With earthquake prediction appearing now as a possibly unrealizable goal, the contribution that seismologists can make to protecting society against the disastrous effects of earthquakes chiefly revolves around making estimates of likely future levels of earthquake activity that engineers and planners can use in the course of implementing mitigation strategiesc seismic hazard analysis. One of the key issues in this field is the treatment of irreducible uncertainty in some of the input parameters, which has been found to defeat simple attempts to produce unique deterministic values for maximum ground motion. Seismologists handle this by modeling uncertainty with a probabilistic approach, referred to as probabilistic seismic hazard assessment (PSHA). PSHA enables one to start with an a priori definition of a probability level that society can consider to be an acceptable risk (which will be different according to whether we are dealing with the possible collapse of a radio mast or a nuclear power plant) and work out the level of ground shaking that has that likelihood of occurring in the lifetime of the structure.