Three children have now died in New York state from a possible complication from the coronavirus involving swollen blood vessels and heart problems, Gov. Andrew Cuomo said Saturday. At least 73 children in New York have been diagnosed with symptoms similar to Kawasaki disease — a rare inflammatory condition in children — and toxic shock syndrome.

Reaction and analysis from Fox News contributor Byron York and former Florida Attorney General Pam Bondi.

Vice President Pence’s trip to Iowa shows how the Trump administration’s aims to move past coronavirus are sometimes complicated by the virus itself.

Boeing CEO Dave Calhoun said the company was aiming to resume production this month, despite the ongoing grounding and coronavirus pandemic.

For millions of Americans, working at home isn't an option. NBC News identified seven occupations in which employees are at especially high risk of COVID-19.

Delta said it is making the move to protect employees amid the coronavirus pandemic, but planes have been flying near empty

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

The bombastic military parade through Moscow's Red Square on Saturday was slated to be the spectacle of the year on the Kremlin's calendar. Standing with Chinese leader Xi Jinping and French President Emmanuel Macron, President Vladimir Putin would have overseen a 90-minute procession of Russia's military might, showcasing 15,000 troops and the latest hardware. Now, military jets will roar over an eerily quiet Moscow, spurting red, white and blue smoke to mark 75 years since the defeat of Nazi Germany.

The New York City police department (NYPD) is conducting an internal investigation into a May 2 incident involving the violent arrests of multiple people, allegedly members of a group who were not social distancing

The staffer of Vice President Mike Pence who tested positive for coronavirus is apparently his press secretary and the wife of White House senior adviser Stephen Miller.Reports emerged on Friday that a member of Pence's staff had tested positive for COVID-19, creating a delay in his flight to Iowa amid concern over who may have been exposed. Later in the day, Trump said the staffer is a "press person" named Katie.Politico reported he was referring to Katie Miller, Pence's press secretary and the wife of Stephen Miller. This report noted this raises the risk that "a large swath of the West Wing's senior aides may also have been exposed." She confirmed her positive diagnosis to NBC News, saying she does not have symptoms.Trump spilled the beans to reporters, saying Katie Miller "hasn't come into contact with me" but has "spent some time with the vice president." This news comes one day after a personal valet to Trump tested positive for COVID-19, which reportedly made the president "lava level mad." Pence and Trump are being tested for COVID-19 every day.Asked Friday if he's concerned about the potential spread of coronavirus in the White House, Trump said "I'm not worried, no," adding that "we've taken very strong precautions."More stories from theweek.com Outed CIA agent Valerie Plame is running for Congress, and her launch video looks like a spy movie trailer 7 scathing cartoons about America's rush to reopen Trump says he couldn't have exposed WWII vets to COVID-19 because the wind was blowing the wrong way

The infections and deaths are spread across roughly two farms and 189 meat and processed food factories.

After his haircut, Sen. Ted Cruz said, "It was ridiculous to see somebody sentenced to seven days in jail for cutting hair."

Some Democrats took "Believe Women" literally until Joe Biden was accused. Now they're relearning that guilt-by-accusation doesn't serve justice.

The Democracy Fund + UCLA Nationscape Project found some misinformation about the coronavirus is more widespread that you might think.

The news comes shortly after a valet who served meals to President Trump also tested positive for the virus.

China says it will improve public health systems after criticism of its early response to the virus.

Zhi-Qiang Wang, Nian-Sheng Tang.

Source: Bayesian Analysis, Volume 15, Number 2, 579--604.

Abstract:
Bayesian inference on quantile regression (QR) model with mixed discrete and non-ignorable missing covariates is conducted by reformulating QR model as a hierarchical structure model. A probit regression model is adopted to specify missing covariate mechanism. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is developed to simultaneously produce Bayesian estimates of unknown parameters and latent variables as well as their corresponding standard errors. Bayesian variable selection method is proposed to recognize significant covariates. A Bayesian local influence procedure is presented to assess the effect of minor perturbations to the data, priors and sampling distributions on posterior quantities of interest. Several simulation studies and an example are presented to illustrate the proposed methodologies.

Maxim Rabinovich, Aaditya Ramdas, Michael I. Jordan, Martin J. Wainwright.

Source: Bayesian Analysis, Volume 15, Number 2, 505--532.

