Antony Overstall, James McGree.

Source: Bayesian Analysis, Volume 15, Number 1, 103--131.

Abstract:
A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the utility and expected utility are rarely available in closed form and require approximation. Secondly, the design space can be of high-dimensionality. In the case of intractable likelihood models, these problems are compounded by the fact that the likelihood function, whose evaluation is required to approximate the expected utility, is not available in closed form. A strategy is proposed to find Bayesian designs for intractable likelihood models. It relies on the development of an automatic, auxiliary modelling approach, using multivariate Gaussian process emulators, to approximate the likelihood function. This is then combined with a copula-based approach to approximate the marginal likelihood (a quantity commonly required to evaluate many utility functions). These approximations are demonstrated on examples of stochastic process models involving experimental aims of both parameter estimation and model comparison.

Nicolas Garcia Trillos, Daniel Sanz-Alonso.

Source: Bayesian Analysis, Volume 15, Number 1, 29--56.

Abstract:
The Bayesian update can be viewed as a variational problem by characterizing the posterior as the minimizer of a functional. The variational viewpoint is far from new and is at the heart of popular methods for posterior approximation. However, some of its consequences seem largely unexplored. We focus on the following one: defining the posterior as the minimizer of a functional gives a natural path towards the posterior by moving in the direction of steepest descent of the functional. This idea is made precise through the theory of gradient flows, allowing to bring new tools to the study of Bayesian models and algorithms. Since the posterior may be characterized as the minimizer of different functionals, several variational formulations may be considered. We study three of them and their three associated gradient flows. We show that, in all cases, the rate of convergence of the flows to the posterior can be bounded by the geodesic convexity of the functional to be minimized. Each gradient flow naturally suggests a nonlinear diffusion with the posterior as invariant distribution. These diffusions may be discretized to build proposals for Markov chain Monte Carlo (MCMC) algorithms. By construction, the diffusions are guaranteed to satisfy a certain optimality condition, and rates of convergence are given by the convexity of the functionals. We use this observation to propose a criterion for the choice of metric in Riemannian MCMC methods.

Andrea Cremaschi, Raffaele Argiento, Katherine Shoemaker, Christine Peterson, Marina Vannucci.

Source: Bayesian Analysis, Volume 14, Number 4, 1271--1301.

Abstract:
Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate $t$ -distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet $t$ -distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.

Lutz F. Gruber, Erica F. Stuber, Lyndsie S. Wszola, Joseph J. Fontaine.

Source: Bayesian Analysis, Volume 14, Number 4, 1173--1199.

Abstract:
We present an integrated open population model where the population dynamics are defined by a differential equation, and the related statistical model utilizes a Poisson binomial convolution likelihood. Key advantages of the proposed approach over existing open population models include the flexibility to predict related, but unobserved quantities such as total immigration or emigration over a specified time period, and more computationally efficient posterior simulation by elimination of the need to explicitly simulate latent immigration and emigration. The viability of the proposed method is shown in an in-depth analysis of outdoor recreation participation on public lands, where the surveyed populations changed rapidly and demographic population closure cannot be assumed even within a single day.

Lizhen Lin, Niu Mu, Pokman Cheung, David Dunson.

Source: Bayesian Analysis, Volume 14, Number 3, 907--926.

Abstract:
Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications, methods, theory and algorithms related to GPs, the overwhelming majority of this literature focuses on the case in which the input domain corresponds to a Euclidean space. However, particularly in recent years with the increasing collection of complex data, it is commonly the case that the input domain does not have such a simple form. For example, it is common for the inputs to be restricted to a non-Euclidean manifold, a case which forms the motivation for this article. In particular, we propose a general extrinsic framework for GP modeling on manifolds, which relies on embedding of the manifold into a Euclidean space and then constructing extrinsic kernels for GPs on their images. These extrinsic Gaussian processes (eGPs) are used as prior distributions for unknown functions in Bayesian inferences. Our approach is simple and general, and we show that the eGPs inherit fine theoretical properties from GP models in Euclidean spaces. We consider applications of our models to regression and classification problems with predictors lying in a large class of manifolds, including spheres, planar shape spaces, a space of positive definite matrices, and Grassmannians. Our models can be readily used by practitioners in biological sciences for various regression and classification problems, such as disease diagnosis or detection. Our work is also likely to have impact in spatial statistics when spatial locations are on the sphere or other geometric spaces.

Mengyang Gu.

Source: Bayesian Analysis, Volume 14, Number 3, 877--905.

