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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 ...
Stan is a probabilistic programming language for statistical inference written in C++ ArviZ a Python library for exploratory analysis of Bayesian models Bambi is a high-level Bayesian model-building interface based on PyMC
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 ().
The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
Engine for Likelihood-Free Inference. ELFI is a statistical software package written in Python for Approximate Bayesian Computation (ABC), also known e.g. as likelihood-free inference, simulator-based inference, approximative Bayesian inference etc. [83] ABCpy: Python package for ABC and other likelihood-free inference schemes.
In numerous publications on Bayesian experimental design, it is (often implicitly) assumed that all posterior probabilities will be approximately normal. This allows for the expected utility to be calculated using linear theory, averaging over the space of model parameters. [2]
Bayesian inference; Bayesian probability; Bayes' theorem; Bernstein–von Mises theorem; Coherence; Cox's theorem; Cromwell's rule; Likelihood principle; Principle of indifference; Principle of maximum entropy; Model building; Conjugate prior; Linear regression; Empirical Bayes; Hierarchical model; Posterior approximation; Markov chain Monte ...
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.