Abstract:
Slow mixing is the central hurdle is applications of Markov chains, especially those used for Monte Carlo approximations (MCMC). In the setting of Bayesian inference, it is often only of interest to estimate the stationary expectations of a small set of functions, and so the usual definition of mixing based on total variation convergence may be too conservative. Accordingly, we introduce function-specific analogs of mixing times and spectral gaps, and use them to prove Hoeffding-like function-specific concentration inequalities. These results show that it is possible for empirical expectations of functions to concentrate long before the underlying chain has mixed in the classical sense, and we show that the concentration rates we achieve are optimal up to constants. We use our techniques to derive confidence intervals that are sharper than those implied by both classical Markov-chain Hoeffding bounds and Berry-Esseen-corrected central limit theorem (CLT) bounds. For applications that require testing, rather than point estimation, we show similar improvements over recent sequential testing results for MCMC. We conclude by applying our framework to real-data examples of MCMC, providing evidence that our theory is both accurate and relevant to practice.

Xuan Cao, Kshitij Khare, Malay Ghosh.

Source: Bayesian Analysis, Volume 15, Number 1, 241--262.

Abstract:
The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an important tuning parameter which reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. Current approaches treat the scale parameter as given, and suggest choices based on prior coverage/asymptotic considerations. In this paper, we consider the fully Bayesian approach introduced in (Wu, 2016) with the pMOM non-local prior and an appropriate Inverse-Gamma prior on the tuning parameter to analyze the underlying theoretical property. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where $p$ is allowed to increase at a polynomial rate with $n$ or even at a sub-exponential rate with $n$ . Through simulation studies, we demonstrate that our model selection procedure can outperform other Bayesian methods which treat the scale parameter as given, and commonly used penalized likelihood methods, in a range of simulation settings.

Abhishek Bishoyi, Xiaojing Wang, Dipak K. Dey.

Source: Bayesian Analysis, Volume 15, Number 1, 215--239.

Abstract:
Missing data often appear as a practical problem while applying classical models in the statistical analysis. In this paper, we consider a semiparametric regression model in the presence of missing covariates for nonparametric components under a Bayesian framework. As it is known that Gaussian processes are a popular tool in nonparametric regression because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, in the absence of covariates, the most frequently used covariance functions of a Gaussian process will not be well defined. We propose an imputation method to solve this issue and perform our analysis using Bayesian inference, where we specify the objective priors on the parameters of Gaussian process models. Several simulations are conducted to illustrate effectiveness of our proposed method and further, our method is exemplified via two real datasets, one through Langmuir equation, commonly used in pharmacokinetic models, and another through Auto-mpg data taken from the StatLib library.

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.

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.

Nadja Klein, Michael Stanley Smith.

Source: Bayesian Analysis, Volume 14, Number 4, 1143--1171.

Abstract:
We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors—a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection—and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions.

Claudia Kirch, Matthew C. Edwards, Alexander Meier, Renate Meyer.

Source: Bayesian Analysis, Volume 14, Number 4, 1037--1073.

Abstract:
Nonparametric Bayesian inference has seen a rapid growth over the last decade but only few nonparametric Bayesian approaches to time series analysis have been developed. Most existing approaches use Whittle’s likelihood for Bayesian modelling of the spectral density as the main nonparametric characteristic of stationary time series. It is known that the loss of efficiency using Whittle’s likelihood can be substantial. On the other hand, parametric methods are more powerful than nonparametric methods if the observed time series is close to the considered model class but fail if the model is misspecified. Therefore, we suggest a nonparametric correction of a parametric likelihood that takes advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. We use a nonparametric Bernstein polynomial prior on the spectral density with weights induced by a Dirichlet process and prove posterior consistency for Gaussian stationary time series. Bayesian posterior computations are implemented via an MH-within-Gibbs sampler and the performance of the nonparametrically corrected likelihood for Gaussian time series is illustrated in a simulation study and in three astronomy applications, including estimating the spectral density of gravitational wave data from the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO).

Jon Cockayne, Chris J. Oates, Ilse C.F. Ipsen, Mark Girolami.

Source: Bayesian Analysis, Volume 14, Number 3, 937--1012.

Abstract:
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about, for example, the magnitude of the error. In this paper we propose a novel statistical model for this error, set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging.

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.

Luis Gutiérrez, Andrés F. Barrientos, Jorge González, Daniel Taylor-Rodríguez.

Source: Bayesian Analysis, Volume 14, Number 2, 649--675.

Abstract:
We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.

Marcos Oliveira Prates, Renato Martins Assunção, Erica Castilho Rodrigues.

Source: Bayesian Analysis, Volume 14, Number 2, 623--647.

Abstract:
Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Techniques to alleviate this problem are based on decomposing the spatial random effect and fitting a restricted spatial regression. In this paper, we propose a different approach: a transformation of the geographic space to ensure that the unobserved spatial random effect added to the regression is orthogonal to the fixed effects covariates. Our approach, named SPOCK, has the additional benefit of providing a fast and simple computational method to estimate the parameters. Also, it does not constrain the distribution class assumed for the spatial error term. A simulation study and real data analyses are presented to better understand the advantages of the new method in comparison with the existing ones.

