An axiomatic model of non bayesian updating
Larry Epstein () No 498, RCER Working Papers from University of Rochester - Center for Economic Research (RCER) Abstract: This paper models an agent in a three-period setting who does not update according to Bayes'Rule, and who is self-aware and anticipates her updating behavior when formulating plans.
The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on a domain of state-contingent menus of acts.
Ian Hacking noted that traditional "Dutch book" arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books.
The only difference is that the posterior predictive distribution uses the updated values of the hyperparameters (applying the Bayesian update rules given in the conjugate prior article), while the prior predictive distribution uses the values of the hyperparameters that appear in the prior distribution.
If evidence is simultaneously used to update belief over a set of exclusive and exhaustive propositions, Bayesian inference may be thought of as acting on this belief distribution as a whole.
Bayesian updating is particularly important in the dynamic analysis of a sequence of data.
Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.