**I**n 2018, Panayiota Touloupou, research fellow at Warwick, and her co-authors published a paper in Bayesian analysis that somehow escaped my radar, despite standing in my first circle of topics of interest! They construct an importance sampling approach to the approximation of the marginal likelihood, the importance function being approximated from a preliminary MCMC run, and consider the special case when the sampling density (i.e., the likelihood) can be represented as the marginal of a joint density. While this demarginalisation perspective is rather usual, the central point they make is that it is more efficient to estimate the sampling density based on the auxiliary or latent variables than to consider the joint posterior distribution of parameter and latent in the importance sampler. This induces a considerable reduction in dimension and hence explains (in part) why the approach should prove more efficient. Even though the approximation itself is costly, at about 5 seconds per marginal likelihood. But a nice feature of the paper is to include the above graph that includes both computing time and variability for different methods (the blue range corresponding to the marginal importance solution, the red range to RJMCMC and the green range to Chib’s estimate). Note that bridge sampling does not appear on the picture but returns a variability that is similar to the proposed methodology.

## Archive for University of Warwick

## marginal likelihood with large amounts of missing data

Posted in Books, pictures, Statistics with tags Bayesian Analysis, Chib's approximation, evidence, harmonic mean estimator, importance sampling, marginal likelihood, normalising constant, reversible jump, University of Warwick on October 20, 2020 by xi'an## David Frazier’s talk on One World ABC seminar tomorrow [watch for the time!]

Posted in pictures, Statistics, Travel, University life with tags ABC, Australia, Bayesian robustness, daylight saving time, Melbourne, Monash University, One World ABC Seminar, University of Warwick, Victoria, webinar on October 14, 2020 by xi'an**M**y friend and coauthor from Melbourne is giving the One World ABC seminar tomorrow. He will be talking at 10:30 UK time, 11:30 Brussels time, and 20:30 Melbourne time! On Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach. Be on time!

## MCMC, variational inference, invertible flows… bridging the gap?

Posted in Books, Mountains, Running, Statistics, Travel, University life with tags acronym, alpine climbing, École Polytechnique, biking, Eric Moulines, flat tyre, Hamiltonian Monte Carlo, HMC, invertible flows, MCMC, Pic du Midi d'Ossau, prairie, Pyrennées, teaching, University of Warwick, variational autoencoders, variational inference, webinar on October 2, 2020 by xi'an**T**wo weeks ago, my friend [see here when climbing Pic du Midi d’Ossau in 2005!] and coauthor Éric Moulines gave a very interesting on-line talk entitled *MCMC, Variational Inference, Invertible Flows… Bridging the gap?,* which was merging MCMC, variational autoencoders, and variational inference. I paid close attention as I plan to teach an advanced course on acronyms next semester in Warwick. (By acronyms, I mean ABC+GAN+VAE!)

The notion in this work is that variational autoencoders are based on over-simple mean-field variational distributions, that usually produce a poor approximation of the target distribution. Éric and his coauthors propose to introduce a Metropolis step in the VAE. This leads to a more general notion of Markov transitions and a global balance condition. Hamiltonian Monte Carlo can be used as well and it improves the latent distribution approximation, namely the encoder, which is surprising to me. The steps of the Markov kernel produce a manageable transform of the initial mean field approximation, a random version of the original VAE. Manageable provided not too many MCMC steps are implemented. (Now, the flow of slides was much too fast for me to get a proper understanding of the implementation of the method, of the degree of its calibration, and of the computing cost. I need to read the associated papers.)

Once the talk was over, I went back to changing tires and tubes, as two bikes of mine had flat tires, the latest being a spectacular explosion (!) that seemingly went through the tire (although I believe the opposite happened, namely the tire got slashed and induced the tube to blow out very quickly). Blame the numerous bits of broken glass over bike paths.

## one World ABC seminar [term #2]

Posted in Statistics with tags ABC, ABCruise, Approximate Bayesian computation, approximate Bayesian inference, Bayesian synthetic likelihood, gaussian process, MCMC, One World ABC Seminar, online seminar, University of Warwick, webinar on September 29, 2020 by xi'an**T**he on-line One World ABC seminar continues on-line this semester! With talks every other Thursday at 11:30 UK time (12:30 central European time). Incoming speakers are

- Marko Järvenpää, on Batch simulations and uncertainty quantification in Gaussian process surrogate ABC, on the first of October
- David Frazier, on a minimum distance approach to ABC, on 15 October
**[Warning: 10:30 UK time, 11:30 EU time, 8:30 Victoria time!!!]** - David Nott, on Marginally calibrated deep distributional regression, on 12 November
- Matti Vihola, on the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction, on 10 December

with presenters to be confirmed for 29 October. Anyone interested in presenting at this webinar in a near future should not hesitate in contacting Massimiliano Tamborrino in Warwick or any of the other organisers of the seminar!

## Approximate Bayesian analysis of (un)conditional copulas [webinar]

Posted in Books, pictures, Statistics, University life with tags ABC, Algorithms & Computationally Intensive Inference, Australia, copulas, New South Wales, Sydney, Sydney Harbour, University of Warwick, UNSW, webinar on September 17, 2020 by xi'an**T**he Algorithms & Computationally Intensive Inference seminar (access by request) will virtually resume this week in Warwick U on Friday, 18 Sept., at noon (UK time, ie +1GMT) with a talk by (my coauthor and former PhD student) Clara Grazian (now at UNSW), talking about approximate Bayes for copulas:

Many proposals are now available to model complex data, in particular thanks to the recent advances in computational methodologies and algorithms which allow to work with complicated likelihood function in a reasonable amount of time. However, it is, in general, difficult to analyse data characterized by complicated forms of dependence. Copula models have been introduced as probabilistic tools to describe a multivariate random vector via the marginal distributions and a copula function which captures the dependence structure among the vector components, thanks to the Sklar’s theorem, which states that any d-dimensional absolutely continuous density can be uniquely represented as the product of the marginal distributions and the copula function. Major areas of application include econometrics, hydrological engineering, biomedical science, signal processing and finance. Bayesian methods to analyse copula models tend to be computational intensive or to rely on the choice of a particular copula function, in particular because methods of model selection are not yet fully developed in this setting. We will present a general method to estimate some specific quantities of interest of a generic copula by adopting an approximate Bayesian approach based on an approximation of the likelihood function. Our approach is general, in the sense that it could be adapted both to parametric and nonparametric modelling of the marginal distributions and can be generalised in presence of covariates. It also allow to avoid the definition of the copula function. The class of algorithms proposed allows the researcher to model the joint distribution of a random vector in two separate steps: first the marginal distributions and, then, a copula function which captures the dependence structure among the vector components.