Marko Järvenpää, Michael U. Gutmann, Arijus Pleska, Aki Vehtari, Pekka Marttinen.

Source: Bayesian Analysis, Volume 14, Number 2, 595--622.

Abstract:
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.

Quan Zhou, Yongtao Guan.

Source: Bayesian Analysis, Volume 14, Number 2, 573--594.

Abstract:
Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special class of linear systems, which can increase the speed of the BVSR model-fitting tenfold. The iterative method hinges on the complex factorization of the sum of two matrices and the solution path resides in the complex domain (instead of the real domain). Compared to the Gauss-Seidel method, the complex factorization converges almost instantaneously and its error is several magnitude smaller than that of the Gauss-Seidel method. More importantly, the error is always within the pre-specified precision while the Gauss-Seidel method is not. For large problems with thousands of covariates, the complex factorization is 10–100 times faster than either the Gauss-Seidel method or the direct method via the Cholesky decomposition. In BVSR, one needs to repetitively solve large penalized regression systems whose design matrices only change slightly between adjacent MCMC steps. This slight change in design matrix enables the adaptation of the iterative complex factorization method. The computational innovation will facilitate the wide-spread use of BVSR in reanalyzing genome-wide association datasets.

Joris Mulder, Jean-Paul Fox.

Source: Bayesian Analysis, Volume 14, Number 2, 521--552.

Abstract:
The intraclass correlation plays a central role in modeling hierarchically structured data, such as educational data, panel data, or group-randomized trial data. It represents relevant information concerning the between-group and within-group variation. Methods for Bayesian hypothesis tests concerning the intraclass correlation are proposed to improve decision making in hierarchical data analysis and to assess the grouping effect across different group categories. Estimation and testing methods for the intraclass correlation coefficient are proposed under a marginal modeling framework where the random effects are integrated out. A class of stretched beta priors is proposed on the intraclass correlations, which is equivalent to shifted $F$ priors for the between groups variances. Through a parameter expansion it is shown that this prior is conditionally conjugate under the marginal model yielding efficient posterior computation. A special improper case results in accurate coverage rates of the credible intervals even for minimal sample size and when the true intraclass correlation equals zero. Bayes factor tests are proposed for testing multiple precise and order hypotheses on intraclass correlations. These tests can be used when prior information about the intraclass correlations is available or absent. For the noninformative case, a generalized fractional Bayes approach is developed. The method enables testing the presence and strength of grouped data structures without introducing random effects. The methodology is applied to a large-scale survey study on international mathematics achievement at fourth grade to test the heterogeneity in the clustering of students in schools across countries and assessment cycles.

Benjamin Letham, Brian Karrer, Guilherme Ottoni, Eytan Bakshy.

Source: Bayesian Analysis, Volume 14, Number 2, 495--519.

Abstract:
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error. Bayesian optimization is a promising technique for efficiently optimizing multiple continuous parameters, but existing approaches degrade in performance when the noise level is high, limiting its applicability to many randomized experiments. We derive an expression for expected improvement under greedy batch optimization with noisy observations and noisy constraints, and develop a quasi-Monte Carlo approximation that allows it to be efficiently optimized. Simulations with synthetic functions show that optimization performance on noisy, constrained problems outperforms existing methods. We further demonstrate the effectiveness of the method with two real-world experiments conducted at Facebook: optimizing a ranking system, and optimizing server compiler flags.

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.

Peter D. Hoff

Source: Bayesian Anal., Volume 6, Number 2, 179--196.

Abstract:
Modern datasets are often in the form of matrices or arrays, potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as well as correlation among the variables. A possible model for matrix-valued data is the class of matrix normal distributions, which is parametrized by two covariance matrices, one for each index set of the data. In this article we discuss an extension of the matrix normal model to accommodate multidimensional data arrays, or tensors. We show how a particular array-matrix product can be used to generate the class of array normal distributions having separable covariance structure. We derive some properties of these covariance structures and the corresponding array normal distributions, and show how the array-matrix product can be used to define a semi-conjugate prior distribution and calculate the corresponding posterior distribution. We illustrate the methodology in an analysis of multivariate longitudinal network data which take the form of a four-way array.

Ruosi Guo, Chunming Zhang, Zhengjun Zhang.

Source: Statistical Science, Volume 35, Number 1, 145--157.

