Application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring

1992 ◽  
Vol 11 (5) ◽  
pp. 621-631 ◽  
Author(s):  
Motomi Mori ◽  
George G. Woodworth ◽  
Robert F. Woolson
Keyword(s):  
Empirical Bayes ◽  
Rate Of Change ◽  
Right Censoring ◽  
Bayes Inference ◽  
Informative Right Censoring

scholarly journals Empirical Bayes Inference for the Parameter of Power Distribution Based on Ranked Set Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Naiyi Li ◽  
Yuan Li ◽  
Yongming Li ◽  
Yang Liu
Keyword(s):  
Power Distribution ◽  
Empirical Bayes ◽  
Ranked Set Sampling ◽  
Bayes Inference ◽  
Bayes Test

This research is based on ranked set sampling. Through the analysis and proof, the empirical Bayes test rule and asymptotical property for the parameter of power distribution are obtained.

scholarly journals Oscillatory Biomedical Signals: Frontiers in Mathematical Models and Statistical Analysis

2021 ◽  
Vol 7 ◽  
Author(s):  
Hau-Tieng Wu ◽  
Tze Leung Lai ◽  
Gabriel G. Haddad ◽  
Alysson Muotri
Keyword(s):  
Statistical Analysis ◽  
Empirical Bayes ◽  
Network Formation ◽  
Markov Models ◽  
Hidden Markov ◽  
Biomedical Signals ◽  
Time Frequency ◽  
Bayes Inference ◽  
Cardiorespiratory Patterns ◽  
Parameter Estimators

Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time–frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.

Parametric Empirical Bayes Inference: Theory and Applications: Comment

1983 ◽  
Vol 78 (381) ◽  
pp. 61 ◽  
Author(s):  
Dennis V. Lindley
Keyword(s):  
Empirical Bayes ◽  
Bayes Inference ◽  
Inference Theory

scholarly journals Empirical Bayes Inference of Pairwise FST and Its Distribution in the Genome

Genetics ◽  
2007 ◽  
Vol 177 (2) ◽  
pp. 861-873 ◽  
Author(s):  
Shuichi Kitada ◽  
Toshihide Kitakado ◽  
Hirohisa Kishino
Keyword(s):  
Empirical Bayes ◽  
Bayes Inference

Parametric Empirical Bayes Inference: Theory and Applications

1983 ◽  
Vol 78 (381) ◽  
pp. 47-55 ◽  
Author(s):  
Carl N. Morris
Keyword(s):  
Empirical Bayes ◽  
Bayes Inference ◽  
Inference Theory

scholarly journals Bayes Empirical Bayes Inference of Amino Acid Sites Under Positive Selection

2005 ◽  
Vol 22 (4) ◽  
pp. 1107-1118 ◽  
Author(s):  
Z. Yang
Keyword(s):  
Amino Acid ◽  
Positive Selection ◽  
Empirical Bayes ◽  
Acid Sites ◽  
Bayes Inference

scholarly journals Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1387
Author(s):  
Chi-Ken Lu ◽  
Patrick Shafto
Keyword(s):  
Gaussian Process ◽  
Empirical Bayes ◽  
Bayesian Learning ◽  
Marginal Likelihood ◽  
Expressive Power ◽  
Kernel Learning ◽  
Bayes Inference ◽  
Latent Space ◽  
Kernel Composition ◽  
Non Gaussian

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

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