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.

Scott Sisson’s ABC seminar in Paris [All about that Bayes]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on January 20, 2020 by xi'an

On the “All about that Bayes” seminar tomorrow (Tuesday 21 at 3p.m., room 42, AgroParisTech, 16 rue Claude Bernard, Paris 5ième), Scott Sisson, School of Mathematics and Statistics at UNSW, and visiting Paris-Dauphine this month, will give a talk on

Approximate posteriors and data for Bayesian inference

Abstract
For various reasons, including large datasets and complex models, approximate inference is becoming increasingly common. In this talk I will provide three vignettes of recent work. These cover a) approximate Bayesian computation for Gaussian process density estimation, b) likelihood-free Gibbs sampling, and c) MCMC for approximate (rounded) data.

Australia’s burning and it ain’t gonna stop anytime soon…

Posted in pictures with tags , , , , , , on January 2, 2020 by xi'an

Australian theocracy

Posted in Kids, pictures, Travel with tags , , , , on December 25, 2019 by xi'an

Examples from The Guardian at which discrimination based on religious arguments should become legal in Australia:

• A doctor may tell a transgender patient of their religious belief that God made men and women in his image and that gender is therefore binary (EM)

• A single mother who, when dropping her child off at daycare, may be told by a worker that she is sinful for denying her child a father (Public Interest Advocacy Centre)

• A woman may be told by a manager that women should submit to their husbands or that women should not be employed outside the home (PIAC)

• A student with disability may be told by a teacher their disability is a trial imposed by God (PIAC)

• A person of a minority faith may be told by a retail assistant from another religion that they are a “heathen destined for eternal damnation” (PIAC).

• A Catholic doctor refusing to provide contraception to all patients (EM) or to prescribe hormone treatment for gender transition (Equality Australia, Just Equal, LGBTI Health Alliance)

• A Catholic nurse who refused to participate in abortion procedures (EM) or to provide the morning-after pill to a woman admitted to hospital after a sexual assault (Equality Australia)

• A pharmacist refusing to provide the pill to women for contraceptive use (EM), or hormone treatment (Public Interest Advocacy Centre, LGBTI Health Alliance)

• A doctor could refuse to prescribe post-exposure prophylaxis (PEP) within the required 72-hour window to a patient whose condom broke during a sexual encounter on the basis of religious beliefs that forbid sexual activity outside of marriage (Equality Australia)

• A psychiatrist could say to a woman with depression that “she should be looking forward to the kingdom of heaven”. (Equality Australia)

• A Jewish school may require that its staff and students be Jewish and accordingly refuse to hire or admit someone because they were not Jewish (EM)

• A student attends the same religious school through their primary and secondary education. At 16 they lose faith in the religion of the school and tell a teacher that they are now agnostic. The school would be able to expel, suspend or otherwise punish, for example, give detention to the student (PIAC)

• A homeowner seeking a tenant for their spare room may require that the tenant be of the same religious belief or activity as the homeowner (EM).

common derivation for Metropolis–Hastings and other MCMC algorithms

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , on July 25, 2016 by xi'an

Khoa Tran and Robert Kohn from UNSW just arXived a paper on a comprehensive derivation of a large range of MCMC algorithms, beyond Metropolis-Hastings. The idea is to decompose the MCMC move into

1. a random completion of the current value θ into V;
2. a deterministic move T from (θ,V) to (ξ,W), where only ξ matters.

If this sounds like a new version of Peter Green’s completion at the core of his 1995 RJMCMC algorithm, it is because it is indeed essentially the same notion. The resort to this completion allows for a standard form of the Metropolis-Hastings algorithm, which leads to the correct stationary distribution if T is self-inverse. This representation covers Metropolis-Hastings algorithms, Gibbs sampling, Metropolis-within-Gibbs and auxiliary variables methods, slice sampling, recursive proposals, directional sampling, Langevin and Hamiltonian Monte Carlo, NUTS sampling, pseudo-marginal Metropolis-Hastings algorithms, and pseudo-marginal Hamiltonian  Monte Carlo, as discussed by the authors. Given this representation of the Markov chain through a random transform, I wonder if Peter Glynn’s trick mentioned in the previous post on retrospective Monte Carlo applies in this generic setting (as it could considerably improve convergence…)