Archive for state space model

Statistical modeling and computation [apologies]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , on June 11, 2014 by xi'an

In my book review of the recent book by Dirk Kroese and Joshua Chan,  Statistical Modeling and Computation, I mistakenly and persistently typed the name of the second author as Joshua Chen. This typo alas made it to the printed and on-line versions of the subsequent CHANCE 27(2) column. I am thus very much sorry for this mistake of mine and most sincerely apologise to the authors. Indeed, it always annoys me to have my name mistyped (usually as Roberts!) in references.  [If nothing else, this typo signals it is high time for a change of my prescription glasses.]

Statistical modeling and computation [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , on January 22, 2014 by xi'an

Dirk Kroese (from UQ, Brisbane) and Joshua Chan (from ANU, Canberra) just published a book entitled Statistical Modeling and Computation, distributed by Springer-Verlag (I cannot tell which series it is part of from the cover or frontpages…) The book is intended mostly for an undergrad audience (or for graduate students with no probability or statistics background). Given that prerequisite, Statistical Modeling and Computation is fairly standard in that it recalls probability basics, the principles of statistical inference, and classical parametric models. In a third part, the authors cover “advanced models” like generalised linear models, time series and state-space models. The specificity of the book lies in the inclusion of simulation methods, in particular MCMC methods, and illustrations by Matlab code boxes. (Codes that are available on the companion website, along with R translations.) It thus has a lot in common with our Bayesian Essentials with R, meaning that I am not the most appropriate or least unbiased reviewer for this book. Continue reading

particle efficient importance sampling

Posted in Statistics with tags , , , , , , on October 15, 2013 by xi'an

Marcel Scharth and Robert Kohn just arXived a new article entitled “particle efficient importance sampling“. What is—the efficiency—about?! The spectacular diminution in variance—(the authors mention a factor of 6,000 when compared with regular particle filters!—in a stochastic volatility simulation study.

If I got the details right, the improvement stems from a paper by Richard and Zhang (Journal of  Econometrics, 2007). In a state-space/hidden Markov model setting, (non-sequential) importance sampling tries to approximate the smoothing distribution one term at a time, ie p(xt|xt-1,y1:n), but Richard and Zhang (2007) modify the target by looking at

p(yt|xt)p(xt|xt-1(xt-1,y1:n),

where the last term χ(xt-1,y1:n) is the normalising constant of the proposal kernel for the previous (in t-1) target, k(xt-1|xt-2,y1:n). This kernel is actually parameterised as k(xt-1|xt-2,at(y1:n)) and the EIS algorithm optimises those parameters, one term at a time. The current paper expands Richard and Zhang (2007) by using particles to approximate the likelihood contribution and reduce the variance once the “optimal” EIS solution is obtained. (They also reproduce Richard’s and Zhang’s tricks of relying on the same common random numbers.

This approach sounds like a “miracle” to me, in the sense(s) that (a) the “normalising constant” is far from being uniquely defined (and just as far from being constant in the parameter at) and (b) it is unrelated with the target distribution (except for the optimisation step). In the extreme case when the normalising constant is also constant… in at, this step clearly is useless. (This also opens the potential for an optimisation in the choice of χ(xt-1,y1:n)…)

The simulation study starts from a univariate stochastic volatility model relying on two hidden correlated AR(1) models. (There may be a typo in the definition in Section 4.1, i.e. a Φi missing.) In those simulations, EIS brings a significant variance reduction when compared with standard particle filters and particle EIS further improves upon EIS by a factor of 2 to 20 (in the variance). I could not spot in the paper which choice had been made for χ()… which is annoying as I gathered from my reading that it must have a strong impact on the efficiency attached to the name of the method!

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