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Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary…

Methodology · Statistics 2014-08-05 P. Richard Hahn , Carlos M. Carvalho

We consider the asymptotic properties of Approximate Bayesian Computation (ABC) for the realistic case of summary statistics with heterogeneous rates of convergence. We allow some statistics to converge faster than the ABC tolerance, other…

Computation · Statistics 2023-11-17 Caroline Lawless , Christian P. Robert , Judith Rousseau , Robin J. Ryder

This extended preface [to the Book `Bayesian Nonparametrics', Cambridge University Press, 2010, by NL Hjort, CC Holmes, P Mueller, SG Walker] is meant to explain why you are right to be curious about Bayesian nonparametrics -- why you may…

Methodology · Statistics 2026-05-22 Nils Lid Hjort , Chris Holmes , Peter Mueller , Stephen G. Walker

This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…

Probability · Mathematics 2021-08-24 Aladji Babacar Niang , Gane Samb Lo , Moumouni Diallo

This is the rejoinder to the discussion by Kennedy, Balakrishnan and Wasserman on the paper "On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning" published in…

Methodology · Statistics 2020-08-10 Lin Liu , Rajarshi Mukherjee , James M. Robins

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

Machine Learning · Statistics 2021-04-13 Mattias Åkesson , Prashant Singh , Fredrik Wrede , Andreas Hellander

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…

Computation · Statistics 2014-01-03 Ajay Jasra

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

Computation · Statistics 2010-07-28 Michael Blum

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…

Statistics Theory · Mathematics 2017-11-21 Sergio Alvarez-Andrade , Salim Bouzebda , Aimé Lachal

This is a collection of three written discussions of the paper "sequential quasi-Monte Carlo sampling" by M. Gerber and N. Chopin, following the presentation given before the Royal Statistical Society in London on December 10th, 2014.

Computation · Statistics 2015-05-27 Julyan Arbel , Igor Prunster , Christian P. Robert , Robin J. Ryder

In this rejoinder we summarize the comments, questions and remarks on the paper "A novel algorithmic approach to Bayesian Logic Regression" from the discussants. We then respond to those comments, questions and remarks, provide several…

Methodology · Statistics 2020-05-29 Aliaksandr Hubin , Geir Storvik , Florian Frommlet

Contribution to the discussion of the paper "Causal inference using invariant prediction: identification and confidence intervals" by Peters, B\"uhlmann and Meinshausen, to appear in the Journal of the Royal Statistical Society, Series B.

Methodology · Statistics 2016-05-27 Chris J. Oates , Jessica Kasza , Sach Mukherjee

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Statistics Theory · Mathematics 2015-09-08 Subhashis Ghosal

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Statistics Theory · Mathematics 2015-09-08 Mark G. Low , Zongming Ma

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Statistics Theory · Mathematics 2015-09-08 Judith Rousseau

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Statistics Theory · Mathematics 2015-09-08 Ismaël Castillo

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Statistics Theory · Mathematics 2015-09-08 Richard Nickl

This is a discussion of the paper "Safe testing" by Gr\"unwald, de Heide, and Koolen, Read before The Royal Statistical Society at a meeting organized by the Research Section on Wednesday, 24 January, 2024

Methodology · Statistics 2024-02-23 Joshua Bon , Christian P Robert

Discussion paper on "Fast Approximate Inference for Arbitrarily Large Semiparametric Regression Models via Message Passing" by Wand [arXiv:1602.07412].

Computation · Statistics 2016-09-20 Dustin Tran , David M. Blei

This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the…

Machine Learning · Statistics 2026-02-02 Getachew K. Befekadu