Abstract:
Gaussian stochastic process (GaSP) has been widely used in two fundamental problems in uncertainty quantification, namely the emulation and calibration of mathematical models. Some objective priors, such as the reference prior, are studied in the context of emulating (approximating) computationally expensive mathematical models. In this work, we introduce a new class of priors, called the jointly robust prior, for both the emulation and calibration. This prior is designed to maintain various advantages from the reference prior. In emulation, the jointly robust prior has an appropriate tail decay rate as the reference prior, and is computationally simpler than the reference prior in parameter estimation. Moreover, the marginal posterior mode estimation with the jointly robust prior can separate the influential and inert inputs in mathematical models, while the reference prior does not have this property. We establish the posterior propriety for a large class of priors in calibration, including the reference prior and jointly robust prior in general scenarios, but the jointly robust prior is preferred because the calibrated mathematical model typically predicts the reality well. The jointly robust prior is used as the default prior in two new R packages, called “RobustGaSP” and “RobustCalibration”, available on CRAN for emulation and calibration, respectively.

Joseph Antonelli, Giovanni Parmigiani, Francesca Dominici.

Source: Bayesian Analysis, Volume 14, Number 3, 825--848.

Abstract:
In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ( $p$ ) is larger than the number of observations ( $n$ ), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable $X_{j}$ is strongly associated with the treatment $T$ but weakly with the outcome $Y$ , the coefficient $eta_{j}$ will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients $eta_{j}$ corresponding to the potential confounders $X_{j}$ . Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients ( $eta_{j}$ s) of the $X_{j}$ s that are strongly associated with $T$ but weakly associated with $Y$ . We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.

Stefano Peluso, Siddhartha Chib, Antonietta Mira.

Source: Bayesian Analysis, Volume 14, Number 3, 727--751.

Abstract:
We develop a general Bayesian semiparametric change-point model in which separate groups of structural parameters (for example, location and dispersion parameters) can each follow a separate multiple change-point process, driven by time-dependent transition matrices among the latent regimes. The distribution of the observations within regimes is unknown and given by a Dirichlet process mixture prior. The properties of the proposed model are studied theoretically through the analysis of inter-arrival times and of the number of change-points in a given time interval. The prior-posterior analysis by Markov chain Monte Carlo techniques is developed on a forward-backward algorithm for sampling the various regime indicators. Analysis with simulated data under various scenarios and an application to short-term interest rates are used to show the generality and usefulness of the proposed model.

Divyansh Agarwal, Jingshu Wang, Nancy R. Zhang.

Source: Statistical Science, Volume 35, Number 1, 112--128.

Abstract:
Single cell sequencing technologies are transforming biomedical research. However, due to the inherent nature of the data, single cell RNA sequencing analysis poses new computational and statistical challenges. We begin with a survey of a selection of topics in this field, with a gentle introduction to the biology and a more detailed exploration of the technical noise. We consider in detail the problem of single cell data denoising, sometimes referred to as “imputation” in the relevant literature. We discuss why this is not a typical statistical imputation problem, and review current approaches to this problem. We then explore why the use of denoised values in downstream analyses invites novel statistical insights, and how denoising uncertainty should be accounted for to yield valid statistical inference. The utilization of denoised or imputed matrices in statistical inference is not unique to single cell genomics, and arises in many other fields. We describe the challenges in this type of analysis, discuss some preliminary solutions, and highlight unresolved issues.

Yazhen Wang, Xinyu Song.

Source: Statistical Science, Volume 35, Number 1, 51--74.

Abstract:
Quantum science and quantum technology are of great current interest in multiple frontiers of many scientific fields ranging from computer science to physics and chemistry, and from engineering to mathematics and statistics. Their developments will likely lead to a new wave of scientific revolutions and technological innovations in a wide range of scientific studies and applications. This paper provides a brief review on quantum communication, quantum information, quantum computation, quantum simulation, and quantum metrology. We present essential quantum properties, illustrate relevant concepts of quantum science and quantum technology, and discuss their scientific developments. We point out the need for statistical analysis in their developments, as well as their potential applications to and impacts on statistics and data science.

Adam R. Brentnall, Jack Cuzick.

Source: Statistical Science, Volume 35, Number 1, 14--30.

