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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 ...
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 reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
Bayesian inference of phylogeny combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees, which is the probability that the tree is correct given the data, the prior and the likelihood model.
Bayesian-specific workflow stratifies this approach to include three sub-steps: (b)–(i) formalizing prior distributions based on background knowledge and prior elicitation; (b)–(ii) determining the likelihood function based on a nonlinear function ; and (b)–(iii) making a posterior inference. The resulting posterior inference can be used ...
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 ...
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
Bayesian inference, demographic history, population splits: I. J. Wilson, Weale, D.Balding BayesPhylogenies [8] Bayesian inference of trees using Markov chain Monte Carlo methods: Bayesian inference, multiple models, mixture model (auto-partitioning) M. Pagel, A. Meade BayesTraits [9]