## 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
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### 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.
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