Bayes Factors for Forensic Decision Analyses with R [book review]

My friend EJ Wagenmaker pointed me towards an entire book on the BF by Bozza (from Ca’Foscari, Venezia), Taroni and Biederman. It is providing a sort of blueprint for using Bayes factors in forensics for both investigative and evaluative purposes. With R code and free access. I am of course unable to judge of the relevance of the approach for forensic science (I was under the impression that Bayesian arguments were usually not well-received in the courtroom) but find that overall the approach is rather one of repositioning the standard Bayesian tools within a forensic framework.

“The [evaluative] purpose is to assign a value to the result of a comparison between an item of unknown source and an item from a known source.”

And thus I found nothing shocking or striking from this standard presentation of Bayes factors, including the call to loss functions, if a bit overly expansive in its exposition. The style is also classical, with a choice of grey background vignettes for R coding parts that we also picked in our R books! If anything, I would have expected more realistic discussions and illustrations of prior specification across the hypotheses (see e.g. page 34), while the authors are mostly centering on conjugate priors and the (de Finetti) trick of the equivalent prior sample size. Bayes factors are mostly assessed using a conservative version of Jeffreys’ “scale of evidence”. The computational section of the book introduces MCMC (briefly) and mentions importance sampling, harmonic mean (with a minimalist warning), and Chib’s formula (with no warning whatsoever).

“The [investigative] purpose is to provide information in investigative proceedings (…) The scientist (…) uses the findings to generate hypotheses and suggestions for explanations of observations, in order to give guidance to investigators or litigants.”

Chapter 2 is about standard models: inferring about a proportion, with some Monte Carlo illustration,  and the complication of background elements, normal mean, with an improper prior making an appearance [on p.69] with no mention being made of the general prohibition of such generalised priors when using Bayes factors or even of the Lindley-Jeffreys paradox. Again, the main difference with Bayesian textbooks stands with the chosen examples.

Chapter 3 focus on evidence evaluation [not in the computational sense] but, again, the coverage is about standard models: processing the Binomial, multinomial, Poisson models, again though conjugates. (With the side remark that Fig 3.2 is rather unhelpful: when moving the prior probability of the null from zero to one, its posterior probability also moves from zero to one!) We are back to the Normal mean case with the model variance being known then unknown. (An unintentionally funny remark (p.96) about the dependence between mean and variance being seen as too restrictive and replaced with… independence!). At last (for me!), the book is pointing [p.99] out that the BF is highly sensitive to the choice of the prior variance (Lindley-Jeffreys, where art thou?!), but with a return of the improper prior (on said variance, p.102) with no debate on the ensuing validity of the BF. Multivariate Normals are also presented, with Wishart priors on the precision matrix, and more details about Chib’s estimate of the evidence. This chapter also contains illustrations of the so-called score-based BF which is simply (?) a Bayes factor using a distribution on a distance summary (between an hypothetical population and the data) and an approximation of the distributions of these summaries, provided enough data is available… I also spotted a potentially interesting foray into BF variability (Section 3.4.2), although not reaching all the way to a notion of BF posterior distributions.

Chapter 4 stands for Bayes factors for investigation, where alternative(s) is(are) less specified, as testing eg Basmati rice vs non-Basmati rice. But there is no non-parametric alternative considered in the book. Otherwise, it looks to me rather similar to Chapter 3, i.e. being back to binomial, multinomial models, with more discussions onm prior specification, more normal, or non-normal model, where the prior distribution is puzzingly estimated by a kernel density estimator, a portmanteau alternative (p.157), more multivariate Normals with Wishart priors and an entry on classification & discrimination.

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about Chance!]

ISBA 2021.3

Now on the third day which again started early with a 100% local j-ISBA session. (After a group run to and around Mont Puget, my first real run since 2020!!!) With a second round of talks by junior researchers from master to postdoc level. Again well-attended. A talk about Bayesian non-parametric sequential taxinomy by Alessandro Zito used the BayesANT acronym, which reminded me of the new vave group Adam and the Ants I was listening to forty years ago, in case they need a song as well as a logo! (Note that BayesANT is also used for a robot using Bayesian optimisation!) And more generally a wide variety in the themes. Thanks to the j-organisers of this 100% live session!

The next session was on PDMPs, which I helped organise, with Manon Michel speaking from Marseille, exploiting the symmetry around the gradient, which is distribution-free! Then, remotely, Kengo Kamatani, speaking from Tokyo, who expanded the high-dimensional scaling limit to the Zig-Zag sampler, exhibiting an argument against small refreshment rates, and Murray Pollock, from Newcastle, who exposed quite clearly the working principles of the Restore algorithm, including why coupling from the past was available in this setting. A well-attended session despite the early hour (in the USA).

Another session of interest for me [which I attended by myself as everyone else was at lunch in CIRM!] was the contributed C16 on variational and scalable inference that included a talk on hierarchical Monte Carlo fusion (with my friends Gareth and Murray as co-authors), Darren’s call to adopt functional programming in order to save Bayesian computing from extinction, normalising flows for modularisation, and Dennis’ adversarial solutions for Bayesian design, avoiding the computation of the evidence.

Wes Johnson’s lecture was about stories with setting prior distributions based on experts’ opinions. Which reminded me of the short paper Kaniav Kamary and myself wrote about ten years ago, in response to a paper on the topic in the American Statistician. And could not understand the discrepancy between two Bayes factors based on Normal versus Cauchy priors, until I was told they were mistakenly used repeatedly.

