BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS

By Thomas S. Ferguson. 1983

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Citations in the corpus

Online Continual Learning in Image Classification: An Empirical Survey (2021, methodology): “Continual Neural Dirichlet Process Mixture (CN-DPM).”
A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning (2020, methodology): “We briefly review the Dirichlet process mixture (DPM) model (Antoniak, 1974; Ferguson, 1983), and a variational method to approximate the posterior of DPM models in an online setting: Sequential Variational Approximation (SVA) (Lin, 2013).”
Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data (2017, methodology): “To compare the performance of the foregoing predictions with more classical Bayesian methods we have also considered an alternative nonparametric formulation of the binomial model employing a Dirichlet process prior as introduced by Ferguson (1973), Antoniak (1974) and Ferguson (1983).”
Modelling of extreme wave heights and periods through copulas (2005, methodology): “The Dirichlet process based mixture (DPM) model was introduced by Ferguson (1983) and Lo (1984) and briefly it states that Yið1 n) is a collection of scalar or vector-valued independent observations and suppose that the distribution of these observations is modeled by a general Dirichlet process…”
Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities (2001, methodology): “Such an approach was taken by Ferguson (1983) and Lo (1984) who used a Dirichlet process prior on the mixing distribution and obtained expressions for Bayes estimates.”
Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation (2009, methodology): “[75] From a Bayesian perspective, the second posterior density p(qM*Tjs1:M,1:T) in (A1) can be estimated using a Dirichlet process prior [Ferguson, 1983; Muller et al., 1996].”
Correcting the mathematical structure of a hydrological model via Bayesian data assimilation (2011, background): “Although other choices might be made (i.e., kernel density estimation [Silverman, 1986]), the BESt approach estimates this density as a weighed sum of a relatively small number (as compared with kernel density methods) of multivariate Gaussian pdfs [ Ferguson, 1983; Mulleretal.,1996];fordetails,see”
Bayesian Nonparametric Modelling of the Return Distribution with Stochastic Volatility (2011, unknown): “The Dirichlet process mixture of normals model (DPM) was introduced by Lo (1984) and Ferguson (1983) and has become one of the most popular models in Bayesian nonparametrics (for other models in the Bayesian nonparametrics see Müller and Quintana (2004)).”
Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes. (2003, methodology): “…reason, mixtures of normal distributions are often used to provide an approximation to complex or intractable distributions (Escobar & West, 1995; Ferguson, 1983; Roeder & Wasserman, 1997; Sorenson & Alspach, 1971; for a review, see Everitt & Hand, 1981, pp. 118–124; McLachlan & Peel, 2000, pp.…”
Bayesian Semiparametric Regression for Median Residual Life (2003, background): “The closure of the family of densities corresponding to distributions F Y ð ;GÞ ¼ Z U l r Gðdl; drÞ; ð6Þ where U is the standard normal distribution function, contains all densities on R1 (Ferguson, 1983; Lo, 1984).”
A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model (2004, methodology): “This model may be regarded as a countably in nite mixture model (Ferguson 1983), a view that is adopted in the remainder of this article.”
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis (2007, background): “The use of the DP prior in the generic mixture setting of the form in (3) is standard when the mixture kernel is supported by R, R+ or Rd. Related work dates back to Ferguson (1983), Lo (1984), Kuo (1986), and Brunner and Lo (1989).”
Rational approximations to rational models: alternative algorithms for category learning. (2010, methodology): “When used in this fashion, the resulting model is referred to as a DP mixture model (DPMM; Antoniak, 1974; Ferguson, 1983; Neal, 1998).”
Advanced Lectures on Machine Learning (2004, methodology): “An important example of this are infinite mixture models, more formally known as Dirichlet Process mixtures [76, 77].”
Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density (2010, background): “Dirichlet mixtures have been introduced by [2, 9] and have been widely used ever since, but their asymptotic properties are not well known apart from a few cases such as Gaussian mixtures, triangular mixtures and Bernstein polynomials.”
On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions (2012, background): “To date, much effort has focused on constructions that generalize the widely used class of Dirichlet process (DP) priors (Ferguson 1973, 1974), and, consequently, the class of DP mixture models (Ferguson 1983; Lo 1984; Escobar and West 1995) for single density estimation.”