Thomas Sellke

Bio: Thomas Sellke is an academic researcher from Purdue University. The author has contributed to research in topics: Null hypothesis & Hausdorff dimension. The author has an hindex of 20, co-authored 36 publications receiving 5332 citations. Previous affiliations of Thomas Sellke include Indiana University.

Redefine statistical significance

Abstract: We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.

Redefine Statistical Significance

Abstract: We propose to change the default P-value threshold for statistical significance for claims of new discoveries from 0.05 to 0.005.

Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence

Abstract: The problem of testing a point null hypothesis (or a “small interval” null hypothesis) is considered. Of interest is the relationship between the P value (or observed significance level) and conditional and Bayesian measures of evidence against the null hypothesis. Although one might presume that a small P value indicates the presence of strong evidence against the null, such is not necessarily the case. Expanding on earlier work [especially Edwards, Lindman, and Savage (1963) and Dickey (1977)], it is shown that actual evidence against a null (as measured, say, by posterior probability or comparative likelihood) can differ by an order of magnitude from the P value. For instance, data that yield a P value of .05, when testing a normal mean, result in a posterior probability of the null of at least .30 for any objective prior distribution. (“Objective” here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null; other definiti...

Calibration of p Values for Testing Precise Null Hypotheses

Abstract: P values are the most commonly used tool to measure evidence against a hypothesis or hypothesized model. Unfortunately, they are often incorrectly viewed as an error probability for rejection of the hypothesis or, even worse, as the posterior probability that the hypothesis is true. The fact that these interpretations can be completely misleading when testing precise hypotheses is first reviewed, through consideration of two revealing simulations. Then two calibrations of a ρ value are developed, the first being interpretable as odds and the second as either a (conditional) frequentist error probability or as the posterior probability of the hypothesis.

Impulse Control of Brownian Motion

Abstract: Consider a storage system, such as an inventory or cash fund, whose content fluctuates as a (μ, σ2) Brownian motion in the absence of control. Holding costs are continuously incurred at a rate proportional to the storage level and we may cause the storage level to jump by any desired amount at any time except that the content must be kept nonnegative. Both positive and negative jumps entail fixed plus proportional costs, and our objective is to minimize expected discounted costs over an infinite planning horizon. A control band policy is one that enforces an upward jump to q whenever level zero is hit, and enforces a downward jump to Q whenever level S is hit (0 < q < Q < S). We prove the existence of an optimal control band policy and calculate explicitly the optimal values of the critical numbers (q, Q, S).

Experimental Design and Data Analysis for Biologists

Abstract: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

Machine Learning : A Probabilistic Perspective

Abstract: Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Bayesian Model Selection in Social Research

Abstract: It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms.

Evaluation: from Precision, Recall and F-measure to ROC, Informedness, Markedness and Correlation

Abstract: Commonly used evaluation measures including Recall, Precision, F-Measure and Rand Accuracy are biased and should not be used without clear understanding of the biases, and corresponding identification of chance or base case levels of the statistic. Using these measures a system that performs worse in the objective sense of Informedness, can appear to perform better under any of these commonly used measures. We discuss several concepts and measures that reflect the probability that prediction is informed versus chance. Informedness and introduce Markedness as a dual measure for the probability that prediction is marked versus chance. Finally we demonstrate elegant connections between the concepts of Informedness, Markedness, Correlation and Significance as well as their intuitive relationships with Recall and Precision, and outline the extension from the dichotomous case to the general multi-class case.

Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests

Abstract: Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus (genus Carabus) ground beetles described by Sota and Vogler (2001). (AIC; Bayes factors; BIC; likelihood ratio tests; model averaging; model uncertainty; model selection; multimodel inference.) It is clear that models of nucleotide substitution (henceforth models of evolution) play a significant role in molecular phylogenetics, particularly in the context of distance, maximum likelihood (ML), and Bayesian es- timation. We know that the use of one or other model affects many, if not all, stages of phylogenetic inference. For example, estimates of phylogeny, substitution rates, bootstrap values, posterior probabilities, or tests of the molecular clock are clearly influenced by the model of evolution used in the analysis (Buckley, 2002; Buckley