exhibits significant theoretical and empirical improvements. We show that the bias of the G-ACvF estimator is smaller than the bias of the current state-of-the-art. The impact of this improved estimator is evident in three critical output analysis applications: (1) ACF plots, (2) estimates of the Monte Carlo asymptotic covariance matrix, and (3) estimates of the effective sample size. Under weak conditions, we establish strong consistency of our improved asymptotic covariance estimator, and obtain its large-sample bias and variance. The performance of the new estimators is demonstrated through various examples.

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Analyzing Markov chain Monte Carlo output

Cited by 13 publications

References 63 publications

Bayesian MCMC Approach in Prognostic Modelling of Cardiovascular Disease in Malaysia: A Convergence Diagnostic

Bayesian MCMC Approach in Prognostic Modelling of Cardiovascular Disease in Malaysia: A Convergence Diagnostic

Probabilistic predictions of SIS epidemics on networks based on population-level observations

Globally-centered autocovariances in MCMC

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