Markov Flow Models and the Flood Warning Problem

Let { Y j } represent periodically sampled river discharge values. For simplicity, say that a flood occurs at epoch n + 1 if, for some fixed T, Y n +1 > T . Assume that at epoch n , the decision maker must decide whether or not to issue a flood warning, this decision being based on the past flow record { Y j } j≤n . Finally, assume that costs have been assigned to the two types of mistakes: the “false alarm” event, and the event that a flood occurs when no warning was issued. It is argued that outside the Gaussian assumption, standard time series methodology is inappropriate for the flood warning problem. The purpose of this paper is to relate recent progress based on alternate principles. A nonparametric inference procedure is described which converges to the optimal decision function for the flood warning problem as the length of the historical record increases for any stationary G 2 ‐ergodic Markov process. Under additional assumptions, rates can be established and shown to be optimal in a certain sense. The new methodology is compared with autoregressive moving average predictors on simulated and river flow data.