Archive for Laplace’s approximation

ISBA on INLA [webinar]

Posted in R, Statistics, University life with tags , , , , , , on April 3, 2013 by xi'an

If you have missed the item of information, Håvard Rue is giving an ISBA webinar tomorrow on INLA:

the ISBA Webinar on INLA is scheduled for April 4th, 2013
from 8:30 - 12:30 EDT.

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To join the online meeting (Now from mobile devices using the Cisco WebEx
Meeting App)
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2. Enter the meeting number  730 293 070 and click Join Now
3. Enter your name and email address, the meeting password and
click "Join Now"

A recording of the webinar will be provided shortly after the event.

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Harmonic means, again again

Posted in Books, R, Statistics, University life with tags , , , , , , , , on January 10, 2012 by xi'an

Another arXiv posting I had had no time to comment is Nial Friel’s and Jason Wyse’s “Estimating the model evidence: a review“. This is a review in the spirit of two of our papers, “Importance sampling methods for Bayesian discrimination between embedded models” with Jean-Michel Marin (published in Jim Berger Feitschrift, Frontiers of Statistical Decision Making and Bayesian Analysis: In Honor of James O. Berger, but not mentioned in the review) and “Computational methods for Bayesian model choice” with Darren Wraith (referred to by the review). Indeed, it considers a series of competing computational methods for approximating evidence, aka marginal likelihood:

The paper correctly points out the difficulty with the naïve harmonic mean estimator. (But it does not cover the extension to the finite variance solutions found in”Importance sampling methods for Bayesian discrimination between embedded models” and in “Computational methods for Bayesian model choice“.)  It also misses the whole collection of bridge and umbrella sampling techniques covered in, e.g., Chen, Shao and Ibrahim, 2000 . In their numerical evaluations of the methods, the authors use the Pima Indian diabetes dataset we also used in “Importance sampling methods for Bayesian discrimination between embedded models“. The outcome is that the Laplace approximation does extremely well in this case (due to the fact that the posterior is very close to normal), Chib’s method being a very near second. The harmonic mean estimator does extremely poorly (not a suprise!) and the nested sampling approximation is not as accurate as the other (non-harmonic) methods. If we compare with our 2009 study, importance sampling based on the normal approximation (almost the truth!) did best, followed by our harmonic mean solution based on the same normal approximation. (Chib’s solution was then third, with a standard deviation ten times larger.)

principles of uncertainty

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , on October 14, 2011 by xi'an

Bayes Theorem is a simple consequence of the axioms of probability, and is therefore accepted by all as valid. However, some who challenge the use of personal probability reject certain applications of Bayes Theorem.”  J. Kadane, p.44

Principles of uncertainty by Joseph (“Jay”) Kadane (Carnegie Mellon University, Pittsburgh) is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. Jay Kadane wrote Principles of uncertainty over a period of several years and, more or less in his own words, it represents the legacy he wants to leave for the future. The book starts with a large section on Jay’s definition of a probability model, with rigorous mathematical derivations all the way to Lebesgue measure (or more exactly the McShane-Stieltjes measure). This section contains many side derivations that pertain to mathematical analysis, in order to explain the subtleties of infinite countable and uncountable sets, and the distinction between finitely additive and countably additive (probability) measures. Unsurprisingly, the role of utility is emphasized in this book that keeps stressing the personalistic entry to Bayesian statistics. Principles of uncertainty also contains a formal development on the validity of Markov chain Monte Carlo methods that is superb and missing in most equivalent textbooks. Overall, the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. Continue reading

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