Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
A Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov.
Ian MacDougall Hacking was a Canadian philosopher specializing in the philosophy of science. Throughout his career, he won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and was a member of many prestigious groups, including the Order of Canada, the Royal Society of Canada and the British Academy.
Eliyahu Rips was an Israeli mathematician of Latvian origin known for his research in geometric group theory. He became known to the general public following his co-authoring a paper on what is popularly known as Bible code, the supposed coded messaging in the Hebrew text of the Torah.
Sir David John Spiegelhalter is a British statistician and a Fellow of Churchill College, Cambridge. From 2007 to 2018 he was Winton Professor of the Public Understanding of Risk in the Statistical Laboratory at the University of Cambridge. Spiegelhalter is an ISI highly cited researcher.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Peter James Green, FRS is a British Bayesian statistician. He is emeritus Professor and Professorial Research Fellow at the University of Bristol, and a professor at the University of Technology, Sydney. He is distinguished for his contributions to computational statistics, in particular his contributions to spatial statistics and semi-parametric regression models and also his development of reversible-jump Markov chain Monte Carlo.
Murray Rosenblatt was a statistician specializing in time series analysis who was a professor of mathematics at the University of California, San Diego. He received his Ph.D. at Cornell University. He was also a recipient of a Guggenheim Fellowship, in 1965, and was a member of the National Academy of Sciences. He wrote about 140 research articles, 4 books, and co-edited 6 books.
Andrew Eric Gelman is an American statistician and professor of statistics and political science at Columbia University.
Samuel Kotz was a professor and research scholar in the Department of Engineering Management and Systems Engineering, School of Engineering and Applied Science at The George Washington University from 1997 until his death on March 16, 2010. He was an author or editor of several standard reference works in statistics and probability theory.
Gábor J. Székely is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: the distance correlation, which is a bona fide dependence measure, equals zero exactly when the variables are independent; the distance skewness, which equals zero exactly when the probability distribution is diagonally symmetric; the E-statistic for normality test; and the E-statistic for clustering.
Eugene B. Seneta is Professor Emeritus, School of Mathematics and Statistics, University of Sydney, known for his work in probability and non-negative matrices, applications and history. He is known for the variance gamma model in financial mathematics. He was Professor, School of Mathematics and Statistics at the University of Sydney from 1979 until retirement, and an Elected Fellow since 1985 of the Australian Academy of Science. In 2007 Seneta was awarded the Hannan Medal in Statistical Science by the Australian Academy of Science, for his seminal work in probability and statistics; for his work connected with branching processes, history of probability and statistics, and many other areas.
Nancy Margaret Reid is a Canadian theoretical statistician. She is a professor at the University of Toronto where she holds a Canada Research Chair in Statistical Theory. In 2015 Reid became Director of the Canadian Institute for Statistical Sciences.
Robert Tibshirani is a professor in the Departments of Statistics and Biomedical Data Science at Stanford University. He was a professor at the University of Toronto from 1985 to 1998. In his work, he develops statistical tools for the analysis of complex datasets, most recently in genomics and proteomics.
Cyrus Derman was an American mathematician and amateur musician who did research in Markov decision process, stochastic processes, operations research, statistics and a variety of other fields.
Peter Michael Rosenthal was an American-Canadian mathematician, lawyer, and activist who was Professor of Mathematics at the University of Toronto, and an adjunct professor of Law at the University of Toronto Law School.
Grace Yun Yi is a professor of the University of Western Ontario where she currently holds a Tier I Canada Research Chair in Data Science. She was a professor at the University of Waterloo, Canada, where she holds a University Research Chair in Statistical and Actuarial Science. Her research concerns event history analysis with missing data and its applications in medicine, engineering, and social science.
Jesper Møller is a Danish mathematician.
Bruno N Rémillard is a Canadian mathematical statistician and an honorary professor at HEC Montréal. He is the 2019 Gold Medalist of the Statistical Society of Canada and was inducted as a 2019 Fellow of the Institute of Mathematical Statistics. Rémillard was President of the Statistical Society of Canada in 2022-23.
