Conjugate Priors for Exponential Families

By Persi Diaconis, D. Ylvisaker. 1979

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Automatic Differentiation Variational Inference (2016, neutral): “The mean-field Gaussian becomes q(ζ ; φ) = N ζ ; µ, diag(exp(ω)2) , where the vector φ = (µ1, · · · ,µK ,ω1, · · · ,ωK) concatenates the mean and logarithm of the standard deviation of each factor.”
The estimation of phase-type related functionals using Markov chain Monte Carlo methods (2003, methodology): “For a general discussion of conjugate distributions, see e.g. Diaconis & Ylvisaker (1979) and Giutérrez-Peña & Smith (1995).”
Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family (2017, methodology): “It follows from Diaconis and Ylvisaker (1979) that the conjugate prior distribution for Y is given by, f (Y |α,κ) = K(α,κ)exp{αY −κψ(Y )} ; Y ∈ Y , α κ ∈ Z ,κ > 0, (2) where K(α,κ) is a normalizing constant.”
Conjugate priors for generalized linear models (2003, methodology): “As shown in Diaconis and Ylvisaker (1979), y0 = E(ḃ(θ)), where ḃ(θ) is the gradient vector of b(θ) and the expectation is taken with respect to the prior distribution in (2.4).”
Wishart distributions for decomposable covariance graph models (2011, methodology): “No general theory is available for Bayesian inference in curved exponential families for continuous random variables, akin to the Diaconis–Ylvisaker [10] or standard conjugate theory for natural exponential families.”
EXCHANGEABILITY, PREDICTIVE DISTRIBUTIONS AND PARAMETRIC MODELS* (2000, background): “From the theory in Diaconis and Ylvisaker (1979), general exponential families together with their conjugate priors yield predictive p.d.’s of the above type.”
Inducing Features of Random Fields (1995, background): “While there is a natural class of conjugate priors for the class of exponential models that we use [14], the problem of incorporating prior knowledge about the set of candiate features is more challenging.”
Sequential Change-Point Detection When the Pre- and Post-Change Parameters are Unknown (2010, unknown): “7) to conclude that ≥ E 0 1 e T 1Cs , and then proceed as in the proof of Theorem 2 in Lai (1998, p. 2920) to derive (3.5). To prove Theorem 3.1, we can in fact apply Theorem 2 of Lai (1998), since the asymptotic lower bound in (a) is the same as (and that in (b) can be shown to be smaller than) the”
The History of the Dirichlet and Liouville Distributions (2001, background): “Again in the context of Bayesian analysis, Diaconis & Ylvisaker (1979) characterized the Dirichlet distributions as the unique family allowing linear posterior expectation for multinomial observations (cf., DeGroot, 1970, p. 174).”
A SIMPLE BAYESIAN APPROACH TO MULTIPLE CHANGE-POINTS (2011, methodology): “An alternative approach that is computationally more convenient, especially when k is not small, is the binary segmentation procedure of Vostrikova (1981) and its recent refinement by Olshen et al. (2004). The choice of k for this approach is carried out by a model selection criterion dating back to”
The trouble with overconfidence. (2008, unknown): “, 1999; Koriat, Sheffer, & Ma’ayan, 2002; Krueger & Mueller, 2002; Kruger & Dunning, 1999; Lichtenstein & Fischhoff, 1977; Lichtenstein, Fischhoff, & Phillips, 1982; May, 1986; Sniezek, 1990; Stankov & Crawford, 1997). Erev, Wallsten, and Budescu (1994) pointed out that when people have imperfect kn”