Abstract:
In many scientific disciplines, finding hidden influential factors behind observational data is essential but challenging. The majority of existing approaches, such as the independent component analysis (${mathrm{ICA}}$), rely on linear transformation, that is, true signals are linear combinations of hidden components. Motivated from analyzing nonlinear temporal signals in neuroscience, genetics, and finance, this paper proposes the “maximum independent component analysis” (${mathrm{MaxICA}}$), based on max-linear combinations of components. In contrast to existing methods, ${mathrm{MaxICA}}$ benefits from focusing on significant major components while filtering out ignorable components. A major tool for parameter learning of ${mathrm{MaxICA}}$ is an augmented genetic algorithm, consisting of three schemes for the elite weighted sum selection, randomly combined crossover, and dynamic mutation. Extensive empirical evaluations demonstrate the effectiveness of ${mathrm{MaxICA}}$ in either extracting max-linearly combined essential sources in many applications or supplying a better approximation for nonlinearly combined source signals, such as $mathrm{EEG}$ recordings analyzed in this paper.

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.

Thomas Staudt, Timo Aspelmeier, Oskar Laitenberger, Claudia Geisler, Alexander Egner, Axel Munk.

Source: Statistical Science, Volume 35, Number 1, 92--111.

Abstract:
Super-resolution microscopy is rapidly gaining importance as an analytical tool in the life sciences. A compelling feature is the ability to label biological units of interest with fluorescent markers in (living) cells and to observe them with considerably higher resolution than conventional microscopy permits. The images obtained this way, however, lack an absolute intensity scale in terms of numbers of fluorophores observed. In this article, we discuss state of the art methods to count such fluorophores and statistical challenges that come along with it. In particular, we suggest a modeling scheme for time series generated by single-marker-switching (SMS) microscopy that makes it possible to quantify the number of markers in a statistically meaningful manner from the raw data. To this end, we model the entire process of photon generation in the fluorophore, their passage through the microscope, detection and photoelectron amplification in the camera, and extraction of time series from the microscopic images. At the heart of these modeling steps is a careful description of the fluorophore dynamics by a novel hidden Markov model that operates on two timescales (HTMM). Besides the fluorophore number, information about the kinetic transition rates of the fluorophore’s internal states is also inferred during estimation. We comment on computational issues that arise when applying our model to simulated or measured fluorescence traces and illustrate our methodology on simulated data.

Peter J. Diggle, Emanuele Giorgi, Julienne Atsame, Sylvie Ntsame Ella, Kisito Ogoussan, Katherine Gass.

Source: Statistical Science, Volume 35, Number 1, 42--50.

Abstract:
Vector-borne diseases have long presented major challenges to the health of rural communities in the wet tropical regions of the world, but especially in sub-Saharan Africa. In this paper, we describe the contribution that statistical modelling has made to the global elimination programme for one vector-borne disease, onchocerciasis. We explain why information on the spatial distribution of a second vector-borne disease, Loa loa, is needed before communities at high risk of onchocerciasis can be treated safely with mass distribution of ivermectin, an antifiarial medication. We show how a model-based geostatistical analysis of Loa loa prevalence survey data can be used to map the predictive probability that each location in the region of interest meets a WHO policy guideline for safe mass distribution of ivermectin and describe two applications: one is to data from Cameroon that assesses prevalence using traditional blood-smear microscopy; the other is to Africa-wide data that uses a low-cost questionnaire-based method. We describe how a recent technological development in image-based microscopy has resulted in a change of emphasis from prevalence alone to the bivariate spatial distribution of prevalence and the intensity of infection among infected individuals. We discuss how statistical modelling of the kind described here can contribute to health policy guidelines and decision-making in two ways. One is to ensure that, in a resource-limited setting, prevalence surveys are designed, and the resulting data analysed, as efficiently as possible. The other is to provide an honest quantification of the uncertainty attached to any binary decision by reporting predictive probabilities that a policy-defined condition for action is or is not met.

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.

Alessandro Rinaldo, Ryan J. Tibshirani, Larry Wasserman.

Source: Statistical Science, Volume 34, Number 4, 599--603.

Abstract:
What is the meaning of a regression parameter? Why is this the de facto standard object of interest for statistical inference? These are delicate issues, especially when the model is misspecified. We argue that focusing on predictive quantities may be a desirable alternative.

David Whitney, Ali Shojaie, Marco Carone.

Source: Statistical Science, Volume 34, Number 4, 591--598.

Anthony C. Davison, Erwan Koch, Jonathan Koh.

Source: Statistical Science, Volume 34, Number 4, 584--590.

Abstract:
This discussion focuses on areas of disagreement with the papers, particularly the target of inference and the case for using the robust ‘sandwich’ variance estimator in the presence of moderate mis-specification. We also suggest that existing procedures may be appreciably more powerful for detecting mis-specification than the authors’ RAV statistic, and comment on the use of the pairs bootstrap in balanced situations.

Roderick J. Little.

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

Nikki L. B. Freeman, Xiaotong Jiang, Owen E. Leete, Daniel J. Luckett, Teeranan Pokaprakarn, Michael R. Kosorok.

Source: Statistical Science, Volume 34, Number 4, 572--574.

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.

Andreas Buja, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 523--544.

Abstract:
In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x extrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x extrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.