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Exploratory Inference

 Kathryn Ziegler, PhD Candidate, Johns Hopkins Department of Biostatistics

Building on the work of Royall, Blume, Tsou and others various likelihoods are explored from the evidential perspective. Included in the exploration are multinomial likelihoods resulting from grouping data, order statistic likelihoods, likelihoods for quantiles and marginal likelihoods. Quantile likelihood is equivalent to Empirical Likelihood as introduced by Owens. It is also the case that multinomial likelihoods are a special case of Empirical likelihood. This equivalence suggests that evidential properties hold in for certain Empirical likelihoods. Graphical displays of these likelihood functions allow us to explore parameter support based on observed data and distributional assumptions (a working model). Additionally the non-central t and F distributions are used to obtain marginal likelihoods for several important parameters including the coefficient of variation, the one and two sample effect size, the overlapping coefficient, the area under an ROC curve, and the shrinkage parameter. These likelihoods are true likelihoods. The probabilities of misleading and weak evidence can be obtained and the universal bound on the probability of observing misleading evidence applies. In addition use of reference priors allows for Bayesian analysis. The graphical display of parameter support and uncertainty provide clean alternatives to typically computationally intensive confidence interval calculations.

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