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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Group invariant inferred distributions via noncommutative probability
B. Heller, M. Wang · 2006-11-22 · via math.ST updates on arXiv.org

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Bayes' method and in particular without using a joint distribution of random variable and parameter. In the Poisson and binomial cases, the final formulas for inferred distributions coincide with the formulas for Bayes posteriors with uniform priors.

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