AbstractOn July 16, 1945 the first nuclear weapon test (code named Trinity) began an evolution in warfare that led to the cold war where mutually assured destruction (MAD) prevented nuclear conflict between nations. The generation that fought the cold war understood the destructive power of a nuclear weapon—many had observed first hand the ruins of Nagasaki and Hiroshima. The modern nuclear weapon has the potential to kill over 1,000,000 people in seconds if detonated in a large metropolitan city. In contrast to the man‐made threat of nuclear weapons, there are an estimated 230,000 people dead or presumed so as a result of the 2004 Indian Ocean tsunami. Seismology is the core science in monitoring for nuclear weapon tests worldwide—an essential function in global efforts to eliminate nuclear weapons. Equally important, seismology provides the theory and methods to monitor and warn for natural threats such as the Indian Ocean tsunami. Today, many scientists continue research and development efforts to more effectively monitor natural seismic activity and eliminate nuclear weapons from the globe. This article reviews an important aspect of that research—mathematical statistics contributions to seismic monitoring with emphasis on underground nuclear weapon test monitoring. Copyright © 2010 John Wiley & Sons, Inc.This article is categorized under:Applications of Computational Statistics > Computational Physics and Computational Geophysics