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Model building; Conjugate prior; Linear regression; Empirical Bayes; Hierarchical model; Posterior approximation; Markov chain Monte Carlo; Laplace's approximation; Integrated nested Laplace approximations; Variational inference; Approximate Bayesian computation; Estimators; Bayesian estimator; Credible interval; Maximum a posteriori estimation ...
The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as ...
The likelihood estimate needs to be as large as possible; because it's a lower bound, getting closer improves the approximation of the log likelihood. By substituting in the factorized version of , (), parameterized over the hidden nodes as above, is simply the negative relative entropy between and plus other terms independent of if is defined as
Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
Devising a good model for the data is central in Bayesian inference. In most cases, models only approximate the true process, and may not take into account certain factors influencing the data. [2] In Bayesian inference, probabilities can be assigned to model parameters. Parameters can be represented as random variables. Bayesian inference uses ...
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Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model.. In, for example, a two-stage hierarchical Bayes model, observed data = {,, …,} are assumed to be generated from an unobserved set of parameters = {,, …,} according to a probability distribution ().