**R**ecently, I have been contacted by a mainstream statistics journal to write a review of Rao-Blackwellisation techniques in computational statistics, in connection with an issue celebrating C.R. Rao’s 100th birthday. As many many techniques can be interpreted as weak forms of Rao-Blackwellisation, as e.g. all auxiliary variable approaches, I am clearly facing an abundance of riches and would thus welcome suggestions from Og’s readers on the major advances in Monte Carlo methods that can be connected with the Rao-Blackwell-Kolmogorov theorem. (On the personal and anecdotal side, I only met C.R. Rao once, in 1988, when he came for a seminar at Purdue University where I was spending the year.)

## Archive for review

## Rao-Blackwellisation, a review in the making

Posted in Statistics with tags Andrei Kolmogorov, birthday, C.R. Rao, computational statistics, David Blackwell, Monte Carlo methods, Purdue University, Rao-Blackwell theorem, Rao-Blackwellisation, review, survey on March 17, 2020 by xi'an## open reviews

Posted in Statistics with tags brutalism, cross validated, ICLR, Peer Community, proceedings, refereeing, review on September 13, 2019 by xi'an**W**hen looking at a question on X validated, on the expected Metropolis-Hastings ratio being one (not all the time!), I was somewhat bemused at the OP linking to an anonymised paper under review for ICLR, as I thought this was breaching standard confidentiality rules for reviews. Digging a wee bit deeper, I realised this was a paper from the previous ICLR conference, already published both on arXiv and in the 2018 conference proceedings, and that ICLR was actually resorting to an open review policy where both papers and reviews were available and even better where anyone could comment on the paper while it was under review. And after. Which I think is a great idea, the worst possible situation being a poor paper remaining un-discussed. While I am not a big fan of the brutalist approach of many machine-learning conferences, where the restrictive format of both submissions and reviews is essentially preventing in-depth reviews, this feature should be added to statistics journal webpages (until PCIs become the norm).

## ABC intro for Astrophysics

Posted in Books, Kids, Mountains, R, Running, Statistics, University life with tags ABC, Approximate Bayesian computation, Autrans, Bayesian foundations, Bayesian methodology, Book, computational astrophysics, review, Statistics for Astrophysics, summer course, survey, Vercors on October 15, 2018 by xi'an**T**oday I received in the mail a copy of the short book published by edp sciences after the courses we gave last year at the astrophysics summer school, in Autrans. Which contains a quick introduction to ABC extracted from my notes (which I still hope to turn into a book!). As well as a longer coverage of Bayesian foundations and computations by David Stenning and David van Dyk.

## accelerating MCMC

Posted in Statistics with tags acceleration of MCMC algorithms, coupling, Hamiltonian Monte Carlo, India, MCMC, Monte Carlo Statistical Methods, motorbike, NUTS, Rajasthan, review, survey, tempering, WIREs on May 29, 2017 by xi'an**I** have recently [well, not so recently!] been asked to write a review paper on ways of accelerating MCMC algorithms for the [review] journal WIREs Computational Statistics and would welcome all suggestions towards the goal of accelerating MCMC algorithms. Besides [and including more on]

- coupling strategies using different kernels and switching between them;
- tempering strategies using flatter or lower dimensional targets as intermediary steps, e.g., à la Neal;
- sequential Monte Carlo with particle systems targeting again flatter or lower dimensional targets and adapting proposals to this effect;
- Hamiltonian MCMC, again with connections to Radford (and more generally ways of avoiding rejections);
- adaptive MCMC, obviously;
- Rao-Blackwellisation, just as obviously (in the sense that increasing the precision in the resulting estimates means less simulations).

## estimation versus testing [again!]

Posted in Books, Statistics, University life with tags Bayes factors, Bayesian inference, Harold Jeffreys, hypothesis testing, parameter estimation, point null hypotheses, psychology, refereeing, review, spike-and-slab prior, unification on March 30, 2017 by xi'an**T**he following text is a review I wrote of the paper “Parameter estimation and Bayes factors”, written by J. Rouder, J. Haff, and J. Vandekerckhove. (As the journal to which it is submitted gave me the option to sign my review.)

The opposition between estimation and testing as a matter of prior modelling rather than inferential goals is quite unusual in the Bayesian literature. In particular, if one follows Bayesian decision theory as in Berger (1985) there is no such opposition, but rather the use of different loss functions for different inference purposes, while the Bayesian model remains single and unitarian.

Following Jeffreys (1939), it sounds more congenial to the Bayesian spirit to return the posterior probability of an hypothesis * H⁰* as an answer to the question whether this hypothesis holds or does not hold. This however proves impossible when the “null” hypothesis

*has prior mass equal to zero (or is not measurable under the prior). In such a case the mathematical answer is a probability of zero, which may not satisfy the experimenter who asked the question. More fundamentally, the said prior proves inadequate to answer the question and hence to incorporate the information contained in this very question. This is how Jeffreys (1939) justifies the move from the original (and deficient) prior to one that puts some weight on the null (hypothesis) space. It is often argued that the move is unnatural and that the null space does not make sense, but this only applies when believing very strongly in the model itself. When considering the issue from a modelling perspective, accepting the null*

**H⁰***means using a new model to represent the model and hence testing becomes a model choice problem, namely whether or not one should use a complex or simplified model to represent the generation of the data. This is somehow the “unification” advanced in the current paper, albeit it does appear originally in Jeffreys (1939) [and then numerous others] rather than the relatively recent Mitchell & Beauchamp (1988). Who may have launched the spike & slab denomination.*

**H⁰**I have trouble with the analogy drawn in the paper between the spike & slab estimate and the Stein effect. While the posterior mean derived from the spike & slab posterior is indeed a quantity drawn towards zero by the Dirac mass at zero, it is rarely the point in using a spike & slab prior, since this point estimate does not lead to a conclusion about the hypothesis: for one thing it is never exactly zero (if zero corresponds to the null). For another thing, the construction of the spike & slab prior is both artificial and dependent on the weights given to the spike and to the slab, respectively, to borrow expressions from the paper. This approach thus leads to model averaging rather than hypothesis testing or model choice and therefore fails to answer the (possibly absurd) question as to which model to choose. Or refuse to choose. But there are cases when a decision must be made, like continuing a clinical trial or putting a new product on the market. Or not.

In conclusion, the paper surprisingly bypasses the decision-making aspect of testing and hence ends up with a inconclusive setting, staying midstream between Bayes factors and credible intervals. And failing to provide a tool for decision making. The paper also fails to acknowledge the strong dependence of the Bayes factor on the tail behaviour of the prior(s), which cannot be [completely] corrected by a finite sample, hence its relativity and the unreasonableness of a fixed scale like Jeffreys’ (1939).