Archive for ABC

David Frazier’s talk on One World ABC seminar tomorrow [watch for the time!]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on October 14, 2020 by xi'an

My 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!

one World ABC seminar [term #2]

Posted in Statistics with tags , , , , , , , , , , on September 29, 2020 by xi'an

The 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

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 , , , , , , , , , on September 17, 2020 by xi'an

The 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.

 

transport Monte Carlo

Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , , , , , , , , on August 31, 2020 by xi'an

Read this recent arXival by Leo Duan (from UF in Gainesville) on transport approaches to approximate Bayesian computation, in connection with normalising flows. The author points out a “lack of flexibility in a large class of normalizing flows”  to bring forward his own proposal.

“…we assume the reference (a multivariate uniform distribution) can be written as a mixture of many one-to-one transforms from the posterior”

The transportation problem is turned into defining a joint distribution on (β,θ) such that θ is marginally distributed from the posterior and β is one of an infinite collection of transforms of θ. Which sounds quite different from normalizing flows, to be sure. Reverting the order, if one manages to simulate β from its marginal the resulting θ is one of the transforms. Chosen to be a location-scale modification of β, s⊗β+m. The weights when going from θ to β are logistic transforms with Dirichlet distributed scales. All with parameters to be optimised by minimising the Kullback-Leibler distance between the reference measure on β and its inverse mixture approximation, and resorting to gradient descent. (This may sound a wee bit overwhelming as an approximation strategy and I actually had to make a large cup of strong macha to get over it, but this may be due to the heat wave occurring at the same time!) Drawing θ from this approximation is custom-made straightforward and an MCMC correction can even be added, resulting in an independent Metropolis-Hastings version since the acceptance ratio remains computable. Although this may defeat the whole purpose of the exercise by stalling the chain if the approximation is poor (hence suggesting this last step being used instead as a control.)

The paper also contains a theoretical section that studies the approximation error, going to zero as the number of terms in the mixture, K, goes to infinity. Including a Monte Carlo error in log(n)/n (and incidentally quoting a result from my former HoD at Paris 6, Paul Deheuvels). Numerical experiments show domination or equivalence with some other solutions, e.g. being much faster than HMC, the remaining $1000 question being of course the on-line evaluation of the quality of the approximation.

right place, wrong version

Posted in Statistics with tags , , , , , , , , , on August 12, 2020 by xi'an