## beyond objectivity, subjectivity, and other ‘bjectivities

Posted in Statistics with tags , , , , , , , , , , , , , on April 12, 2017 by xi'an

Here is my discussion of Gelman and Hennig at the Royal Statistical Society, which I am about to deliver!

## objective and subjective RSS Read Paper next week

Posted in Books, pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , on April 5, 2017 by xi'an

Andrew Gelman and Christian Hennig will give a Read Paper presentation next Wednesday, April 12, 5pm, at the Royal Statistical Society, London, on their paper “Beyond subjective and objective in statistics“. Which I hope to attend and else to write a discussion. Since the discussion (to published in Series A) is open to everyone, I strongly encourage ‘Og’s readers to take a look at the paper and the “radical” views therein to hopefully contribute to this discussion. Either as a written discussion or as comments on this very post.

## latest issue of Significance

Posted in Statistics with tags , , , , on March 20, 2017 by xi'an

The latest issue of Significance is bursting with exciting articles and it is a shame I do not receive it any longer (not that I stopped subscribing to the RSS or the ASA, but it simply does not get delivered to my address!). For instance, a tribune by Tom Nicolls (from whom I borrowed this issue for the weekend!) on his recent assessment of false positive in brain imaging [I covered in a blog entry a few months ago] when checking the cluster inference and the returned p-values. And the British equivalent of Gelman et al. book cover on the seasonality of births in England and Wales, albeit witout a processing of the raw data and without mention being made of the Gelmanesque analysis: the only major gap in the frequency is around Christmas and New Year, while there is a big jump around September (also there in the New York data).

A neat graph on the visits to four feeders by five species of birds. A strange figure in Perils of Perception that [which?!] French people believe 31% of the population is Muslim and that they are lacking behind many other countries in terms of statistical literacy. And a rather shallow call to Popper to running decision-making in business statistics.

## a somewhat hasty announcement

Posted in Books, Statistics, University life with tags , , , , , on March 13, 2017 by xi'an

When I received the above RSS newsletter on Thursday, I was a bit shocked as I had not planned to make the existence of the Series B’log known to the entire Society. Even though it was already visible and with unrestricted access. The reason being that experimenting with authors and editors was easier without additional email and password exchanges…

Anyway, now that we have jumped that Rubicon, I would more than welcome comments and suggestions to make the blog structure more efficient and readable. I am still confused as to how the front page should look like, because I want to keep the hierarchy of the Journal, i.e., volume/issue/paper, reflected in this structure, rather than piling up comments and authors’ summaries in an haphazard manner. I have started to tag entries by the volume/issue tag, in order to keep some of this hierarchy respected but I would like to also provide all entries related to a given paper without getting into much extra-work. Given that I already have to process most entries through latex2wp in the best scenario.

## a new Editor for Series B

Posted in Statistics with tags , , , on January 16, 2017 by xi'an

As every odd year, the Royal Statistical Society is seeking a new joint editor for Series B! After four years of dedication to the (The!) journal, Piotr Fryzlewicz is indeed going to retire from this duty by the end of 2017. Many thanks to Piotr for his unfailing involvement in Series B and the preservation of its uncompromising selection of papers! The call thus open for candidates for the next round of editorship, from 2018 to 2021, with a deadline of 31 January, 2017. Interested candidates should contact Martin Owen, at the Society’s address or by email at rss.org.uk with journal as recipient (local-part). The new editor will work with the current joint editor, David Dunson, whose term runs till December 2019. (I am also looking forward working with Piotr’s successor in developing the Series B blog, Series’ Blog!)

## a Bayesian criterion for singular models [discussion]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , on October 10, 2016 by xi'an

[Here is the discussion Judith Rousseau and I wrote about the paper by Mathias Drton and Martyn Plummer, a Bayesian criterion for singular models, which was discussed last week at the Royal Statistical Society. There is still time to send a written discussion! Note: This post was written using the latex2wp converter.]

It is a well-known fact that the BIC approximation of the marginal likelihood in a given irregular model ${\mathcal M_k}$ fails or may fail. The BIC approximation has the form

$\displaystyle BIC_k = \log p(\mathbf Y_n| \hat \pi_k, \mathcal M_k) - d_k \log n /2$

where ${d_k }$ corresponds on the number of parameters to be estimated in model ${\mathcal M_k}$. In irregular models the dimension ${d_k}$ typically does not provide a good measure of complexity for model ${\mathcal M_k}$, at least in the sense that it does not lead to an approximation of

$\displaystyle \log m(\mathbf Y_n |\mathcal M_k) = \log \left( \int_{\mathcal M_k} p(\mathbf Y_n| \pi_k, \mathcal M_k) dP(\pi_k|k )\right) \,.$

A way to understand the behaviour of ${\log m(\mathbf Y_n |\mathcal M_k) }$ is through the effective dimension

$\displaystyle \tilde d_k = -\lim_n \frac{ \log P( \{ KL(p(\mathbf Y_n| \pi_0, \mathcal M_k) , p(\mathbf Y_n| \pi_k, \mathcal M_k) ) \leq 1/n | k ) }{ \log n}$

when it exists, see for instance the discussions in Chambaz and Rousseau (2008) and Rousseau (2007). Watanabe (2009} provided a more precise formula, which is the starting point of the approach of Drton and Plummer:

