30 May was a day of first and last times, if not in capital ways (for me), on the One World ABC webinar. This was the first time we had a talk by Mark Beaumont and also the first time I had team experience of facing a smoking participant, while this was the last time of our monthly webinar for the (Northern) academic year.
The talk was about model misspecification in population genomic, from an ABC perspective with the motivation of common noticeable difference between the distributions of d(s,s⁰) and d(s,s’), distances between the prior predictively simulated summary statistics and the observed ones vs posterior generated ones, which should indicates misspecification, esp with complicated models. Mark and his coauthors then supported a gradual elimination of summary statistics to diminish the discrepancy, hence voluntarily impoverishing the model. While blaming the statistics sounded a bit like shooting the messenger, the resolution is of obvious interest if backing from modelling the misspecification itself.
Some of the presented work was conducted in Ward et al (2022, NeurIPS) with a reference to the outlying Ratmann et al (2009) we later discussed, for including tolerance as an extra parameter ε, thereby reconsidering Wikinson’s exact ABC for noisy observations y by the medium of a normalising flow on the marginal distribution of the denoised x (learned from the prior predictive)
More precisely, the idea is to drop summary statistics by checking whether or not the observed S⁰ belongs to HPD region, removing one component of S at a time, using e.g. a k-NN estimate for the summary density (hence depending on parameterisation of said statistics for the distance). Hopefully, the process stops before loosing identifiability by using too few statistics. I also wondered at multiple uses of the data in this sequential procedure but Mark argued for adopting a meta- or pragma- or Gelmanian- Bayesian perspective in the end!
Another perk was the appearance of (and illustration with) the Scottish Wildcat, mentioned in The Guardian a few months ago and discussed in the ‘Og, with further papers exploring more aspects of this hybridization, like a posterior applied to a much more complex phylogenic tree reconstruction for cats of different creeds and many related parameters.
Last week, our MCMC reading group in PariSanté started reading Explicit convergence bounds for Metropolis Markov chains by my friends Christophe Andrieu, Anthony Lee, Sam Power, and Andi Wang (University of Warwick), recently published in the Annals of Applied Probability. The paper is centred on the bound above. Which may sound cryptic but gives a non-asymptotic explicit bound on the spectral gap γ, when the potential of the target is L-smooth, m-strongly convex and twice continuously differentiable, in dimension d, with a proposal being the Gaussian random walk with scale σ. With C = 1.972 10⁻⁴. if “possibly a few orders of magnitude larger”. This characterisation of the spectral gap leads to a sharper identification of d⁻¹ as the proper rate for σ². Other consequences are finding the order of the number of simulations to reach a χ² distance of ε,
Within a few days of the 
