Bayesian Statistics: Techniques and Models

Start Date: 10/20/2019

 Course Type: Common Course

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This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. It

Course Tag

Gibbs Sampling Bayesian Statistics Bayesian Inference R Programming

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Bayesian statistics Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of "degrees of belief" known as Bayesian probabilities. Such an interpretation is only one of a number of interpretations of probability and there are other statistical techniques that are not based on 'degrees of belief'. One of the key ideas of Bayesian statistics is that "probability is orderly opinion, and that inference from data is nothing other than the revision of such opinion in the light of relevant new information."
Bayesian statistics The formulation of statistical models using Bayesian statistics has the unique feature of requiring the specification of prior distributions for any unknown parameters. These prior distributions are as integral to a Bayesian approach to statistical modelling as the expression of probability distributions. Prior distributions can be either hyperparameters or hyperprior distributions.
Statistics Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models more feasible. The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available.
Bayesian inference Bayesian inference has applications in artificial intelligence and expert systems. Bayesian inference techniques have been a fundamental part of computerized pattern recognition techniques since the late 1950s. There is also an ever growing connection between Bayesian methods and simulation-based Monte Carlo techniques since complex models cannot be processed in closed form by a Bayesian analysis, while a graphical model structure "may" allow for efficient simulation algorithms like the Gibbs sampling and other Metropolis–Hastings algorithm schemes. Recently Bayesian inference has gained popularity amongst the phylogenetics community for these reasons; a number of applications allow many demographic and evolutionary parameters to be estimated simultaneously.
Bayesian statistics The general set of statistical techniques can be divided into a number of activities, many of which have special Bayesian versions.
Bayesian classifier In computer science and statistics, Bayesian classifier may refer to:
Bayesian programming Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian Programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs.
Bayesian Bayesian refers to methods in probability and statistics named after Thomas Bayes (c. 1702–61), in particular methods related to statistical inference:
Bayesian statistics Statistical graphics includes methods for data exploration, for model validation, etc. The use of certain modern computational techniques for Bayesian inference, specifically the various types of Markov chain Monte Carlo techniques, have led to the need for checks, often made in graphical form, on the validity of such computations in expressing the required posterior distributions.
Variable-order Bayesian network Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformatics applications.
Lasso (statistics) Though originally defined for least squares, lasso regularization is easily extended to a wide variety of statistical models including generalized linear models, generalized estimating equations, proportional hazards models, and M-estimators, in a straightforward fashion. Lasso’s ability to perform subset selection relies on the form of the constraint and has a variety of interpretations including in terms of geometry, Bayesian statistics, and convex analysis.
Variable-order Bayesian network These models extend the widely used position weight matrix (PWM) models, Markov models, and Bayesian network (BN) models.
Bayesian econometrics where formula_12 and which is the centerpiece of Bayesian statistics and econometrics. It has the following components:
Bayesian programming Since 2000, Bayesian programming has been used to develop both robotics applications and life sciences models.
Bayesian statistics Bayesian inference is an approach to statistical inference that is distinct from frequentist inference. It is specifically based on the use of Bayesian probabilities to summarize evidence.
Robust Bayesian analysis In statistics, robust Bayesian analysis, also called Bayesian sensitivity analysis, is a type of sensitivity analysis applied to the outcome from Bayesian inference or Bayesian optimal decisions.
Bayesian inference 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. 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 vector autoregression In statistics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR). In that respect, the difference with standard VAR models lies in the fact that the model parameters are treated as random variables, and prior probabilities are assigned to them.
Foundations of statistics Bandyopadhyay & Forster describe four statistical paradigms: "(1) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics".
Bayesian approaches to brain function A wide range of studies interpret the results of psychophysical experiments in light of Bayesian perceptual models. Many aspects of human perceptual and motor behavior can be modeled with Bayesian statistics. This approach, with its emphasis on behavioral outcomes as the ultimate expressions of neural information processing, is also known for modeling sensory and motor decisions using Bayesian decision theory. Examples are the work of Landy, Jacobs, Jordan, Knill, Kording and Wolpert, and Goldreich.