$\displaystyle \log m(\mathbf Y_n |\mathcal M_k) = \log p(\mathbf Y_n| \hat \pi_k, \mathcal M_k) - \lambda_k(\pi_0) \log n + [m_k(\pi_0) - 1] \log \log n + O_p(1)$

where ${\pi_0}$ is the true parameter. The authors propose a clever algorithm to approximate of the marginal likelihood. Given the popularity of the BIC criterion for model choice, obtaining a relevant penalized likelihood when the models are singular is an important issue and we congratulate the authors for it. Indeed a major advantage of the BIC formula is that it is an off-the-shelf crierion which is implemented in many softwares, thus can be used easily by non statisticians. In the context of singular models, a more refined approach needs to be considered and although the algorithm proposed by the authors remains quite simple, it requires that the functions ${ \lambda_k(\pi)}$ and ${m_k(\pi)}$ need be known in advance, which so far limitates the number of problems that can be thus processed. In this regard their equation (3.2) is both puzzling and attractive. Attractive because it invokes nonparametric principles to estimate the underlying distribution; puzzling because why should we engage into deriving an approximation like (3.1) and call for Bayesian principles when (3.1) is at best an approximation. In this case why not just use a true marginal likelihood?

1. Why do we want to use a BIC type formula?

The BIC formula can be viewed from a purely frequentist perspective, as an example of penalised likelihood. The difficulty then stands into choosing the penalty and a common view on these approaches is to choose the smallest possible penalty that still leads to consistency of the model choice procedure, since it then enjoys better separation rates. In this case a ${\log \log n}$ penalty is sufficient, as proved in Gassiat et al. (2013). Now whether or not this is a desirable property is entirely debatable, and one might advocate that for a given sample size, if the data fits the smallest model (almost) equally well, then this model should be chosen. But unless one is specifying what equally well means, it does not add much to the debate. This also explains the popularity of the BIC formula (in regular models), since it approximates the marginal likelihood and thus benefits from the Bayesian justification of the measure of fit of a model for a given data set, often qualified of being a Bayesian Ockham’s razor. But then why should we not compute instead the marginal likelihood? Typical answers to this question that are in favour of BIC-type formula include: (1) BIC is supposingly easier to compute and (2) BIC does not call for a specification of the prior on the parameters within each model. Given that the latter is a difficult task and that the prior can be highly influential in non-regular models, this may sound like a good argument. However, it is only apparently so, since the only justification of BIC is purely asymptotic, namely, in such a regime the difficulties linked to the choice of the prior disappear. This is even more the case for the sBIC criterion, since it is only valid if the parameter space is compact. Then the impact of the prior becomes less of an issue as non informative priors can typically be used. With all due respect, the solution proposed by the authors, namely to use the posterior mean or the posterior mode to allow for non compact parameter spaces, does not seem to make sense in this regard since they depend on the prior. The same comments apply to the author’s discussion on Prior’s matter for sBIC. Indeed variations of the sBIC could be obtained by penalizing for bigger models via the prior on the weights, for instance as in Mengersen and Rousseau (2011) or by, considering repulsive priors as in Petralia et al. (20120, but then it becomes more meaningful to (again) directly compute the marginal likelihood. Remains (as an argument in its favour) the relative computational ease of use of sBIC, when compared with the marginal likelihood. This simplification is however achieved at the expense of requiring a deeper knowledge on the behaviour of the models and it therefore looses the off-the-shelf appeal of the BIC formula and the range of applications of the method, at least so far. Although the dependence of the approximation of ${\log m(\mathbf Y_n |\mathcal M_k)}$ on ${\mathcal M_j }$, \$latex {j \leq k} is strange, this does not seem crucial, since marginal likelihoods in themselves bring little information and they are only meaningful when compared to other marginal likelihoods. It becomes much more of an issue in the context of a large number of models.

2. Should we care so much about penalized or marginal likelihoods ?

Marginal or penalized likelihoods are exploratory tools in a statistical analysis, as one is trying to define a reasonable model to fit the data. An unpleasant feature of these tools is that they provide numbers which in themselves do not have much meaning and can only be used in comparison with others and without any notion of uncertainty attached to them. A somewhat richer approach of exploratory analysis is to interrogate the posterior distributions by either varying the priors or by varying the loss functions. The former has been proposed in van Havre et l. (2016) in mixture models using the prior tempering algorithm. The latter has been used for instance by Yau and Holmes (2013) for segmentation based on Hidden Markov models. Introducing a decision-analytic perspective in the construction of information criteria sounds to us like a reasonable requirement, especially when accounting for the current surge in studies of such aspects.

[Posted as arXiv:1610.02503]

## [Royal] Series B’log

Posted in Books, Statistics, University life, Wines with tags , , , , , , on September 12, 2016 by xi'an

[Thanks to Ingmar for suggesting the additional Royal!]

Last week, I got an email from Piotr Fryzlewicz on behalf of the Publication Committee of the Royal Statistical Society enquiring about my interest in becoming a blog associate editor for Series B! Although it does not come exactly as a surprise, as I had previously heard about this interest in creating a dedicated blog, this is great news as I think a lively blog can only enhance the visibility and impact of papers published in Series B and hence increase the influence of Series B. Being quite excited by this on-line and interactive extension to the journal, I have accepted the proposal and we are now working on designing the new blog (Series B’log!) to get it on track as quickly as possible.

Suggestions towards this experiment are most welcome! I am thinking of involving authors to write blog summaries of their paper, AEs and reviewers to voice their expert opinions about the paper, anonymously or not, and of course anyone interested in commenting the paper. The idea is to turn (almost) all papers into on-line Read Papers, with hopefully the backup of authors through their interactions with the commentators. I certainly do not intend to launch discussions on each and every paper, betting on the AEs or referees to share their impressions. And if a paper ends up being un-discussed, this may prove enough of an incentive for some. (Someone asked me if we intended to discuss rejected papers as well. This is an interesting concept, but not to be considered at the moment!)