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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. 

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. 

Abstract Phased array radars (PARs) are a promising observing technology, at the cusp of being available to the broader meteorological community. PARs offer near-instantaneous sampling of the atmosphere with flexible beam forming, multifunctionality, and low operational and maintenance costs and without mechanical inertia limitations. These PAR features are transformative compared to those offered by our current reflector-based meteorological radars. The integration of PARs into meteorological research has the potential to revolutionize the way we observe the atmosphere. The rate of adoption of PARs in research will depend on many factors, including (i) the need to continue educating the scientific community on the full technical capabilities and trade-offs of PARs through an engaging dialogue with the science and engineering communities and (ii) the need to communicate the breadth of scientific bottlenecks that PARs can overcome in atmospheric measurements and the new research avenues that are now possible using PARs in concert with other measurement systems. The former is the subject of a companion article that focuses on PAR technology while the latter is the objective here. 

Abstract Tropical Storm Bill produced over 400 mmof rainfall to portions of southern Oklahoma from 16-20 June 2015, adding to the catastrophic urban and river flooding that occurred throughout the region in the month prior to landfall. The unprecedented excessive precipitation event that occurred across Oklahoma and Texas during May and June 2015 resulted in anomalously high soil moisture and latent heat fluxes over the region, acting to increase the available boundary layer moisture. Tropical Storm Bill progressed inland over the region of anomalous soil moisture and latent heat fluxes which helped maintain polarimetric radar signatures associated with tropical, warm rain events. Vertical profiles of polarimetric radar variables such as Z H , Z DR , K DP , and ρ hv were analyzed in time and space over Texas and Oklahoma. The profiles suggest that Tropical Storm Bill maintained warm rain signatures and collision-coalescence processes as it tracked hundreds of kilometers inland away from the landfall point consistent with tropical cyclone precipitation characteristics. Dual-frequency precipitation radar observations from the NASA GPM DPR were also analyzed post-landfall and showed similar signatures of collision-coalescence while Bill moved over north Texas, southern Oklahoma, eastern Missouri, and western Kentucky.