×

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.

MSC:

62F15 Bayesian inference
60F99 Limit theorems in probability theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.