Solving the Empirical Bayes Normal Means Problem with Correlated Noise

arXiv.org Machine Learning

The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Means problem assume that the observations are independent. In practice correlations are ubiquitous in real-world applications, and these correlations can grossly distort EB estimates. Here, exploiting theory from Schwartzman (2010), we develop new EB methods for solving the Normal Means problem that take account of unknown correlations among observations. We provide practical software implementations of these methods, and illustrate them in the context of large-scale multiple testing problems and False Discovery Rate (FDR) control. In realistic numerical experiments our methods compare favorably with other commonly-used multiple testing methods.


Bayesian Inference of Spreading Processes on Networks

arXiv.org Machine Learning

Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because the structure of these interactions matters for spreading processes, the pairwise relationships between individuals in a population can be usefully represented by a network. Although the underlying processes of transmission are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumors in an online social network. We study simulated simple and complex epidemics on synthetic networks and on two empirical networks, a social / contact network in an Indian village and an online social network in the U.S. Our goal is to learn simultaneously about the spreading process parameters and the source node (first infected node) of the epidemic, given a fixed and known network structure, and observations about state of nodes at several points in time. Our inference scheme is based on approximate Bayesian computation (ABC), an inference technique for complex models with likelihood functions that are either expensive to evaluate or analytically intractable. ABC enables us to adopt a Bayesian approach to the problem despite the posterior distribution being very complex. Our method is agnostic about the topology of the network and the nature of the spreading process. It generally performs well and, somewhat counter-intuitively, the inference problem appears to be easier on more heterogeneous network topologies, which enhances its future applicability to real-world settings where few networks have homogeneous topologies.


A Bayesian Group Sparse Multi-Task Regression Model for Imaging Genetics

arXiv.org Machine Learning

Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach for the analysis of imaging genomic studies using penalized multi-task regression with regularization based on a novel group $l_{2,1}$-norm penalty which encourages structured sparsity at both the gene level and SNP level. While incorporating a number of useful features, the proposed method only furnishes a point estimate of the regression coefficients; techniques for conducting statistical inference are not provided. A new Bayesian method is proposed here to overcome this limitation. Results: We develop a Bayesian hierarchical modeling formulation where the posterior mode corresponds to the estimator proposed by Wang et al. (Bioinformatics, 2012), and an approach that allows for full posterior inference including the construction of interval estimates for the regression parameters. We show that the proposed hierarchical model can be expressed as a three-level Gaussian scale mixture and this representation facilitates the use of a Gibbs sampling algorithm for posterior simulation. Simulation studies demonstrate that the interval estimates obtained using our approach achieve adequate coverage probabilities that outperform those obtained from the nonparametric bootstrap. Our proposed methodology is applied to the analysis of neuroimaging and genetic data collected as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI), and this analysis of the ADNI cohort demonstrates clearly the value added of incorporating interval estimation beyond only point estimation when relating SNPs to brain imaging endophenotypes.


The Flawed Reasoning Behind the Replication Crisis - Issue 74: Networks

Nautilus

Suppose we scan 1 million similar women, and we tell everyone who tests positive that they have cancer. Then we will have correctly told all 10,000 women with cancer that they have it. Of the remaining 990,000 women whose lumps were benign, we will incorrectly tell 49,500 women that they have cancer. Therefore, of the women we identify as having cancer, about 83 percent will have been incorrectly diagnosed. Imagine you or a loved one received a positive test result.


A comparative study of artificial intelligence and human doctors for the purpose of triage and diagnosis

arXiv.org Artificial Intelligence

Online symptom checkers have significant potential to improve patient care, however their reliability and accuracy remain variable. We hypothesised that an artificial intelligence (AI) powered triage and diagnostic system would compare favourably with human doctors with respect to triage and diagnostic accuracy. We performed a prospective validation study of the accuracy and safety of an AI powered triage and diagnostic system. Identical cases were evaluated by both an AI system and human doctors. Differential diagnoses and triage outcomes were evaluated by an independent judge, who was blinded from knowing the source (AI system or human doctor) of the outcomes. Independently of these cases, vignettes from publicly available resources were also assessed to provide a benchmark to previous studies and the diagnostic component of the MRCGP exam. Overall we found that the Babylon AI powered Triage and Diagnostic System was able to identify the condition modelled by a clinical vignette with accuracy comparable to human doctors (in terms of precision and recall). In addition, we found that the triage advice recommended by the AI System was, on average, safer than that of human doctors, when compared to the ranges of acceptable triage provided by independent expert judges, with only a minimal reduction in appropriateness.