A Generalized Bayes Rule for Prediction

1999 ◽  
Vol 26 (2) ◽  
pp. 265-279 ◽  
Author(s):  
Jose Manuel Corcuera ◽  
Federica Giummole
Keyword(s):  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan

This chapter contains many classroom activities and demonstrations to help students understand basic probability calculations, including conditional probability and Bayes rule. Many of the activities alert students to misconceptions about randomness. They create dramatic settings where the instructor discerns real coin flips from fake ones, students modify dice and coins in order to load them, students “accused” of lying based on the outcome of an inaccurate simulated lie detector face their classmates. Additionally, probability models of real outcomes offer good value: first we can do the probability calculations, and then can go back and discuss the potential flaws of the model.


Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 19
Author(s):  
Hsiuying Wang

High-dimensional data recognition problem based on the Gaussian Mixture model has useful applications in many area, such as audio signal recognition, image analysis, and biological evolution. The expectation-maximization algorithm is a popular approach to the derivation of the maximum likelihood estimators of the Gaussian mixture model (GMM). An alternative solution is to adopt a generalized Bayes estimator for parameter estimation. In this study, an estimator based on the generalized Bayes approach is established. A simulation study shows that the proposed approach has a performance competitive to that of the conventional method in high-dimensional Gaussian mixture model recognition. We use a musical data example to illustrate this recognition problem. Suppose that we have audio data of a piece of music and know that the music is from one of four compositions, but we do not know exactly which composition it comes from. The generalized Bayes method shows a higher average recognition rate than the conventional method. This result shows that the generalized Bayes method is a competitor to the conventional method in this real application.


2016 ◽  
Vol 48 (7) ◽  
pp. 502-512 ◽  
Author(s):  
Barbara Medvar ◽  
Viswanathan Raghuram ◽  
Trairak Pisitkun ◽  
Abhijit Sarkar ◽  
Mark A. Knepper

Aquaporin-2 (AQP2) is regulated in part via vasopressin-mediated changes in protein half-life that are in turn dependent on AQP2 ubiquitination. Here we addressed the question, “What E3 ubiquitin ligase is most likely to be responsible for AQP2 ubiquitination?” using large-scale data integration based on Bayes' rule. The first step was to bioinformatically identify all E3 ligase genes coded by the human genome. The 377 E3 ubiquitin ligases identified in the human genome, consisting predominant of HECT, RING, and U-box proteins, have been used to create a publically accessible and downloadable online database ( https://hpcwebapps.cit.nih.gov/ESBL/Database/E3-ligases/ ). We also curated a second database of E3 ligase accessory proteins that included BTB domain proteins, cullins, SOCS-box proteins, and F-box proteins. Using Bayes' theorem to integrate information from multiple large-scale proteomic and transcriptomic datasets, we ranked these 377 E3 ligases with respect to their probability of interaction with AQP2. Application of Bayes' rule identified the E3 ligases most likely to interact with AQP2 as (in order of probability): NEDD4 and NEDD4L (tied for first), AMFR, STUB1, ITCH, ZFPL1. Significantly, the two E3 ligases tied for top rank have also been studied extensively in the reductionist literature as regulatory proteins in renal tubule epithelia. The concordance of conclusions from reductionist and systems-level data provides strong motivation for further studies of the roles of NEDD4 and NEDD4L in the regulation of AQP2 protein turnover.


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