# MCMC

### Example 8.17: Logistic regression via MCMC

December 6, 2010 |

In examples 8.15 and 8.16 we considered Firth logistic regression and exact logistic regression as ways around the problem of separation, often encountered in logistic regression. (Re-cap: Separation happens when all the observations in a category sha...
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### Random variable generation (Pt 2 of 3)

December 2, 2010 |

Acceptance-rejection methods This post is based on chapter 1.4 of Advanced Markov Chain Monte Carlo. Another method of generating random variates from distributions is to use acceptance-rejection methods. Basically to generate a random number from , we generate a RN from an envelope distribution , where .  The acceptance-rejection algorithm is as follows: Repeat ... [Read more...]

### Slices and crumbs [arXiv:1011.4722]

November 29, 2010 |

An interesting note was arXived a few days ago by Madeleine Thompson and Radford Neal. Beside the nice touch of mixing crumbs and slices, the neat idea is to have multiple-try proposals for simulating within a slice and to decrease the dimension of the simulation space at each try. This ... [Read more...]

### Computing evidence

November 28, 2010 |

The book Random effects and latent variable model selection, edited by David Dunson in 2008 as a Springer Lecture Note. contains several chapters dealing with evidence approximation in mixed effect models. (Incidentally, I would be interested in the story behind the  Lecture Note as I found no explanation in the backcover ... [Read more...]

### Advanced Markov Chain Monte Carlo Methods (AMCMC)

November 27, 2010 |

I’ve just received my copy of Advanced Markov Chain Monte Carlo Methods, by Liang, Liu, & Carroll. Although my PhD didn’t really involve any Bayesian methodology (and my undergrad was devoid of any Bayesian influence), I’ve found that the sort of problems I’m now tackling in systems ... [Read more...]

### Particle learning [rejoinder]

November 9, 2010 |

Following the posting on arXiv of the Statistical Science paper of Carvalho et al., and the publication by the same authors in Bayesian Analysis of Particle Learning for general mixtures I noticed on Hedibert Lopes’ website his rejoinder to the discussion of his Valencia 9 paper has been posted. Since the ... [Read more...]

### Monte Carlo Statistical Methods third edition

September 23, 2010 |

Last week, George Casella and I worked around the clock on starting the third edition of Monte Carlo Statistical Methods by detailing the changes to make and designing the new table of contents. The new edition will not see a revolution in the presentation of the material but rather a ...
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### News on MCMSki III

September 14, 2010 |

Here is a message sent by the organisers of MCMSki III in Utah next early January. When registering, make sure to tick the free registration for Adap’skiii as well! The fourth joint international meeting of the IMS (Institute of Mathematical Statistics) and ISBA (International Society for Bayesian Analysis), nicknamed “... [Read more...]

### Hyper-g priors

August 30, 2010 |

Earlier this month, Daniel Sabanés Bové and Leo Held posted a paper about g-priors on arXiv. While I glanced at it for a few minutes, I did not have the chance to get a proper look at it till last Sunday. The g-prior was first introduced by the late ... [Read more...]

### Julian Besag 1945-2010

August 7, 2010 |

I have just learned that Julian Besag passed away last morning in Bristol after being admitted to the hospital two weeks ago. He was a leading figure of our field, a fiercely independent thinker, a brilliant statistician, and undoubtedly the clearest pretendent to having fathered MCMC. His influence on the ... [Read more...]

### Recent arXiv postings

August 4, 2010 |

With too little time, too many things to do on my plate, here are some recent arXiv postings I won’t have time to comment: Adaptive Monte Carlo on multivariate binary sampling spaces. (arXiv:1008.0055v1) Mixture Decomposition of Distributions using a Decomposition of the Sample Space. (arXiv:1008.0204v1) Bayesian Model ... [Read more...]

### Vanilla Rao-Blackwellisation [re]revised

May 31, 2010 |

Although the revision is quite minor, it took us two months to complete from the time I received the news in the Atlanta airport lounge… The vanilla Rao-Blackwellisation paper with Randal Douc has thus been resubmitted to the Annals of Statistics. And rearXived. The only significant change is the inclusion ... [Read more...]

### Computational Statistics

May 9, 2010 |

Do not resort to Monte Carlo methods unnecessarily. When I received this 2009 Springer-Verlag book, Computational Statistics, by James Gentle a while ago, I briefly took a look at the table of contents and decided to have a better look later… Now that I have gone through the whole book, I ...
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### Bayes vs. SAS

May 6, 2010 |

Glancing perchance at the back of my Amstat News, I was intrigued by the SAS advertisement Bayesian Methods Specify Bayesian analysis for ANOVA, logistic regression, Poisson regression, accelerated failure time models and Cox regression through the GENMOD, LIFEREG and PHREG procedures. Analyze a wider variety of models with the MCMC ...
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### The Bernoulli factory

April 22, 2010 |

A few months ago, Latuszyński, Kosmidis, Papaspiliopoulos and Roberts arXived a paper I should have noticed earlier as its topic is very much related to our paper with Randal Douc on the vanilla Rao-Blackwellisation scheme. It is motivated by the Bernoulli factory problem, which aims at (unbiasedly) estimating f(... [Read more...]

### Vanilla Rao-Blackwellisation for revision

March 17, 2010 |

The vanilla Rao-Blackwellisation paper with Randal Douc that had been resubmitted to the Annals of Statistics is now back for a revision, with quite encouraging comments: The paper has been reviewed by two referees both of whom comment on the clear exposition and the novelty of the results. Both referees ... [Read more...]

### t-walk on the banana side

March 14, 2010 |

Following my remarks on the t-walk algorithm in the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that acts like a general purpose MCMC algorithm, Darren Wraith tested it on the generic (10 dimension) banana target we used in the cosmology paper. ... [Read more...]

### t-walk on the wild side

March 11, 2010 |

When I read in the abstract of the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. I am slightly bemused. The proposal of the ... [Read more...]

### Example 7.24: Sampling from a pathological distribution

March 1, 2010 |

Evans and Rosenthal consider ways to sample from a distribution with density given by:f(y) = c e^(-y^4)(1+|y|)^3where c is a normalizing constant and y is defined on the whole real line.Use of the probability integral transform (section 1.10.8) is not feasible in this setting, given the ...
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### Typos in Chapter 8

January 16, 2010 |

Phew!, we are now done with the solution manual in the sense that we have compiled solutions for all odd-numberedd exercises (but one!) and solved a fair number of even-numbered exercises. As it stands, the manual is 120 pages long and I am exhausted by the run to produce it over ...
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