Optimal Information Processing and Bayes's Theorem

By A. Zellner. 1988

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In Information Theory

Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, neutral): “The tightness of the ELBO is determined by the expressiveness of the variational family [69], so it is natural to consider using ﬂexible EIMs as the variational family.”
General Bayesian updating and the loss-likelihood bootstrap (2017, background): “Additionally, the rate at which the Bayesian learns about the parameter of a misspecified model is not necessarily optimal, as it is in the well-specified case; see Zellner (1988).”
Vanilla PP for Philosophers: A Primer on Predictive Processing (2017, background): “12 Here, “rationally” means in accordance with the axioms of probability, and with the definition of conditional probability; it can also be shown that Bayesian inference is optimal in an information-theoretic sense (see Zellner 1988).”
Nonasymptotic convergence rates for cooperative learning over time-varying directed graphs (2014, background): “Standard Bayes’ rule can be described as the solution of a constrained optimization problem [19], [20], [21].”
Assigning a value to a power likelihood in a general Bayesian model (2017, background): “See Lindley (2000), Bernardo & Smith (2004) and Zellner (1988).”
Information and Entropy Econometrics - A Review and Synthesis (2008, background): “34 Information and Entropy — Background, Definitions, and Examples It has been further shown (Golan, 2002) that all of these measures (including Cressie–Read) are connected: DRα+1(p‖q) = − 1 α log[1 − αDTα+1(p‖q)] = − 1 α log[1 + α(α + 1)DCRα (p‖q)] (3.9) where the Tsallis and Rényi measures of…”
Approximate Entropy and Sample Entropy: A Comprehensive Tutorial (2019, background): “The relationship between IT, MEP and Bayesian probability is of great mathematical importance, and the interested reader can ﬁnd out more about their relationship and implications in Zellner’s texts [11–13].”
Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods (2001, methodology): “In this approach, an `eý cient’ estimator satis® es what Zellner (1988) describes as the Ìnformation Conservation Principle’ : the estimation procedure should neither ignore any of the input information nor inject any false information.”
Information and Entropy Econometrics—Editor's View (2002, background): “ME in particular in economics=econometrics appears in Zellner (1991) and Maasoumi (1993).”
Evolution of Forecast Disagreement in a Bayesian Learning Model (2008, background): “(23) Zellner (1988) has shown that the above Bayesian information updating rule is 100% efficient, since no information is lost or added when (23) is employed.”
Default priors for Bayesian and frequentist inference (2010, methodology): “Divergence methods can be framed in the context of the information processing that takes a prior distribution to a posterior distribution, as in Zellner (1988).”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “…may reflect a priori belief about the parameter 𝜃 ∈ Θ , and determines their a posteriori belief according to (1) In the M-closed setting there exists 𝜃 0 ∈ Θ for which P = P 𝜃 0 , and the Bayesian update is optimal from an information-theoretic perspective (see Williams, 1980; Zellner, 1988).”
Provable Bayesian Inference via Particle Mirror Descent (2015, background): “PMD applies to many probabilistic models, even with non-conjugate priors .”
Reconciling Household Surveys and National Accounts Data Using a Cross Entropy Estimation Method (2003, background): “Zellner (1988) calls this procedure an efficient "information processing rule" in that it uses all the information available but does not introduce any assumptions about information we do not have.”