scholarly journals Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Entropy ◽  
2017 ◽  
Vol 19 (6) ◽  
pp. 274
Author(s):  
Hea-Jung Kim
Keyword(s):  
Bayesian Hierarchical ◽  
Scale Mixtures ◽  
Log Normal ◽  
Hierarchical Scale

scholarly journals Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

2017 ◽  
Author(s):  
Hea-Jung Kim
Keyword(s):  
Bayesian Inference ◽  
Method Development ◽  
Failure Time ◽  
A Priori ◽  
Data Sets ◽  
Bayesian Hierarchical ◽  
Scale Mixtures ◽  
Model Reliability ◽  
Heavy Tailed ◽  
Log Normal

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

Bias and significance of relative reproductive success estimates based on steelhead trout (Oncorhynchus mykiss) data: a Bayesian meta-analysis

2011 ◽  
Vol 68 (10) ◽  
pp. 1827-1835 ◽  
Author(s):  
Shuichi Kitada ◽  
Hirohisa Kishino ◽  
Katsuyuki Hamasaki
Keyword(s):  
Reproductive Success ◽  
Oncorhynchus Mykiss ◽  
Meta Analysis ◽  
Wild Fish ◽  
Steelhead Trout ◽  
Bayesian Hierarchical ◽  
Hatchery Fish ◽  
In The Wild ◽  
The Mean ◽  
Log Normal

The evaluation of the reproductive success (RS) of hatchery fish in the wild is one of the most important issues in hatchery supplementation, aquaculture, and conservation. Estimates of the relative reproductive success (RRS) have been used to evaluate RS. Because RRS may vary greatly depending on cross, years of release, and environmental conditions, we introduced a log-normal distribution to quantify the variation. The classical estimator of RRS based on multiple measurements is contrasted with the mean of this distribution. We derived the mean, variance, and relative bias and applied our Bayesian hierarchical model to 42 empirical RRS estimates of steelhead trout ( Oncorhynchus mykiss ) in the Hood River, Oregon, USA. The RRS estimate generally had an upward bias. Although the average level of RRS implied the reproductive decline of hatchery fish and wild-born hatchery descendants, we could not reject the null hypothesis that hatchery fish and their descendants have the same chance of having smaller RS than wild fish as they do of having larger RS than wild fish.

scholarly journals A Pan-Cancer and Polygenic Bayesian Hierarchical Model for the Effect of Somatic Mutations on Survival

2020 ◽  
Vol 19 ◽  
pp. 117693512090739
Author(s):  
Sarah Samorodnitsky ◽  
Katherine A Hoadley ◽  
Eric F Lock
Keyword(s):  
Cancer Survival ◽  
Selection Procedure ◽  
Training Data ◽  
Survival Models ◽  
Cancer Type ◽  
Forward Selection ◽  
Bayesian Hierarchical ◽  
Cancer Types ◽  
Log Normal ◽  
Pan Cancer

We built a novel Bayesian hierarchical survival model based on the somatic mutation profile of patients across 50 genes and 27 cancer types. The pan-cancer quality allows for the model to “borrow” information across cancer types, motivated by the assumption that similar mutation profiles may have similar (but not necessarily identical) effects on survival across different tissues of origin or tumor types. The effect of a mutation at each gene was allowed to vary by cancer type, whereas the mean effect of each gene was shared across cancers. Within this framework, we considered 4 parametric survival models (normal, log-normal, exponential, and Weibull), and we compared their performance via a cross-validation approach in which we fit each model on training data and estimate the log-posterior predictive likelihood on test data. The log-normal model gave the best fit, and we investigated the partial effect of each gene on survival via a forward selection procedure. Through this we determined that mutations at TP53 and FAT4 were together the most useful for predicting patient survival. We validated the model via simulation to ensure that our algorithm for posterior computation gave nominal coverage rates. The code used for this analysis can be found at https://github.com/sarahsamorodnitsky/Pan-Cancer-Survival-Modeling.git , and the results are summarized at http://ericfrazerlock.com/surv_figs/SurvivalDisplay.html .

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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