Detection and explanation of statistical differences across a pair of groups

The task of explaining differences across groups is a task that people encounter often, not only in the research environment, but also in less formal settings. Existing statistical tools designed specifically for discovering and understanding differences are limited. The methods developed in this dissertation provide such tools and help understand what properties such tools should have to be successful and to motivate further development of new approaches to discovering and understanding differences. This dissertation presents a novel approach to comparing groups of data points. The process of comparing groups of data is divided into multiple stages: The learning of maximum a posteriori models for the data in each group, the identification of statistical differences between model parameters, the construction of a single model that captures those differences, and finally, the explanation of inferences of differences in marginal distributions in the form of an account of clinically significant contributions of elemental model differences to the marginal difference. A general framework for the process, applicable to a broad range of model types, is presented. This dissertation focuses on applying this framework to Bayesian networks over multinomial variables. To evaluate model learning and the detection of parameter differences an empirical evaluation of methods for identifying statistically significant differences and clinically significant differences is performed. To evaluate the generated explanations of how differences in the models account for the differences in probabilities computed from those models, case studies with real clinical data are presented, and the findings generated by explanations are discussed. An interactive prototype that allows a user to navigate through such an explanation is presented, and ideas are discussed for further development of data analysis tools for comparing groups of data

A brief summary of reviewed methods.

<p>Icons arranged in the table represent individual methods. The columns represent the various experiment selection criteria, and the methods are divided vertically between de novo methods and methods that use prior knowledge. Visual elements in each icon indicate whether the method is deterministic (cog) or stochastic (die), whether it models continuous (circle) or discrete (diamond) variables, what is specified in a query for an experiment (G for genetic and E for environmental perturbations), and the dimensionality of the data used (dot array for multidimensional data and a ruler for one-dimensional data).</p

Spatial cluster detection using dynamic programming

<p>Abstract</p> <p>Background</p> <p>The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster.</p> <p>Methods</p> <p>We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum <it>a-posteriori </it>(MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data.</p> <p>Results</p> <p>When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging.</p> <p>Conclusions</p> <p>We conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm.</p