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Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to approximate distributions of interest and their normalizing constants. These samplers originate from particle filtering for state space models and have become general and scalable sampling techniques. This article describes sequential Monte Carlo samplers and their possible implementations, arguing that they remain under-used in statistics, despite their ability to perform sequential inference and to leverage parallel processing resources among other potential benefits. Supplementary materials for this article are available online. 

TIR domains are NAD-degrading enzymes that function during immune signaling in prokaryotes, plants, and animals. In plants, most TIR domains are incorporated into intracellular immune receptors termed TNLs. In Arabidopsis, TIR-derived small molecules bind and activate EDS1 heterodimers, which in turn activate RNLs, a class of cation channel–forming immune receptors. RNL activation drives cytoplasmic Ca 2+ influx, transcriptional reprogramming, pathogen resistance, and host cell death. We screened for mutants that suppress an RNL activation mimic allele and identified a TNL, SADR1. Despite being required for the function of an autoactivated RNL, SADR1 is not required for defense signaling triggered by other tested TNLs. SADR1 is required for defense signaling initiated by some transmembrane pattern recognition receptors and contributes to the unbridled spread of cell death in lesion simulating disease 1 . Together with RNLs, SADR1 regulates defense gene expression at infection site borders, likely in a non-cell autonomous manner. RNL mutants that cannot sustain this pattern of gene expression are unable to prevent disease spread beyond localized infection sites, suggesting that this pattern corresponds to a pathogen containment mechanism. SADR1 potentiates RNL-driven immune signaling not only through the activation of EDS1 but also partially independently of EDS1. We studied EDS1-independent TIR function using nicotinamide, an NADase inhibitor. Nicotinamide decreased defense induction from transmembrane pattern recognition receptors and decreased calcium influx, pathogen growth restriction, and host cell death following intracellular immune receptor activation. We demonstrate that TIR domains can potentiate calcium influx and defense and are thus broadly required for Arabidopsis immunity. 

Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing couplings of the Metropolis-Hastings algorithm handle the proposal and acceptance steps separately and fall short of the upper bound on one-step meeting probabilities given by the coupling inequality. This paper introduces maximal couplings which achieve this bound while retaining the practical advantages of current methods. We consider the properties of these couplings and examine their behavior on a selection of numerical examples. 

We present a Gibbs sampler for the Dempster–Shafer (DS) approach to statistical inference for categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities “for,” “against,” and “don’t know” about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate the DS inference. The sampler relies on an equivalence between the iterative constraints of the vertex configuration and the nonnegativity of cycles in a fully connected directed graph. Illustrations include the testing of independence in 2 × 2 contingency tables and parameter estimation of the linkage model. 

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov chain Monte Carlo (MCMC) algorithms have been proposed for this setting, such as the pseudo-marginal method for latent variable models and the exchange algorithm for a class of undirected graphical models. As with any MCMC algorithm, the resulting estimators are justified asymptotically in the limit of the number of iterations, but exhibit a bias for any fixed number of iterations due to the Markov chains starting outside of stationarity. This "burn-in" bias is known to complicate the use of parallel processors for MCMC computations. We show how to use coupling techniques to generate unbiased estimators in finite time, building on recent advances for generic MCMC algorithms. We establish the theoretical validity of some of these procedures by extending existing results to cover the case of polynomially ergodic Markov chains. The efficiency of the proposed estimators is compared with that of standard MCMC estimators, with theoretical arguments and numerical experiments including state space models and Ising models.