Ester Mariucci, Kolyan Ray, Botond Szabó.

Source: Bernoulli, Volume 26, Number 2, 1070--1097.

Abstract:
The estimation of a log-concave density on $mathbb{R}$ is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.

Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons.

Source: Bernoulli, Volume 26, Number 1, 352--386.

Abstract:
In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $Hin (0,1)$. The drift term is assumed to be globally Lipschitz. We prove that the solution of each of the above equations is continuous in terms of the index $H$, with respect to the convergence in law in the space of continuous functions.

Kay Bogerd, Rui M. Castro, Remco van der Hofstad.

Source: Bernoulli, Volume 26, Number 1, 253--285.

Abstract:
We study the asymptotic behavior of the clique number in rank-1 inhomogeneous random graphs, where edge probabilities between vertices are roughly proportional to the product of their vertex weights. We show that the clique number is concentrated on at most two consecutive integers, for which we provide an expression. Interestingly, the order of the clique number is primarily determined by the overall edge density, with the inhomogeneity only affecting multiplicative constants or adding at most a $log log (n)$ multiplicative factor. For sparse enough graphs the clique number is always bounded and the effect of inhomogeneity completely vanishes.

Names, Personal -- England.

St. Philip and St. James Church (Noarlunga, S.A.)

St. Philip and St. James Church (Noarlunga, S.A.)

Dissenters, Religious -- Great Britain.

Names, Personal -- Welsh.

Names, Personal -- Scottish.

Fox News contributor Jason Chaffetz and Andy McCarthy react to House Intelligence transcripts on Russia probe.

Ilaria Bianchini, Alessandra Guglielmi, Fernando A. Quintana.

Source: Bayesian Analysis, Volume 15, Number 1, 187--214.

Abstract:
We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead of using the rather restrictive case where analytical results are partially available, we adopt a spectral representation from which approximations to the DPP density functions can be readily computed. For the sake of concreteness the presentation focuses on a power exponential spectral density, but the proposed approach is in fact quite general. We later extend our model to incorporate covariate information in the likelihood and also in the assignment to mixture components, yielding a trade-off between repulsiveness of locations in the mixtures and attraction among subjects with similar covariates. We develop full Bayesian inference, and explore model properties and posterior behavior using several simulation scenarios and data illustrations. Supplementary materials for this article are available online (Bianchini et al., 2019).

Ioannis Ntzoufras, Claudia Tarantola, Monia Lupparelli.

Source: Bayesian Analysis, Volume 14, Number 3, 797--823.

Abstract:
We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

Haolun Shi, Guosheng Yin.

Source: Bayesian Analysis, Volume 14, Number 2, 399--425.

Abstract:
Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. To effectively maintain the overall type I error rate, we propose solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities. We present both theoretical and numerical methods for finding the optimal posterior probability boundaries with $alpha$ -spending functions that mimic those of the frequentist group sequential designs. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. We apply least-square fitting to find the $alpha$ -spending function closest to the target. We discuss the application of our method to single-arm and double-arm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.

Zhixiang Lin, Mahdi Zamanighomi, Timothy Daley, Shining Ma, Wing Hung Wong.

Source: Statistical Science, Volume 35, Number 1, 2--13.

Abstract:
Unsupervised methods, including clustering methods, are essential to the analysis of single-cell genomic data. Model-based clustering methods are under-explored in the area of single-cell genomics, and have the advantage of quantifying the uncertainty of the clustering result. Here we develop a model-based approach for the integrative analysis of single-cell chromatin accessibility and gene expression data. We show that combining these two types of data, we can achieve a better separation of the underlying cell types. An efficient Markov chain Monte Carlo algorithm is also developed.

Iain M. Johnstone.

Source: Statistical Science, Volume 34, Number 4, 657--668.

Abstract:
Many papers in the early part of Brown’s career focused on the admissibility or otherwise of estimators of a vector parameter. He established that inadmissibility of invariant estimators in three and higher dimensions is a general phenomenon, and found deep and beautiful connections between admissibility and other areas of mathematics. This review touches on several of his major contributions, with a focus on his celebrated 1971 paper connecting admissibility, recurrence and elliptic partial differential equations.

Nathan B. Cruze, Andreea L. Erciulescu, Balgobin Nandram, Wendy J. Barboza, Linda J. Young.

Source: Statistical Science, Volume 34, Number 2, 301--316.

Abstract:
In the United States, county-level estimates of crop yield, production, and acreage published by the United States Department of Agriculture’s National Agricultural Statistics Service (USDA NASS) play an important role in determining the value of payments allotted to farmers and ranchers enrolled in several federal programs. Given the importance of these official county-level crop estimates, NASS continually strives to improve its crops county estimates program in terms of accuracy, reliability and coverage. In 2015, NASS engaged a panel of experts convened under the auspices of the National Academies of Sciences, Engineering, and Medicine Committee on National Statistics (CNSTAT) for guidance on implementing models that may synthesize multiple sources of information into a single estimate, provide defensible measures of uncertainty, and potentially increase the number of publishable county estimates. The final report titled Improving Crop Estimates by Integrating Multiple Data Sources was released in 2017. This paper discusses several needs and requirements for NASS county-level crop estimates that were illuminated during the activities of the CNSTAT panel. A motivating example of planted acreage estimation in Illinois illustrates several challenges that NASS faces as it considers adopting any explicit model for official crops county estimates.

Eitan Greenshtein, Ya’acov Ritov.

Source: Statistical Science, Volume 34, Number 2, 224--228.

Abstract:
We present some personal reflections on empirical Bayes/ compound decision (EB/CD) theory following Efron (2019). In particular, we consider the role of exchangeability in the EB/CD theory and how it can be achieved when there are covariates. We also discuss the interpretation of EB/CD confidence interval, the theoretical efficiency of the CD procedure, and the impact of sparsity assumptions.

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