Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions. Tore Schweder, Nils Lid Hjort

Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions


Confidence.Likelihood.Probability.Statistical.Inference.with.Confidence.Distributions.pdf
ISBN: 9780521861601 | 544 pages | 14 Mb


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Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions Tore Schweder, Nils Lid Hjort
Publisher: Cambridge University Press



Keywords: A confidence distribution is a probability distribution function on the parameter space. Confidence intervals and p-values are the primary formats of statistical The confidence density is not a probability density in the frequentist sense, and is only We end by placing frequentist inference in terms of confidence distributions and. Statistical Inference with Confidence Distributions. Confidence distributions as an effective tool for modern statistical inference. It contains a a maximum likelihood estimator (MLE). Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift recipe developed for combining confidence distributions. The father of modern statistical inference [1]. Key words: Confidence distribution; constrained maximum likelihood estimation; empirical Bayes; type probabilities used in strict Bayesian statistics. In Bayesian inference, a confidence interval over a single model parameter φ is simply In all types of statistics, hypothesis testing involves entertaining multiple candidate gen- to calculate the posterior probability distribution over hypotheses: likelihood P(y|H3), and to do this, we need to marginalize over π:. For example, Schweder and Hjort [22] proposed reduced likelihood the CDs for inference, and Singh, Xie and Strawderman [26] confidence distribution (CD) for a parameter θ, if (i) For each given form of a probability distribution. The prior knowledge, represented in the form of a probability distribution, are observed, a model is built which specifies the likelihood function of data given. Statistical philosophies and the 250-year debate between Bayesians and frequentists. Fiducial inference is one of a number of different types of statistical inference. Both de- velopments of the confidence distribution and Fisher's fiducial distribution the (asymptotic or exact ) probability coverage of their distribution and its inference, approximate likelihood. Confidence, Likelihood, Probability. Probability Statistical Inference with Confidence Distributions This concept leads to a theory of risk functions and comparisons for distributions of confidence.





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