Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Fundamentally, Bayesian inference uses prior knowledge, in the form of a prior distribution in order to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation, which views probability as the limit of the relative frequency of an event after many trials. More concretely, analysis in Bayesian methods codifies prior knowledge in the form of a prior distribution.
Judea Pearl is an Israeli-American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks. He is also credited for developing a theory of causal and counterfactual inference based on structural models. In 2011, the Association for Computing Machinery (ACM) awarded Pearl with the Turing Award, the highest distinction in computer science, "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning". He is the author of several books, including the technical Causality: Models, Reasoning and Inference, and The Book of Why, a book on causality aimed at the general public.
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.
Neil Shephard, FBA, is an econometrician, currently Frank B. Baird Jr., Professor of Science in the Department of Economics and the Department of Statistics at Harvard University.
The foundations of statistics consists of the mathematical and philosophical basis for arguments and inferences made using statistics. This includes the justification for methods of statistical inference, estimation and hypothesis testing, the quantification of uncertainty in the conclusions of statistical arguments, and the interpretation of those conclusions in probabilistic terms. A valid foundation can be used to explain statistical paradoxes such as Simpson's paradox, provide a precise description of observed statistical laws, and guide the application of statistical conclusions in social and scientific applications.
Jayanta Kumar Ghosh was an Indian statistician, an emeritus professor at Indian Statistical Institute and a professor of statistics at Purdue University.
Adrian E. Raftery is an Irish and American statistician and sociologist. He is the Boeing International Professor of Statistics and Sociology, and founding Director of the Center for Statistics and Social Sciences at the University of Washington in Seattle, Washington, United States.
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed. The study of why things occur is called etiology, and can be described using the language of scientific causal notation. Causal inference is said to provide the evidence of causality theorized by causal reasoning.
Stan is a probabilistic programming language for statistical inference written in C++. The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function.
David Brian Dunson is an American statistician who is Arts and Sciences Distinguished Professor of Statistical Science, Mathematics and Electrical & Computer Engineering at Duke University. His research focuses on developing statistical methods for complex and high-dimensional data. Particular themes of his work include the use of Bayesian hierarchical models, methods for learning latent structure in complex data, and the development of computationally efficient algorithms for uncertainty quantification. He is currently serving as joint Editor of the Journal of the Royal Statistical Society, Series B.
Alan Enoch Gelfand is an American statistician, and is currently the James B. Duke Professor of Statistics and Decision Sciences at Duke University. Gelfand’s research includes substantial contributions to the fields of Bayesian statistics, spatial statistics and hierarchical modeling.
Victor Chernozhukov is a Russian-American statistician and economist currently at Massachusetts Institute of Technology. His current research focuses on mathematical statistics and machine learning for causal structural models in high-dimensional environments. He graduated from the University of Illinois at Urbana-Champaign with a master's in statistics in 1997 and received his PhD in economics from Stanford University in 2000.
Matthew Walker is a British author, scientist and professor of neuroscience and psychology at the University of California, Berkeley.
Multilevel regression with poststratification (MRP) (sometimes called "Mister P") is a statistical technique used for correcting model estimates for known differences between a sample population (the population of the data you have), and a target population (a population you would like to estimate for).
ArviZ is a Python package for exploratory analysis of Bayesian models. It is specifically designed to work with the output of probabilistic programming libraries like PyMC, Stan, and others by providing a set of tools for summarizing and visualizing the results of Bayesian inference in a convenient and informative way. ArviZ also provides a common data structure for manipulating and storing data commonly arising in Bayesian analysis, like posterior samples or observed data.
Linda Hong Zhao is a Chinese-American statistician. She is a Professor of Statistics and at the Wharton School of the University of Pennsylvania. She is a Fellow of the Institute of Mathematical Statistics. Zhao specializes in modern machine learning methods.
Thomas Lumley is an Australian statistician who serves as the chair of biostatistics at the University of Auckland in New Zealand. Lumley is also a member of the "R Core Team."
Jennifer Lynn Hill is an American statistician specializing in causal inference with applications to social statistics. She is a professor of applied statistics at New York University in the Steinhardt School of Culture, Education, and Human Development.
