General Methods for Monitoring Convergence of Iterative Simulations

Brooks, Stephen; Gelman, Andrew

doi:10.2307/1390675

Cited by 2,373 publications

(1,753 citation statements)

References 14 publications

Supporting

Mentioning

1,742

Contrasting

Unclassified

Order By: Relevance

“…Based on three chains, the scale reduction factors of Gelman and Rubin [ 32 ] and Brooks and Gelman [ 34 ] were all close to 1 suggesting satisfactory convergence. After 8500 burn-in iterations followed by 10000 iterations, all the parameters in the model passed the stationarity test of Heidelberger and Welch [ 33 ].…”

Section: Resultsmentioning

confidence: 92%

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

Capanu

Orlow

Berwick

et al. 2008

Statistics in Medicine

View full text Add to dashboard Cite

For major genes known to influence the risk of cancer, an important task is to determine the risks conferred by individual variants, so that one can appropriately counsel carriers of these mutations. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little empirical evidence available about each individual mutation. Hierarchical modeling offers a natural strategy to leverage the collective evidence from these rare variants with sparse data. This can be accomplished when there are available higher level covariates that characterize the variants in terms of attributes that could distinguish their association with disease. In this article we explore the use of hierarchical modeling for this purpose using data from a large population-based study of the risks of melanoma conferred by variants in the CDKN2A gene. We employ both a pseudolikelihood approach and a Bayesian approach using Gibbs sampling. The results indicate that relative risk estimates tend to be primarily influenced by the individual case-control frequencies when several cases and/or controls are observed with the variant under study, but that relative risk estimates for variants with very sparse data are more influenced by the higher level covariate values, as one would expect. The analysis offers encouragement that we can draw strength from the aggregating power of hierarchical models to provide guidance to medical geneticists when they offer counseling to patients with rare or even hitherto unobserved variants. However, further research is needed to validate the application of asymptotic methods to such sparse data.

show abstract

Section: Resultsmentioning

confidence: 92%

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

Capanu

Orlow

Berwick

et al. 2008

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…This is par ticularly important because (1) it ensures that the posterior has been 'found' and (2) it indicates when sampling of parameters should begin. A common methodology to check the convergence is by tracking the Gelman-Rubin convergence statistic as mod ified by Brooks and Gelman (1998). A Gelman-Rubin statistic under 1.2 indicates approximate convergence and it is used to assess when convergence occurred.…”

Section: Model Convergencementioning

confidence: 99%

On the nature of over-dispersion in motor vehicle crash prediction models

Mitra

Washington

2007

Accident Analysis & Prevention

206

View full text Add to dashboard Cite

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts-variation over and above that accounted for by the Poisson density. The extra-variation -or dispersion -is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models-tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31-40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions.This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with noninformative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites.

show abstract

“…Medians and 95 % credible intervals (CrIs) were on the basis of 50 000 iterations from two chains running in parallel, following a 5000 iteration ' burn-in ' period. Convergence was assessed through the use of the Brooks-Gelman diagnostic [26].…”

Section: Hcv Prevalence Modelmentioning

confidence: 99%

Spatial mapping of hepatitis C prevalence in recent injecting drug users in contact with services

Harris¹,

Hope

Morongiu³

et al. 2011

Epidemiol. Infect.

View full text Add to dashboard Cite

SUMMARYIn developed countries the majority of hepatitis C virus (HCV) infections occur in injecting drug users (IDUs) with prevalence in IDUs often high, but with wide geographical differences within countries. Estimates of local prevalence are needed for planning services for IDUs, but it is not practical to conduct HCV seroprevalence surveys in all areas. In this study survey data from IDUs attending specialist services were collected in 52/149 sites in England between 2006 and 2008. Spatially correlated random-effects models were used to estimate HCV prevalence for all sites, using auxiliary data to aid prediction. Estimates ranged from 14 % to 82 %, with larger cities, London and the North West having the highest HCV prevalence. The methods used generated robust estimates for each area, with a well-identified spatial pattern that improved predictions. Such models may be of use in other areas of study where surveillance data are sparse.

show abstract

General Methods for Monitoring Convergence of Iterative Simulations

Cited by 2,373 publications

References 14 publications

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

On the nature of over-dispersion in motor vehicle crash prediction models

Spatial mapping of hepatitis C prevalence in recent injecting drug users in contact with services

Contact Info

Product

Resources

About