Bayesian Gaussian One- and Two-Parameter Models

Bayesian Gaussian One- and Two-Parameter Models

Bayesian Gaussian Models

One- and two-parameter Bayesian Gaussian models are models with a Gaussian likelihood or Gaussian observation model. They are as stand-alone models of limited scientific value. Instead, their importance lies in being simple statistical toys to allow some 'finger exercises' or cognitive 'etudes' in model conception, data analysis,  formula-based inference with conjugate priors, and simulation-based inference with a probabilistic programming language (PPL; e.g. TURING.jl). Because of their ubiquitousness the probability is high that these models can be found in libraries of other PPLs so that comparisons with respect to utility, comprehensability, and effectiveness are possible.

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This is a draft. Comments or hints for bug fixes are welcome:

Prof. Dr. Claus Möbus:

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1. One-Parameter Model: Unknown Mean and Known Variance

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This is a draft. Comments or hints for bug fixes are welcome:

Prof. Dr. Claus Möbus:

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2. One-Parameter Model: Known Mean and Unknown Variance

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This is a draft. Comments or hints for bug fixes are welcome:

Prof. Dr. Claus Möbus:

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3. Two-parameter Model: Unknown Mean and Variance

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This is a draft. Comments or hints for bug fixes are welcome:

Prof. Dr. Claus Möbus:

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(Changed: 2021-06-07)