Archive for STAN

more air for MCMC

Posted in Books, R, Statistics with tags , , , , , , , , , , , , , , on May 30, 2021 by xi'an

Aki Vehtari, Andrew Gelman, Dan Simpson, Bob Carpenter, and Paul-Christian Bürkner have just published a Bayesian Analysis paper about using an improved R factor for MCMC convergence assessment. From the early days of MCMC, convergence assessment has been a recurring (and recurrent!) question in the community. First leading to a flurry of proposals, [which Kerrie, Chantal, and myself reviewwwed in the Valencia 1998 proceedings], and then slowly disintegrating under the onslaughts of reality—i.e. that none could not be 100% foolproof in full generality—…. This included the (possibly now forgotten) single-versus-multiple-chains debate between Charlie Geyer [for single] and Andrew Gelman and Don Rubin [for multiple]. The later introduced an analysis-of-variance R factor, which remains quite popular up to this day, in part for being part of most MCMC software, like BUGS. That this R may fail to identify convergence issues, even in the more recent split version, does not come as a major surprise, since any situation with a long-term influence of the starting distribution may well fail to identify missing (significant) parts of the posterior support. (It is thus somewhat disconcerting to me to see that the main recommendation is to move the bound on R from 1.1 to 1.01, reminding me to some extent of a recent proposal to move the null rejection boundary from 0.05 to 0.005…) Similarly, the ESS may prove a poor signal for convergence or lack thereof, especially because the approximation of the asymptotic variance relies on stationarity assumptions. While multiplying the monitoring tools (as in CODA) helps with identifying convergence issues, looking at a single convergence indicator is somewhat like looking only at a frequentist estimator! (And with greater automation comes greater responsibility—in keeping a critical perspective.)

Looking for a broader perspective, I thus wonder at what we would instead need to assess the lack of convergence of an MCMC chain without much massaging of the said chain. An evaluation of the (Kullback, Wasserstein, or else) distance between the distribution of the chain at iteration n or across iterations, and the true target? A percentage of the mass of the posterior visited so far, which relates to estimating the normalising constant, with a relatively vast array of solutions made available in the recent years? I remain perplexed and frustrated by the fact that, 30 years later, the computed values of the visited likelihoods are not better exploited. Through for instance machine-learning approximations of the target. that could themselves be utilised for approximating the normalising constant and potential divergences from other approximations.

coupling, donkeys, coins & fish meet in Paris

Posted in Statistics with tags , , , , , , , , , , , , , , , , , , , , , , on March 22, 2021 by xi'an

Hastings 50 years later

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , on January 9, 2020 by xi'an

What is the exact impact of the Metropolis-Hastings algorithm on the field of Bayesian statistics? and what are the new tools of the trade? What I personally find the most relevant and attractive element in a review on the topic is the current role of this algorithm, rather than its past (his)story, since many such reviews have already appeared and will likely continue to appear. What matters most imho is how much the Metropolis-Hastings algorithm signifies for the community at large, especially beyond academia. Is the availability or unavailability of software like BUGS or Stan a help or an hindrance? Was Hastings’ paper the start of the era of approximate inference or the end of exact inference? Are the algorithm intrinsic features like Markovianity a fundamental cause for an eventual extinction because of the ensuing time constraint and the lack of practical guarantees of convergence and the illusion of a fully automated version? Or are emerging solutions like unbiased MCMC and asynchronous algorithms a beacon of hope?

In their Biometrika paper, Dunson and Johndrow (2019) recently wrote a celebration of Hastings’ 1970 paper in Biometrika, where they cover adaptive Metropolis (Haario et al., 1999; Roberts and Rosenthal, 2005), the importance of gradient based versions toward universal algorithms (Roberts and Tweedie, 1995; Neal, 2003), discussing the advantages of HMC over Langevin versions. They also recall the significant step represented by Peter Green’s (1995) reversible jump algorithm for multimodal and multidimensional targets, as well as tempering (Miasojedow et al., 2013; Woodard et al., 2009). They further cover intractable likelihood cases within MCMC (rather than ABC), with the use of auxiliary variables (Friel and Pettitt, 2008; Møller et al., 2006) and pseudo-marginal MCMC (Andrieu and Roberts, 2009; Andrieu and Vihola, 2016). They naturally insist upon the need to handle huge datasets, high-dimension parameter spaces, and other scalability issues, with links to unadjusted Langevin schemes (Bardenet et al., 2014; Durmus and Moulines, 2017; Welling and Teh, 2011). Similarly, Dunson and Johndrow (2019) discuss recent developments towards parallel MCMC and non-reversible schemes such as PDMP as highly promising, with a concluding section on the challenges of automatising and robustifying much further the said procedures, if only to reach a wider range of applications. The paper is well-written and contains a wealth of directions and reflections, including those in my above introduction. Here are some mostly disconnected directions I would have liked to see covered or more covered

  1. convergence assessment today, e.g. the comparison of various approximation schemes
  2. Rao-Blackwellisation and other post-processing improvements
  3. other approximate inference tools than the pseudo-marginal MCMC
  4. importance of the parameterisation of the problem for convergence
  5. dimension issues and connection with quasi-Monte Carlo
  6. constrained spaces of measure zero, as for instance matrix distributions imposing zeros outside a diagonal band
  7. given the rise of the machine(-learners), are exploratory and intrinsically slow algorithms like MCMC doomed or can both fields feed one another? The section on optimisation could be expanded in that direction
  8. the wasteful nature of the random walk feature of MCMC algorithms, as opposed to non-reversible kernels like HMC and other PDMPs, missing from the gradient based methods section (and can we once again learn from physicists?)
  9. finer convergence issues and hence inference difficulties with complex MCMC algorithms like Gibbs samplers with incompatible conditionals
  10. use of the Hastings ratio in other algorithms like ABC or EP (in link with the section on generalised Bayes)
  11. adapting Metropolis-Hastings methods for emerging computing tools like GPUs and quantum computers

or possibly less covered, namely data augmentation put forward when it is a special case of auxiliary variables as in slice sampling and in earlier physics literature. For instance, both probit and logistic regressions do not truly require data augmentation and are more toy examples than really challenging applications. The approach of Carlin & Chib (1995) is another illustration, which has met with recent interest, despite requiring heavy calibration (just like RJMCMC). As well as a a somewhat awkward opposition between Gibbs and Hastings, in that I am not convinced that Gibbs does not remain ultimately necessary to handle high dimension problems, in the sense that the alternative solutions like Langevin, HMC, or PDMP, or…, are relying on Euclidean assumptions for the entire vector, while a direct product of Euclidean structures may prove more adequate.

don’t be late for BayesComp’2020

Posted in Statistics with tags , , , , , , , , , , , , , on October 4, 2019 by xi'an

An important reminder that October 14 is the deadline for regular registration to BayesComp 2020 as late fees will apply afterwards!!! The conference looks attractive enough to agree to pay more, but still…

deadlines for BayesComp’2020

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on August 17, 2019 by xi'an

While I have forgotten to send a reminder that August 15 was the first deadline of BayesComp 2020 for the early registrations, here are further deadlines and dates

  1. BayesComp 2020 occurs on January 7-10 2020 in Gainesville, Florida, USA
  2. Registration is open with regular rates till October 14, 2019
  3. Deadline for submission of poster proposals is December 15, 2019
  4. Deadline for travel support applications is September 20, 2019
  5. There are four free tutorials on January 7, 2020, related with Stan, NIMBLE, SAS, and AutoStat