Аннотация:The paper presents a decision rule forming a mathematical basis of earth-
quake forecasting problem. We develop an axiomatic approach to earth-
quake forecasting in terms of multicomponent random fields on a lattice.
This approach provides a method for constructing point estimates and
confidence intervals for conditional probabilities of strong earthquakes
under conditions on the levels of precursors. Also, it provides an approach
for setting a multilevel alarm system and hypothesis testing for binary
alarms. We use a method of comparison for different algorithms of earth-
quake forecasts in terms of the increase of Shannon information. ‘Fore-
casting’ (the calculation of the probabilities) and ‘prediction’ (the alarm
declaring) of earthquakes are equivalent in this approach.