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A class of algorithms for sampling from a probability distribution by constructing a Markov chain that has the desired distribution as its equilibrium distribution.

The probability of an event before new data is considered, often denoted as $P(A)$.

A prior distribution that, when combined with a likelihood function from a certain family, results in a posterior distribution that is in the same family.

A type of model that includes parameters at multiple hierarchical levels, allowing for structured, hierarchical data analysis.

A framework for making decisions based on the principles of maximizing utility and often incorporates Bayesian probabilities.

The mode of the posterior distribution, which can be used as a point estimate of an unknown parameter.

A technique for numerically estimating the value of an integral, which is especially useful when dealing with high-dimensional integrals often encountered in Bayesian analysis.

Updated probability of a hypothesis after considering new evidence, often denoted as $P(A|B)$.

A non-informative prior that is invariant under reparameterization. Typically used when prior knowledge is minimal.

The process of deducing properties about a population or probability distribution from data using Bayes' theorem.

An interval estimate of a parameter, constructed so that it encloses the parameter with a specified probability, analogous to a confidence interval in frequentist statistics.

A probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG).

The distribution of a new data point, inferred from the model and past observations, without requiring this point's actual observation.

A function of the parameters of a statistical model given data. Often expressed as $P(B|A)$, it measures the plausibility of the data under different hypotheses.

A regression analysis approach where the statistical analysis is undertaken within the context of Bayesian inference.

Interprets probability as a measure of believability or confidence that an individual can place on a statement.

The conditional probability of assignment to a particular treatment given a set of observed covariates, often used in observational studies within a Bayesian framework.

A Bayesian alternative to classical hypothesis testing, the Bayes factor is a ratio of the posterior odds to the prior odds for two competing hypotheses.

A formula that describes how to update the probabilities of hypotheses when given evidence.