Bayesian Monte Carlo methods for interpretation of observed earthquake magnitudes

This thesis presents a Bayesian Monte Carlo (BMC) approach to interpret observed earthquake magnitudes. Current seismological techniques and methods are studied to formally characterize the underestimates and overall error structure of earthquake reporting. Whenever an earthquake is observed, this information can be used to revise a prior distribution of earthquakes. Under the BMC approach, Monte Carlo simulation is performed for each of the earthquake magnitudes of the prior distribution. Each Monte Carlo realization randomly generates a set of observations based on the current seismological techniques. These observations can be used to obtain a posterior distribution using Bayes' theorem. The posterior distribution and posterior quantities obtained from this distribution can be used to evaluate observations of earthquake magnitudes as soon as they are observed.