Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling

Jasra, Ajay; Holmes, Chris; Stephens, David A.

doi:10.1214/088342305000000016

Cited by 575 publications

(478 citation statements)

References 41 publications

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“…We estimated the prevalence of CPTB to be 27% (95% credible interval (CrI): 21,35). The sensitivities of culture, Xpert, and smear microscopy were estimated to be 60% (95% CrI: 46, 76), 49% (95% CrI: 38, 62), and 22% (95% CrI: 16,30), respectively; specificities of these tests were estimated in accordance with prior information and were close to 100%. Chest radiography was estimated to have a sensitivity of 64% (95% CrI: 55, 73) and a specificity of 78% (95% CrI: 73, 83).…”

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confidence: 78%

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Schumacher¹,

Smeden²,

Dendukuri³

et al. 2016

American Journal of Epidemiology

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Evaluation of tests for the diagnosis of childhood pulmonary tuberculosis (CPTB) is complicated by the absence of an accurate reference test. We present a Bayesian latent class analysis in which we evaluated the accuracy of 5 diagnostic tests for CPTB. We used data from a study of 749 hospitalized South African children suspected to have CPTB from 2009 to 2014. The following tests were used: mycobacterial culture, smear microscopy, Xpert MTB/RIF (Cepheid Inc.), tuberculin skin test (TST), and chest radiography. We estimated the prevalence of CPTB to be 27% (95% credible interval (CrI): 21, 35). The sensitivities of culture, Xpert, and smear microscopy were estimated to be 60% (95% CrI: 46, 76), 49% (95% CrI: 38, 62), and 22% (95% CrI: 16, 30), respectively; specificities of these tests were estimated in accordance with prior information and were close to 100%. Chest radiography was estimated to have a sensitivity of 64% (95% CrI: 55, 73) and a specificity of 78% (95% CrI: 73, 83). Sensitivity of the TST was estimated to be 75% (95% CrI: 61, 84), and it decreased substantially among children who were malnourished and infected with human immunodeficiency virus (56%). The specificity of the TST was 69% (95% CrI: 63%, 76%). Furthermore, it was estimated that 46% (95% CrI: 42, 49) of CPTB-negative cases and 93% (95% CrI: 82; 98) of CPTB-positive cases received antituberculosis treatment, which indicates substantial overtreatment and limited undertreatment. childhood pulmonary tuberculosis; diagnosis; latent class analysis; overtreatment; sensitivity; specificity Abbreviations: CPTB, childhood pulmonary tuberculosis; CrI, credible interval; HIV, human immunodeficiency virus; PTB, pulmonary tuberculosis; TST, tuberculin skin test.Tuberculosis in children is an important global health problem. There are an estimated 0.5 to 1 million new cases each year (1, 2), with childhood pulmonary tuberculosis (CPTB) being the most common form. One of the major challenges in diagnosing CPTB is the lack of sensitive diagnostic tests (3-6). In clinical practice, the diagnosis of CPTB therefore relies on a combination of imperfect tests, which gives rise to unknown degrees of under-or overtreatment (7,8).In recent years, new tests for CPTB have been developed, and their accuracy has been evaluated using mycobacterial culture as a reference standard (4, 9). Although culture is currently considered the best available reference standard, its sensitivity for detecting CPTB is acknowledged to be imperfect (3,4,10). The culture reference standard thus inevitably leads to true CPTB case patients being misclassified as being negative for CPTB. If these misclassifications by the reference standard are ignored, then the assessment of the test accuracy can be biased (11)(12)(13)(14).To address the problem of the lack of an accurate reference standard, multivariable diagnostic algorithms for CPTB have been proposed to combine information from multiple imperfect diagnostic tests (including tests for tuberculosis infection and clinical data) in a sy...

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confidence: 78%

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Schumacher¹,

Smeden²,

Dendukuri³

et al. 2016

American Journal of Epidemiology

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“…Another approach is to treat K as an unknown parameter and to estimate it within the modeling process. While the second approach appears more appealing, there are some issues with regard to prior selection for K and the sensitivity of its posterior distribution (Aitkin, 2001;Jasra et al, 2005). For this study, we adopted the first approach since the number of components is pre-specified.…”

Section: Parameter Estimation Methodsmentioning

confidence: 99%

Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

Park

Lord

Hart

2010

Accident Analysis & Prevention

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“…Constructing proposal distributions by creating an approximation of the target in each dimension using fixed dimensional MCMC (Hastie, 2005 (University of Bristol PhD thesis)) is complicated by the label-switching problem (see Jasra et al (2005) for a discussion). Delayed rejection (Green & Mira, 2001) and tempered transitions (Jennison et al, 2003) often do not provide a general solution to the problems highlighted by this example.…”

Section: Alternative Algorithmsmentioning

confidence: 99%

Population-Based Reversible Jump Markov Chain Monte Carlo

Jasra¹,

Stephens²,

Holmes³

2007

Biometrika

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In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm out performs some competing Markov chain samplers.

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Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling

Cited by 575 publications

References 41 publications

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

Population-Based Reversible Jump Markov Chain Monte Carlo

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