A Bayesian Sequential Multi-Decision Problem

A formal Bayesian framework is provided for the problem where some possibly contaminated data item can be collected periodically and where additional information about each period's true data value can be obtained at some cost. A decision is made each period with loss depending on the true data value and the decision. The special case with normal distributions and quadratic loss is formulated as a dynamic programming problem, and results include proof that the optimum policy structure calls for a more expensive form of data collection initially with less expensive data collection after the process parameters are better known.