Sampling-Based Approaches to Calculating Marginal Densities

By Alan E. Gelfand, Adrian F. M. Smith. 1990

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Foundation Posteriors for Approximate Probabilistic Inference (2022, neutral): “Markov Chain Monte Carlo (MCMC) [32, 24] and variational inference (VI) [37, 64, 8] are two widely used examples.”
Stochastic variational inference (2012, methodology): “In variational inference, we deﬁne a ﬂexible family of distributions over the hidden variables, indexed by free parameters (Jordan et al., 1999; Wainwright and Jordan, 2008).”
Variational Inference: A Review for Statisticians (2016, methodology): “…for the class of models where the joint density of the latent and observed variables are in the exponential family—this includes many intractable models from modern Bayesian statistics and reveals deep connections between variational inference and the Gibbs sampler of Gelfand and Smith (1990).”
Lifelong Generative Modeling (2017, methodology): “One method of approximating the posterior, Pφ(z|x), is through MCMC sampling methods such as Gibbs sampling [34] or Hamiltonian MCMC [87].”
Variational inference for Dirichlet process mixtures (2006, background): “This yields a chain with the desired stationary distribution (Geman and Geman, 1984; Gelfand and Smith, 1990; Neal, 1993).”
Hierarchical Bayesian space-time models (1998, methodology): “Also, throughout the paper, we use the following notation, popularized by Gelfand and Smith (1990): For a random vector U, let U represent the joint probability density function of U, and let UjV represent the conditional density of U, given the vector V.”
A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data (2001, methodology): “A Gibbs sampler (Gelfand and Smith 1990) for our two-part model may be constructed by partitioning the joint distribution of 4‚1ƒ1‘ 21 b11 : : : 1 bm1 –5 into conditional distributions.”
Global sensitivity measures from given data (2013, methodology): “In accordance with the classical assumptions of Gelfand and Smith (1990), we assume to have information about the factors probability distribution, either joint or marginal, with or without correlation, and that this knowledge comes from measurements, estimates, expert opinion, physical bounds,…”
Environmental Kuznets curves: Bayesian evidence from switching regime models (2001, methodology): “ŽFor the EBSR model, a Gibbs sampler Gelfand and Smith, 1989; Tanner and .”
A Bayesian approach to non‐parametric monotone function estimation (2009, methodology): “For a discussion of Bayesian inference using MCMC methods see Gelfand and Smith (1990), Casella and George (1992) and Tierney (1994).”
R2WinBUGS: A Package for Running WinBUGS from R (2005, methodology): “This software uses Gibbs sampling (Geman and Geman 1984; Gelfand and Smith 1990; Casella and George 1992) and the Metropolis algorithm (Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller 1953) to generate a Markov chain by sampling from full conditional distributions.”
Software reliability (2011, unknown): “Extensions of the hierarchical model was considered by Kuo and Yang (1995) who assumed a k order polynomial for Ψ(i) and used Gibbs sampling [see Gelfand and Smith (1990)] for Bayesian computations. Another class of Type I models includes Markovian models where the Markov dependence was assumed eith”
Hierarchical Species Distribution Models (2016, methodology): “Following [35] , we use the bracket notation to represent conditional probability density functions and write the hierarchical species distribution model as”
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2004, unknown): “Typically, enough data will be available to estimate µ and σy that one can use any reasonable noninformative prior distribution—for example, p(µ, σy) ∝ 1 or p(µ, log σy) ∝ 1.”