A convergence theorem with application to Bayesian inference. (Spanish. English summary) Zbl 0654.62031

A theorem is proved showing that, under some boundary conditions, the following hypotheses:
1. \(\{X_ n\}\) is a sequence of continuous random variables which “approaches in probability” a numerical sequence \(\{a_ n\},\)
2. \(\{Y_ n\}\) is another sequence of random variables such that, for all n, the density function of \(Y_ n\) is proportional to the product of the density of \(X_ n\) and another density not depending on n,
lead to the fact that the random sequence \(\{Y_ n\}\) also “approaches in probability” \(\{a_ n\}\). We also show some related theorems as well as applications to Bayesian inference.


62F15 Bayesian inference
60F99 Limit theorems in probability theory
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[1] BURRILL, C. W. (1972):Measure, Integration and Probability, New York, McGraw-Hill.
[2] De GROOT, M. H. (1970):Optional Statistical Decisions, New York, McGraw-Hill.
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