Weak Conditional Independence and Relative Invariance in Bayesian Statistics

Jean-Pierre Florens (), Michel Mouchart () and Jean-Marie Rolin
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Jean-Pierre Florens: Université Toulouse Capitole, Toulouse School of Economics
Michel Mouchart: Université Catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences
Jean-Marie Rolin: Université Catholique de Louvain, Institut de Statistique

Chapter Chapter 2 in Nonparametric Bayesian Inference, 2024, pp 19-43 from Springer

Abstract: Abstract In this chapter, the concept of invariance, standard in measure theory, is extended to the conditional case and is shown to provide a suitable framework to define invariant Bayesian experiments, even in the case of improper prior distributions. Also, the concept of conditional independence, standard in probability theory, is extended to the case of σ $$\sigma $$ -finite (but unbounded) measures. Both extensions require, as a preliminary step, to work out necessary conditions for the existence of a well-defined “marginal-conditional” decomposition (actually, a desintegration) or a σ $$\sigma $$ -finite measure. This framework is then used to handle invariance arguments in Bayesian statistics, with a particular emphasis on the search for mutually sufficient pairs of parameters and statistics.

Date: 2024
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DOI: 10.1007/978-3-031-61329-6_2

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