A Bayesian Approach to Calculating Sample Sizes for Multinomial Sampling

1987 ◽  
Vol 36 (2/3) ◽  
pp. 155 ◽  
Author(s):  
C. J. Adcock
Keyword(s):  
Bayesian Approach ◽  
Sample Sizes ◽  
Multinomial Sampling

Investigating protein patterns in human leukemia cell line experiments: A Bayesian approach for extremely small sample sizes

2019 ◽  
Vol 29 (4) ◽  
pp. 1181-1196
Author(s):  
Thierry Chekouo ◽  
Francesco C Stingo ◽  
Caleb A Class ◽  
Yuanqing Yan ◽  
Zachary Bohannan ◽  
...  
Keyword(s):  
Cell Line ◽  
Bayesian Approach ◽  
Human Cancer ◽  
Leukemia Cell ◽  
Small Sample ◽  
Mass Spectrometry Data ◽  
Leukemia Cell Line ◽  
Human Leukemia ◽  
Sample Sizes ◽  
Protein Patterns

Human cancer cell line experiments are valuable for investigating drug sensitivity biomarkers. The number of biomarkers measured in these experiments is typically on the order of several thousand, whereas the number of samples is often limited to one or at most three replicates for each experimental condition. We have developed an innovative Bayesian approach that efficiently identifies clusters of proteins that exhibit similar patterns of expression. Motivated by the availability of ion mobility mass spectrometry data on cell line experiments in myelodysplastic syndrome and acute myeloid leukemia, our methodology can identify proteins that follow biologically meaningful trends of expression. Extensive simulation studies demonstrate good performance of the proposed method even in the presence of relatively small effects and sample sizes.

scholarly journals Noninformative Bayesian $P$-values for testing marginal homogeneity in $2 \times 2$ contingency tables

2009 ◽  
Vol 40 (4) ◽  
pp. 415-427 ◽  
Author(s):  
Lee-Shen Chen ◽  
Ming-Chung Yang
Keyword(s):  
Contingency Tables ◽  
The Other ◽  
P Value ◽  
Posterior Distributions ◽  
Sample Sizes ◽  
P Values ◽  
Large Sample ◽  
Marginal Homogeneity ◽  
Multinomial Sampling ◽  
Preceding Problem

This article considers the problem of testing marginal homogeneity in $2 \times 2$ contingency tables under the multinomial sampling scheme. From the frequentist perspective, McNemar's exact $p$-value ($p_{_{\textsl ME}}$) is the most commonly used $p$-value in practice, but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, one can construct Bayesian $p$-values by using the proper prior and posterior distributions, which are called the prior predictive $p$-value ($p_{prior}$) and the posterior predictive $p$-value ($p_{post}$), respectively. Another Bayesian $p$-value is called the partial posterior predictive $p$-value ($p_{ppost}$), first proposed by [2], which can avoid the double use of the data that occurs in $p_{post}$. For the preceding problem, we derive $p_{prior}$, $p_{post}$, and $p_{ppost}$ based on the noninformative uniform prior. Under the criterion of uniformity in the frequentist sense, comparisons among $p_{prior}$, $p_{_{{\textsl ME}}}$, $p_{post}$ and $p_{ppost}$ are given. Numerical results show that $p_{ppost}$ has the best performance for small to moderately large sample sizes.

scholarly journals A Bayesian approach for unplanned sample sizes in phase II cancer clinical trials

2012 ◽  
Vol 9 (3) ◽  
pp. 293-302 ◽  
Author(s):  
Yimei Li ◽  
Rosemarie Mick ◽  
Daniel F Heitjan
Keyword(s):  
Clinical Trials ◽  
Phase Ii ◽  
Bayesian Approach ◽  
Cancer Clinical Trials ◽  
Sample Sizes

Bayesian Determination of Sample Sizes for Inspections of Feeder Hangers

2009 ◽  
Author(s):  
Fred M. Hoppe ◽  
Jovica Riznic
Keyword(s):  
Bayesian Approach ◽  
Confidence Level ◽  
Sample Sizes ◽  
Predictive Distributions ◽  
Nuclear Plants

The purpose of this paper is to show how a Bayesian approach may be used to determine sample sizes for future inspections of hangers in feeder tubes at nuclear plants. Predictive distributions are obtained and tables given for the number of fretting locations in the uninspected feeder population. If, upon inspection, the number of frets observed is too large for a specified confidence level, then the tables can be used to determine how many additional feeders to inspect.

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