Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm
AbstractA novel class of interacting Markov chain Monte Carlo (MCMC) algorithms, hereby referred to as the Parallel Hierarchical Sampler (PHS), is developed and its mixing properties are assessed. PHS algorithms are modular MCMC samplers designed to produce reliable estimates for multi-modal and heavy-tailed posterior distributions. As such, PHS aims at benefitting statisticians whom, working on a wide spectrum of applications, are more focused on defining and refining models than constructing sophisticated sampling strategies. Convergence of a vanilla PHS algorithm is proved for the case of Metropolis–Hastings within-chain updates. The accuracy of this PHS kernel is compared with that of optimized single-chain and multiple-chain MCMC algorithms for multi-modal mixtures of multivariate Gaussian densities and for ‘banana-shaped’ heavy-tailed multivariate distributions. These examples show that PHS can yield a dramatic improvement in the precision of MCMC estimators over standard samplers. PHS is then applied to two realistically complex Bayesian model uncertainty scenarios. First, PHS is used to select a low number of meaningful predictors for a Gaussian linear regression model in the presence of high collinearity. Second, the posterior probability of survival trees approximated by PHS indicates that the number and size of liver metastases at the time of diagnosis are predictive of substantial differences in the survival distributions of colorectal cancer patients.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 6 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Bayesian covariate selection; Heavy tails; Gaussian mixtures; Multi-modality; Parallel MCMC; Treed survival models;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, 03.
- Jørund G�Semyr, 2003. "On an adaptive version of the Metropolis-Hastings algorithm with independent proposal distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 30(1), pages 159-173.
- Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436.
- Olivier Cappé & Christian P. Robert & Tobias Rydén, 2003. "Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 679-700.
- Jasra, Ajay & Doucet, Arnaud & Stephens, David A. & Holmes, Christopher C., 2008. "Interacting sequential Monte Carlo samplers for trans-dimensional simulation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1765-1791, January.
- Calderhead, Ben & Girolami, Mark, 2009. "Estimating Bayes factors via thermodynamic integration and population MCMC," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4028-4045, October.
- A. Antoniadis & G. Grégoire & G. Nason, 1999. "Density and hazard rate estimation for right-censored data by using wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 63-84.
- Smith, Michael & Kohn, Robert, 1996.
"Nonparametric regression using Bayesian variable selection,"
Journal of Econometrics,
Elsevier, vol. 75(2), pages 317-343, December.
- Smith, M. & Kohn, R., . "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
- Roberts, G. O. & Gilks, W. R., 1994. "Convergence of Adaptive Direction Sampling," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 287-298, May.
- Ajay Jasra & David A. Stephens & Christopher C. Holmes, 2007. "Population-Based Reversible Jump Markov Chain Monte Carlo," Biometrika, Biometrika Trust, vol. 94(4), pages 787-807.
- Cappé, Olivier & Robert, Christian P. & Ryden, Tobias, 2003. "Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers," Economics Papers from University Paris Dauphine 123456789/6040, Paris Dauphine University.
- Hu, Bo & Tsui, Kam-Wah, 2010. "Distributed evolutionary Monte Carlo for Bayesian computing," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 688-697, March.
- Gray, J. Brian & Fan, Guangzhe, 2008. "Classification tree analysis using TARGET," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1362-1372, January.
- Craiu, Radu V. & Rosenthal, Jeffrey & Yang, Chao, 2009. "Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1454-1466.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.