## Archive for Gibbs sampler

## away from CIRM

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags calanques, CIRM, coordinate sampler, Gibbs sampler, Luminy campus, Markov chain Monte Carlo, Marseille, Mont Puget, PDMP, SMF on November 5, 2020 by xi'an**D**ue to the new lockdown measures enforced in France and in particular in Marseilles, the CIRM workshop on QMC and randomness has turned virtual, and I will thus give my talk on ** Coordinate sampler : A non-reversible Gibbs-like sampler ** from Paris. Rather than from the Luminy campus after an early morning run to the top of Mont Puget as we used to do on the previous workshop there. With versions of PDMP running on QMC (which makes sense when considering the deterministic component of the sampler).

## deduplication and population size estimation [discussion]

Posted in Books, Statistics with tags Bayesian Analysis, capture-recapture, COVID-19, discussion paper, Gibbs sampler, record linkage, Syrian civil war on April 23, 2020 by xi'an**[H**ere is my discussion on the paper “A Unified Framework for De-Duplication and Population Size Estimation” by [my friends] Andrea Tancredi, Rebecca Steorts, and Brunero Liseo, to appear on the June 2020 issue of Bayesian Analysis. The deadline is 24 April. Discussions are to be submitted to BA as regular submissions.]

Congratulations to the authors, for this paper that expand the modelling of populations investigated by faulty surveys, a poor quality feature that applies to extreme cases like Syria casualties. And possibly COVID-19 victims.

The model considered in this paper, as given by (2.1), is a latent variable model which appears as hyper-parameterised in the sense it involves a large number of parameters and latent variables. First, this means it is essentially intractable outside a Bayesian resolution. Second, within the Bayesian perspective, it calls for identifiability and consistency questions, namely which fraction of the unknown entities is identifiable and which fraction can be consistently estimated, eventually severing the dependence on the prior modelling. Personal experiences with capture-recapture models on social data like drug addict populations showed me that prior choices often significantly drive posterior inference on the population size. Here, it seems that the generative distortion mechanism between registry of individuals and actual records is paramount.

“We now investigate an alternative aspect of the uniform prior distribution of λ given N.”

Since the practical application stressed in the title, namely some of civil casualties in Syria, interrogations take a more topical flavour as one wonders at the connection between the model and the actual data, between the prior modelling and the available prior information. It is however not the strategy adopted in the paper, which instead proposes a generic prior modelling that could be deemed to be non-informative. I find the property that conditioning on the list sizes eliminates the capture probabilities and the duplication rates quite amazing, reminding me indeed of similar properties for conjugate mixtures, although we found the property hard to exploit from a computational viewpoint. And that the hit-miss model provides computationally tractable marginal distributions for the cluster observations.

“Several records of the VDC data set represent unidentified victims and report only the date of death or do not have the first name and report only the relationship with the head of the family.”

This non-informative choice is however quite informative in the misreporting mechanism and does not address the issue that it presumably is misspecified. It indeed makes the assumption that individual label and type of record are jointly enough to explain the probability of misreporting the exact record. In practical cases, it seems more realistic that the probability to appear in a list depends on the characteristics of an individual, hence far from being uniform as well as independent from one list to the next. The same applies to the probability of being misreported. The alternative to the uniform allocation of individuals to lists found in (3.3) remains neutral to the reasons why (some) individuals are missing from (some) lists. No informative input is indeed made here on how duplicates could appear or on how errors are made in registering individuals. Furthermore, given the high variability observed in inferring the number of actual deaths covered by the collection of the two lists, it would have been of interest to include a model comparison assessment, especially when contemplating the clash between the four posteriors in Figure 4.

The implementation of a manageable Gibbs sampler in such a convoluted model is quite impressive and one would welcome further comments from the authors on its convergence properties, since it is facing a large dimensional space. Are there theoretical or numerical irreducibility issues for instance, created by the discrete nature of some latent variables as in mixture models?

## coordinate sampler on-line

Posted in Statistics with tags coordinate sampler, Gibbs sampler, MCMC, non-reversible diffusion, PDMP, piecewise deterministic, Statistics & Computing on March 13, 2020 by xi'an## Bernoulli mixtures

Posted in pictures, Statistics, University life with tags Bernoulli mixture, cross validated, Gibbs sampler, Helvetia, Jakob Bernoulli, Metropolis-Hastings algorithm, mixtures, stamp on October 30, 2019 by xi'an**An** interesting query on (or from) X validated: given a Bernoulli mixture where the weights are known and the probabilities are jointly drawn from a Dirichlet, what is the most efficient from running a Gibbs sampler including the latent variables to running a basic Metropolis-Hastings algorithm based on the mixture representation to running a collapsed Gibbs sampler that only samples the indicator variables… I provided a closed form expression for the collapsed target, but believe that the most efficient solution is based on the mixture representation!