Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

On making multiple comparisons in clinical and experimental pharmacology and physiology

Abstract: 1. It is a central thesis of this review that in clinical and experimental pharmacology and physiology the goal of statistical analysis should be to minimize the risk of making any false-positive inferences from the results of an experiment (experimentwise Type I error). 2. It is common in clinical and experimental pharmacology and physiology for the effects of several treatments to be tested within a single experiment. Specific intercomparisons of these several effects, made in a pairwise or more complex fashion, inflates the risk of making false-positive inferences unless special statistical procedures are used. 3. A number of multiple comparison procedures is described and their ability to control experimentwise Type I error is evaluated critically. 4. When only a few (less than 5) of all possible pairwise or more complex comparisons are made between treatment groups, the Dunn-Sidak procedure provides maximum protection against excessive experimentwise Type I error and is very convenient to use. 5. When a control group is compared with all other treatment groups in a pairwise fashion, especially when the number of groups is large, the Dunnett procedure is more powerful than the Dunn-Sidak. 6. If investigators insist on making all possible pairwise comparisons among treatment groups, the Tukey-Kramer procedure provides maximum protection against false-positive inferences but inflates the Type II error rate. If it is especially important to avoid Type II error then the more complicated, stepwise procedures of the Ryan-Peritz-Welsch variety should be considered.

Learning Mallows Models with Pairwise Preferences

Abstract: Learning preference distributions is a key problem in many areas (e.g., recommender systems, IR, social choice). However, many existing methods require restrictive data models for evidence about user preferences. We relax these restrictions by considering as data arbitrary pairwise comparisons—the fundamental building blocks of ordinal rankings. We develop the first algorithms for learning Mallows models (and mixtures) with pairwise comparisons. At the heart is a new algorithm, the generalized repeated insertion model (GRIM), for sampling from arbitrary ranking distributions. We develop approximate samplers that are exact for many important special cases—and have provable bounds with pair-wise evidence—and derive algorithms for evaluating log-likelihood, learning Mallows mixtures, and non-parametric estimation. Experiments on large, real-world datasets show the effectiveness of our approach.

Regret theory with general choice sets

Abstract: The regret theory of choice under uncertainty proposed by Loomes and Sugden has performed well in explaining and predicting violations of Expected Utility theory. The original version of the model was confined to pairwise choices, which limited its usefulness as an economic theory of choice. Axioms for a more general form of regret theory have been proposed by Loomes and Sugden. In this article, it is shown that a simple nonmanipulability requirement is sufficient to characterize the functional form for regret theory with general choice sets. The stochastic dominance and comparative static properties of the model are outlined. A number of special cases are derived in which regret theory is equivalent to other well-known theories of choice under uncertainty.