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Approximate Inference in Bayesian Neural Networks

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Variational algorithms for approximate Bayesian inference

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Approximate Bayesian inference for case‐crossover models

Biometrics, 2020
AbstractA case‐crossover analysis is used as a simple but powerful tool for estimating the effect of short‐term environmental factors such as extreme temperatures or poor air quality on mortality. The environment on the day of each death is compared to the one or more “control days” in previous weeks, and higher levels of exposure on death days than ...
Alex Stringer, Patrick Brown, Jamie Stafford   +2 more
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Deep Approximate Bayesian Inference

2023
The strength of the Bayesian paradigm lies in its flexibility through hierarchical modeling and its ability to provide coherent uncertainty quantification. However, the computation costs of classical Bayesian procedures like Markov Chain Monte Carlo (MCMC) can be daunting when confronting big data challenges (large p or large n problems).
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Approximating Bayesian Inference through Model Simulation

Trends in Cognitive Sciences, 2018
The ultimate test of the validity of a cognitive theory is its ability to predict patterns of empirical data. Cognitive models formalize this test by making specific processing assumptions that yield mathematical predictions, and the mathematics allow the models to be fitted to data.
Brandon M. Turner, Trisha Van Zandt
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Approximately Bayesian Inference

Journal of the American Statistical Association, 1994
Abstract Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties.
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Approximate Bayesian inference for quantiles

Journal of Nonparametric Statistics, 2005
Suppose data consist of a random sample from a distribution function F Y , which is unknown, and that interest focuses on inferences on θ, a vector of quantiles of F Y . When the likelihood function is not fully specified, a posterior density cannot be calculated and Bayesian inference is difficult.
David B. Dunson, Jack A. Taylor
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On Bartlett adjustments for approximate Bayesian inference

Biometrika, 1993
SUMMARY In wide generality, the posterior distributions of the likelihood ratio statistic and the posterior ratio statistic are chi-squared to error of order O(n-'), where n is sample size. The error in the chi-squared approximation can be reduced to order O(n-2) by Bartlett correction.
DiCiccio, Thomas J., Stern, Steven E.
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Approximating bayesian inference by weighted likelihood

Canadian Journal of Statistics, 2006
AbstractThe author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss.
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