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Previous versions of PyMC were also used widely, for example in climate science, [21] public health, [22] neuroscience, [23] and parasitology. [ 24 ] [ 25 ] After Theano announced plans to discontinue development in 2017, [ 26 ] the PyMC team evaluated TensorFlow Probability as a computational backend, [ 27 ] but decided in 2020 to fork Theano ...
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 ...
Variational inference; Approximate Bayesian computation; Estimators; Bayesian estimator; Credible interval; Maximum a posteriori estimation; Evidence approximation; Evidence lower bound; Nested sampling; Model evaluation; Bayes factor (Schwarz criterion) Model averaging; Posterior predictive; Mathematics portal
The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
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]
[3] [4] For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics treats probability as a degree of belief, Bayes' theorem can directly assign a probability distribution that quantifies the belief to the parameter or set of parameters.
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 ().
In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models.It states that under some conditions, a posterior distribution converges in total variation distance to a multivariate normal distribution centered at the maximum likelihood estimator ^ with covariance matrix given by (), where is the true ...