During the 1700’s, the Reverend Thomas Bayes was a nonconformist minister at the Mount Sion Chapel in Tunbridge Wells, UK, about 40 miles southeast of central London. Having studied both theology and logic at the University of Edinburgh, he was also a mathematician and developed a strong interest in probability late in life. He was known to have published only one book on theology and one book on mathematics in his lifetime. A third manuscript he never published about the probability of cause made him famous. After his death, a good friend Richard Price [1] recognized the importance of the paper and, after extensive editing, submitted it for publication. More than 20 years later, the great French mathematician, Pierre-Simon Laplace [2] devised the formula for Bayes’ probability of causes and acknowledged Bayes as the discoverer of what we now know as Bayesian inference [3].

This year is the 250^{th} anniversary of Bayesian inference. During its history, the Bayes theory has been doubted, disproven, defended, and challenged again and again and again. It has consistently been an important tool in understanding what we really know, given the evidence and other information we have. It helps incorporate "conditional probabilities" into our conclusions.

Bayesian inference has recently become prominent in many scientific fields due to the availability of simulation-based computational tools for implementation. Researchers at Los Alamos National Laboratory are using Bayes’ theorem to deduce structures of crystals and determine macromolecular structures [4]. The Lawrence Livermore National Laboratory describes how a sequential Bayesian processor would be used to assess harbor security threats [5]. DOE researchers at the University at Buffalo and the Pacific Northwest National Laboratory report the use of Bayesian inference methods to predict irrigation effects, weather, flooding, and contaminant transport [6]. Oak Ridge National Laboratory researchers use Bayesian inference methods to calculate the probabilities in groundwater reactive transport modeling [7]. And Sandia National Laboratory is evaluating the use of Bayesian statistics and energy methods to quantify the reliability and safety of weapon-system components [8].

Dr. William Watson [9], physicist, of OSTI’s staff, provides a detailed overview of Bayesian inference and discusses some of its current uses and conceptual ramifications in his latest white paper In the OSTI Collections: Bayesian Inference [10]. If you need to do research on Bayesian inference, do like William does, investigate OSTI’s extensive research collections [11].