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 sequence of random variables, where the index of the sequence 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 model 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). It is named after the Russian mathematician Andrey Markov.
Persi Warren Diaconis is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.
David Harold Blackwell was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and statistics. He is one of the eponyms of the Rao–Blackwell theorem. He was the first African American inducted into the National Academy of Sciences, the first African American full professor at the University of California, Berkeley, and the seventh African American to receive a Ph.D. in mathematics. In 2012, President Obama posthumously awarded Blackwell the National Medal of Science.
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, loosely based 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.
Eugene 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.
Gordon Douglas Slade is a Canadian mathematician, specializing in probability theory.
Peter Michael Rosenthal is Canadian-American Professor Emeritus of Mathematics at the University of Toronto, an adjunct professor of Law at the University of Toronto, and a lawyer in private practice.
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.
The Kruskal count is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coupling effects and rediscovered as a card trick by the American mathematician Martin David Kruskal in the early 1970s as a side-product while working on another problem. It was published by Kruskal's friend Martin Gardner and magician Karl Fulves in 1975. This is related to a similar trick published by magician Alexander F. Kraus in 1957 as Sum total and later called Kraus principle.
