Markovian Forecast Processes

Abstract

Abstract A sequential forecast process arises when forecasts of a fixed but uncertain state are prepared with decreasing lead times, each subsequent forecast incorporating additional information and, therefore, updating the previous forecast. Bayesian Markov models of such a process are investigated for purposes of rational decision making. The Markov structure, although not universally valid, seems plausible, leads to tractable models, and implies sequential sufficiency of forecasts (roughly speaking, each subsequent forecast is less uncertain than the previous one). Sequential sufficiency, in turn, has implications on modeling Markov stopping-control processes. The normal model for point (categorical) forecasts is studied in detail.