An Application of Empirical Bayes Techniques to the Simultaneous Estimation of Many Probabilities

1984 ◽  
Author(s):  
S. S. Brier ◽  
S. Zacks ◽  
W. H. Marlow
Keyword(s):  
Empirical Bayes ◽  
Simultaneous Estimation

scholarly journals GARPOS: Analysis Software for the GNSS‐A Seafloor Positioning With Simultaneous Estimation of Sound Speed Structure

2020 ◽  
Vol 8 ◽  
Author(s):  
Shun-ichi Watanabe ◽  
Tadashi Ishikawa ◽  
Yusuke Yokota ◽  
Yuto Nakamura
Keyword(s):  
Sound Speed ◽  
Empirical Bayes ◽  
Information Criterion ◽  
Satellite System ◽  
Observation Equation ◽  
Simultaneous Estimation ◽  
Acoustic Ranging ◽  
Observation Network ◽  
Sound Speed Structure ◽  
Global Navigation Satellite

Global Navigation Satellite System–Acoustic ranging combined seafloor geodetic technique (GNSS-A) has extended the geodetic observation network into the ocean. The key issue for analyzing the GNSS-A data is how to correct the effect of sound speed variation in the seawater. We constructed a generalized observation equation and developed a method to directly extract the gradient sound speed structure by introducing appropriate statistical properties in the observation equation, especially the data correlation term. In the proposed scheme, we calculate the posterior probability based on the empirical Bayes approach using the Akaike’s Bayesian Information Criterion for model selection. This approach enabled us to suppress the overfitting of sound speed variables and thus to extract simpler sound speed field and stable seafloor positions from the GNSS-A dataset. The proposed procedure is implemented in the Python-based software “GARPOS” (GNSS-Acoustic Ranging combined POsitioning Solver).

Constrained empirical Bayes estimates for cell values in a two-way table

1992 ◽  
Vol 22 (12) ◽  
pp. 1983-1987
Author(s):  
Edwin J. Green ◽  
Michael Kohl ◽  
William E. Strawderman
Keyword(s):  
Sample Size ◽  
Forest Inventory ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Individual Cell ◽  
Estimation Method ◽  
Simultaneous Estimation ◽  
Bayes Estimates ◽  
Squared Error ◽  
Large Standard Error

It is common to summarize the results of a forest inventory in two-way tables. Unfortunately, while the overall sample size may be large, the sample size for an individual cell in the table may be quite small. Thus the estimate may have a large standard error. We propose a simultaneous estimation method to reduce the variance and (or) mean squared error of individual cell estimates while retaining table additivity, i.e., preserving the observed row and column sums of the table.

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