Rushing out of dinner, I attended both the non-parametric session (live with Marta and Antonio!) and the high-dimension computational session on Bayesian model choice (mute!). A bit of a schizophrenic moment, but allowing to get a rough picture in both areas. At once. Including an adaptive MCMC scheme for selecting models by Jim Griffin. Which could be run directly over the model space. With my ever-going wondering at the meaning of neighbour models.

ISBA 20.2.21

A second day which started earlier and more smoothly with a 100% local j-ISBA session. (Not counting the invigorating swim in Morgiou!) With talks by junior researchers from master to postdoc level, as this ISBA mirror meeting was primarily designed for them, so that they could all present their work, towards gaining more visibility for their research and facilitating more interactions with the participants. CIRM also insisted on this aspect of the workshop, which was well-attended.

I alas had to skip the poster session [and the joys of gather.town] despite skipping lunch [BND], due to organisational constraints. Then attended the Approximate Bayesian computation section, including one talk by Geoff Nicholls on confidence estimation for ABC, following upon the talk given by Kate last evening. And one by Florian Maire on learning the bound in accept-reject algorithms on the go, as in Caffo et al. (2002), which I found quite exciting and opening new possibilities, esp. if the Markov chain thus produced can be recycled towards unbiasedness without getting the constant right! For instance, by Rao-Blackwellisation, multiple mixtures, black box importance sampling, whatever. (This also reminded me of the earlier Goffinet et al. 1996.)

Followed by another Bayesian (modeling and) computation session. With my old friend Peter Müller talking about mixture inference with dependent priors (and a saturated colour scheme!), Matteo Ruggieri [who could not make it to CIRM!] on computable Bayesian inference for HMMs. Providing an impressive improvement upon particle filters for approximating the evidence. Also bringing the most realistic Chinese restaurant with conveyor belt! And Ming Yuan Zhou using optimal transport to define distance between distributions. With two different conditional distributions depending on which marginal is first fixed. And a connection with GANs (of course!).

And it was great to watch and listen to my friend Alicia Carriquiry talking on forensic statistics and the case for (or not?!) Bayes factors. And remembering Dennis Lindley. And my friend Jim Berger on frequentism versus Bayes! Consistency seems innocuous as most Bayes procedures are. Empirical coverage is another kind of consistency, isn’t it?

A remark I made when re-typing the program for CIRM is that there are surprisingly few talks about COVID-19 overall, maybe due to the program being mostly set for ISBA 2020 in Kunming. Maybe because we are more cautious than the competition…?!

And, at last, despite a higher density of boars around the CIRM facilities, no one got hurt yesterday! Unless one counts the impact of the French defeat at the Euro 2021 on the football fans here…

dodging bullets, IEDs, and fingerprint detection at SimStat19

I attended a fairly interesting forensic science session at SimStat 2019 in Salzburg as it concentrated on evidence and measures of evidence rather than on strict applications of Bayesian methodology to forensic problems. Even though American administrations like the FBI or various police departments were involved. It was a highly coherent session and I had a pleasant discussion with some of the speakers after the session. For instance, my friend Alicia Carriquiry presented an approach to determined from images of bullets whether or not they have been fired from the same gun, leading to an interesting case for a point null hypothesis where the point null makes complete sense. The work has been published in Annals of Applied Statistics and is used in practice. The second talk by Danica Ommen on fiducial forensics on IED, asking whether or not copper wires used in the bombs are the same, which is another point null illustration. Which also set an interesting questioning on the dependence of the alternative prior on the distribution of material chosen as it is supposed to cover all possible origins for the disputed item. But more interestingly this talk launched into a discussion of making decision based on finite samplers and unknown parameters, not that specific to forensics, with a definitely surprising representation of the Bayes factor as an expected likelihood ratio which made me first reminiscent of Aitkin’s (1991) infamous posterior likelihood (!) before it dawned on me this was a form of bridge sampling identity where the likelihood ratio only involved parameters common to both models, making it an expression well-defined under both models. This identity could be generalised to the general case by considering a ratio of integrated likelihoods, the extreme case being the ratio equal to the Bayes factor itself. The following two talks by Larry Tang and Christopher Saunders were also focused on the likelihood ratio and their statistical estimates, debating the coherence of using a score function and presenting a functional ABC algorithm where the prior is a Dirichlet (functional) prior. Thus a definitely relevant session from a Bayesian perspective!

 

Introductory overview lecture: the ABC of ABC [JSM19 #1]

Here are my slides [more or less] for the introductory overview lecture I am giving today at JSM 2019, 4:00-5:50, CC-Four Seasons I. There is obviously quite an overlap with earlier courses I gave on the topic, although I refrained here from mentioning any specific application (like population genetics) to focus on statistical and computational aspects.

Along with the other introductory overview lectures in this edition of JSM:

• Sunday 28, 2:00-3:50, CC-Four Seasons I: CSI at the JSM: Forensic Statistics and the Value of Scientific Evidence in Court by Hal Stern (University of California, Irvine)
• Monday 29, 8:30-10:20, CC-205: Assessing Procedures vs. Assessing Evidence by Michael Levine (University of Massachusetts, Amherst)
• Monday 29, 2:00_3:50, CC-205: Causal inference in modern statistics by Jennifer Hill (New York University)and Avi Feller (UC Berkeley)
• Tuesday 30, 8:30-10:20, CC-205: Modern Risk Analysis  by Walter Piergorsch (University of Arizona) and David Banks (Duke University)