Archive for survey
A hundred mirrors shine together, a hundred hubs resonate together!
Posted in Books, pictures, Travel, University life with tags calligraphy, ChatGPT, Chinese Communist Party, committee on the future of ISBA conferences, dictature, ISBA, ISBA 2026, Mao Zedong, Maoist posters, mirror workshop, multi-hub conference, Nagoya, survey, The Hundred Flowers Campaign, traditional Chinese calligraphy on July 2, 2026 by xi'an
Monte Carlo with infinite variances [a surveyal guide]
Posted in Books, Statistics, University life with tags antithetic sampling, control variates, IMS, infinite variance estimators, Monte Carlo Statistical Methods, Pareto smoothed importance sampling, Probability Surveys, Rao-Blackwellisation, reparameterisation, survey, University of Tokyo, University of Warwick, variance reduction on January 14, 2026 by xi'an
Watch out!, Reiichiro Kawai has just published a survey on infinite variance Monte Carlo methods in Probability Surveys, which is most welcomed as this issue is customarily ignored by both the literature and the practitioners. Radford Neal‘s warning about the dangers of using the harmonic mean estimator of the evidence (as in Newton and Raftery 1996) is an illustration that remains pertinent to this day. In that sense, the survey relates to specific, earlier if recent attempts, such as Chatterjee and Diaconis (2015) or Vehtari et al (2015), with its Pareto correction.
In its recapitulation of the basics of Monte Carlo (closely corresponding to my own introduction of the topic in undergraduate classes), the paper indicates that the consistency of the variance estimator is enough to replace the true variance with its estimator and maintain the CLT. I have often if vaguely wondered at the impact (if any) a variance estimator with (itself) an infinite variance would have. A note to this effect appears at the end of Section 1.2. While being involved from the start, importance sampling has to wait till section 3.2 to be formally introduced. It is also interesting to note that the original result on the optimal importance variance being zero when the integrand is always positive (or negative) is extended here, by noting that a zero variance estimator can always be found by breaking the integrand f into its positive and negative parts, and using now two single samples for the respective integrals. I thus find Example 6 rather unhelpful, even though the entire literature contains such examples with no added value of formal optimal importance samplers. A comment at the end of Example 6 is opens the door to a short discussion of reparametrisation in simulation, a topic rarely discussed in the literature. The use of Rao-Blackwellization as a variance reduction technique that is open to switching from infinite to finite variance, is emphasised as well in Section 2.1.
In relation with a recent musing of mine during a seminar in Warwick, the novel part in the survey on the limited usefulness of control variate is of interest, even though one could predict that linear regression is not doing very well in infinite variance environments. Examples 8 and 9 are most helpful in this respect. It is similarly revealing if unsurprising that basic antithetic variables do not help. The warning about detecting or failing to detect infinite variance situations is well-received.
While theoretically correct, the final section about truncation limit is more exploratory, in that truncation can produce biased answers, whose magnitude is not assessed within the experiment.
on the future of ISBA meetings (and others)
Posted in Travel, University life with tags committee on the future of ISBA conferences, ISBA, ISBA 2024, ISBA Bulletin, mirror workshop, multihub conferences, QR code, survey, tyranosaurus, Università Ca' Foscari Venezia on January 4, 2026 by xi'an
As a member of the ad hoc ISBA committee on the future of conferences, along with my friends Guido Consonni, Kate Lee, and Getraud Malsiner-Walli, following a round-table on the topic we held in Venezia for ISBA 2024, I am supporting more sustainability and inclusivity through the creation of mirrors or multiple hubs that allow to broaden the spectrum of major meetings and to multiply the impact of these events to other locations on Earth, for researchers who cannot or are unwilling to travel to these meetings. The following is the link to a survey we designed to assess the opinion of the ISBA membership in this regard, as we realise perspectives can widely differ on this topic. The December ISBA Bulletin also includes a preliminary report of our committee. I obviously encourage all ‘Og’s readers to take part in this survey!
The Committee warmly invites ISBA members to share their perspectives on the environmental sustainability, inclusivity, and accessibility of ISBA meetings, and hopes to stimulate awareness and discussion of these issues within the Society. To this end, we have prepared a five-minute Survey on Meeting Experiences to Inform Future ISBA Events. ISBA members can use the following QR code to access the survey.
oh, dog…!
Posted in Books, Kids with tags American Gods, bad graph, Hell, irrational beliefs, Pew Research Center, religion, religions, religious beliefs, religious right, secularism, survey, The New York Times, US culture, USA on April 22, 2025 by xi'an
gentle importance sampling
Posted in Books, pictures, Statistics with tags BayesComp 2023, Cédric Villani, Comptes Rendus de l'Académie des Sciences, CRAS, George Casella, harmonic mean estimator, Hyvärinen score, importance sampling, infinite variance estimators, Levi, noise contrasting estimation, Pierre Louis Lions, survey on February 24, 2025 by xi'an
A new (and gentle!) survey by Luca Martino! And by Fernando Llorente. On importance sampling, with coverage of normalised and self-normalised versions. And their usage in different configurations (one vs several integrals, one vs several families of distributions). Some points relating to earlier remarks or musing of mine’s:
- the fact that the optimal importance function does not lead to a zero variance importance estimator when the integrand f is not of constant sign (p.7) can be cancelled by first decomposing f as f⁺-f⁻, since both allow for a zero variance importance estimator, if formally requiring two different samples (of size zero!), a trick considered later on p.18 and repeated for the ratio in self-normalised importance (p.19)
- the special case when the integrand f is constant is not of practical interest but relevant for checking properties of different estimators. For instance, this case allowed George and myself to spot a mistake in an early importance paper. In the same volume of the Comptes Rendus as an early paper of Lions and Villani.
- the remark that self-normalised (SNIS) importance sampling can prove more efficient than (properly normalised) importance sampling, although the property that SNIS is always bounded should not be seen as a major point given that it is simply due to using a finite sample and hence a finite set of images of f
- the case of integrals involving several target pdfs or several integrands is not necessarily of major interest if simulating different samples for each unidimensional integral can be implemented (again formally leading to zero variance at no cost)
- the issue of merging several estimators in an optimal way is briefly mentioned in §5.4, a challenge Victor Elvira and I have been approaching over the past years, if not yet concluding satisfactorily (mea culpa)
- when replacing the target with a noisy estimate (p.22), the fact that this estimate must be normalised is correct, but pales against the impact of using this estimate, which may prove catastrophic. And unbiasedness is not particularly crucially important in this setup for the same reason
- the section on evidence approximation (§7) is more standard, with the harmonic mean estimator being called reverse importance sampling, which brings us to the “elephant in the room”, namely that
- the issue of infinite variance of some importance sampling estimators is not directly covered (except once in §8, p.34), thus perceiving importance sampling as a variance reduction method being somewhat misleading (unless the authors consider solely the optimal importance function, which is rarely of practical use)
The paper concludes with an interesting notion that
“we suggest the analysis of the relevant connection between importance sampling and contrastive learning Gutmann and Hyvärinen (2012)”
that I also have been pointing out for a while. All in all, a useful summing-up that I will likely suggest to my students.
