To measure the impact of Bayesian reasoning, this paper investigates the occurrence of two words, "Bayes" and "Bayesian," since 1970 in journal articles in a variety of disciplines, with a focus on economics and statistics. The growth in statistics is documented, but the growth in economics is largely confined to economic theory/mathematical economics rather than econometrics.
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Dale J. Poirier (2006) studied this question.
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