Abstract:
Strategies to prevent cancer and diagnose it early when it is most treatable are needed to reduce the public health burden from rising disease incidence. Risk assessment is playing an increasingly important role in targeting individuals in need of such interventions. For breast cancer many individual risk factors have been well understood for a long time, but the development of a fully comprehensive risk model has not been straightforward, in part because there have been limited data where joint effects of an extensive set of risk factors may be estimated with precision. In this article we first review the approach taken to develop the IBIS (Tyrer–Cuzick) model, and describe recent updates. We then review and develop methods to assess calibration of models such as this one, where the risk of disease allowing for competing mortality over a long follow-up time or lifetime is estimated. The breast cancer risk model model and calibration assessment methods are demonstrated using a cohort of 132,139 women attending mammography screening in the State of Washington, USA.

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.

James O. Berger, Anirban DasGupta.

Source: Statistical Science, Volume 34, Number 4, 621--634.

Abstract:
This article gives a panoramic survey of the general area of parametric statistical inference, decision theory and foundations of statistics for the period 1965–2010 through the lens of Larry Brown’s contributions to varied aspects of this massive area. The article goes over sufficiency, shrinkage estimation, admissibility, minimaxity, complete class theorems, estimated confidence, conditional confidence procedures, Edgeworth and higher order asymptotic expansions, variational Bayes, Stein’s SURE, differential inequalities, geometrization of convergence rates, asymptotic equivalence, aspects of empirical process theory, inference after model selection, unified frequentist and Bayesian testing, and Wald’s sequential theory. A reasonably comprehensive bibliography is provided.

Roderick J. Little.

Source: Statistical Science, Volume 34, Number 4, 580--583.

Jerald F. Lawless.

Source: Statistical Science, Volume 34, Number 4, 569--571.

Abstract:
I comment on the papers Models as Approximations I and II, by A. Buja, R. Berk, L. Brown, E. George, E. Pitkin, M. Traskin, L. Zhao and K. Zhang.

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.

Bradley Efron.

Source: Statistical Science, Volume 34, Number 2, 234--235.

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.

Aad van der Vaart.

Source: Statistical Science, Volume 34, Number 2, 214--218.

Nan Laird.

Source: Statistical Science, Volume 34, Number 2, 206--208.

Thomas A. Louis.

Source: Statistical Science, Volume 34, Number 2, 202--205.

Bradley Efron.

Source: Statistical Science, Volume 34, Number 2, 177--201.

Abstract:
This article concerns the Bayes and frequentist aspects of empirical Bayes inference. Some of the ideas explored go back to Robbins in the 1950s, while others are current. Several examples are discussed, real and artificial, illustrating the two faces of empirical Bayes methodology: “oracle Bayes” shows empirical Bayes in its most frequentist mode, while “finite Bayes inference” is a fundamentally Bayesian application. In either case, modern theory and computation allow us to present a sharp finite-sample picture of what is at stake in an empirical Bayes analysis.

Georg Lindgren.

Source: Statistical Science, Volume 34, Number 1, 100--128.

Abstract:
We describe and compare how methods based on the classical Rice’s formula for the expected number, and higher moments, of level crossings by a Gaussian process stand up to contemporary numerical methods to accurately deal with crossing related characteristics of the sample paths. We illustrate the relative merits in accuracy and computing time of the Rice moment methods and the exact numerical method, developed since the late 1990s, on three groups of distribution problems, the maximum over a finite interval and the waiting time to first crossing, the length of excursions over a level, and the joint period/amplitude of oscillations. We also treat the notoriously difficult problem of dependence between successive zero crossing distances. The exact solution has been known since at least 2000, but it has remained largely unnoticed outside the ocean science community. Extensive simulation studies illustrate the accuracy of the numerical methods. As a historical introduction an attempt is made to illustrate the relation between Rice’s original formulation and arguments and the exact numerical methods.

Vincent Dorie, Jennifer Hill, Uri Shalit, Marc Scott, Dan Cervone.

Source: Statistical Science, Volume 34, Number 1, 94--99.

Abstract:
Response to discussion of Dorie (2017), in which the authors of that piece express their gratitude to the discussants, rebut some specific criticisms, and argue that the limitations of the 2016 Atlantic Causal Inference Competition represent an exciting opportunity for future competitions in a similar mold.

Elizabeth A. Stuart

Source: Statist. Sci., Volume 25, Number 1, 1--21.

Abstract:
When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods—or developing methods related to matching—do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

London : Cleanair, Smoke-free Environment (33 Stillness Rd, London, SE23 1NG), [198-?]

London : Cleanair, Smoke-free Environment (33 Stillness Rd, London, SE23 1NG), [198-?]

[London?], [199-?]

[London], 2019.

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