Nonparametric Convergence Assessment for MCMC Model Selection
By Steve P. Brooks, Paolo Giudici, Anne Philippe. 2003
112 citations recorded by the source corpus.
This article considers the problem of assessing the performance of MCMC model selection algorithms using a variety of nonparametric techniques. We consider a wide range of model selection problems to which MCMC model selection may be applied and propose several distance measures that can be used to quantify the similarity between multiple replications. These measures may be used to assess convergence by examining how “close” these replications of the chain are, since if all chains are at stationarity, then this distance should be small. Finally, we describe an alternative approach based upon the estimation of the convergence rate of the sub-Markov chain represented by the model indicators and finish by illustrating our approaches with several practical examples.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Galin L. Jones
- Andrew Gelman
- Cynthia Rudin
- Xiao-Li Meng
- Gareth O. Roberts
- Benjamin Letham
- Steve P. Brooks
- Malcolm Sambridge
In Statistics and Probability
- Xiao-Li Meng
- Galin L. Jones
- Andrew Gelman
- Steve P. Brooks
- Gareth O. Roberts
- Cynthia Rudin
- Benjamin Letham
- Malcolm Sambridge
Citations in the corpus
- Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions (2003, methodology): “These algorithms aremost commonly applied to (Bayesian)model determination problems (Dellaportas and Forster, 1999; Richardson andGreen, 1997; Fan and Brooks, 2000) though other applications exist (e.g. Møller (1999) and Brooks et al. (2003)).”
- Building Interpretable Classifiers with Rules using Bayesian Analysis (2012, methodology): “[6] use Pearson’s chi-squared test to compute a p-value.”
- Handbook of Markov Chain Monte Carlo: Hardcover: 619 pages Publisher: Chapman and Hall/CRC Press (first edition, May 2011) Language: English ISBN-10: 1420079417 (2012, methodology): “Brooks et al. (2003c), Ehlers and Brooks (2003), and Vermaak et al. (2004) each detail descriptions on the use of reversible jump samplers for this class of problems.”
- Seismic tomography with the reversible jump algorithm (2009, background): “Design of suitable proposal distributions that adapt to the shape of the posterior distribution is a central issue in the development of transdimensional MCMC algorithms and the subject of much research (Stephens 2000; Brooks et al. 2003; Green 2003; Al-Awadhi et al. 2004).”