Bayesian methods for the analysis of mixed categorical and continuous (incomplete) data

2013 ◽  
pp. 189-208 ◽  
Author(s):  
Michael Daniels ◽  
Jeremy Gaskins
Keyword(s):  
Bayesian Methods ◽  
Incomplete Data

Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

1985 ◽  
Vol 10 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Philip J. Smith ◽  
Sung C Choi ◽  
Erdogan Gunel
Keyword(s):  
Experimental Design ◽  
Bayesian Analysis ◽  
Bayesian Methods ◽  
Incomplete Data ◽  
Prior Distribution ◽  
Contingency Table ◽  
Response Variable ◽  
Testing Hypotheses ◽  
Test Conditions ◽  
First Response

A frequently used experimental design is one in which the experimental units are measured twice (e.g., under different test conditions). When the response variable is dichotomous, the equality of the two proportions is usually assessed by a test due to McNemar (1947) . However, in addition to obtaining this complete data where two responses are available for each unit, incomplete data may be available also: In this case observations are available on the first response alone for some units and additional observations are available on the second response alone for other units. In this paper Bayesian methods are presented for estimating and testing hypotheses regarding the two success probabilities in light of both the complete and incomplete data. A method by which the prior distribution may be assessed is sketched and a numerical example to illustrate the method is presented.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

Performance of MAP-Bayesian methods for managing loss of metabolite samples in PET ligand studies

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S627-S627
Author(s):  
Mary E Spilker ◽  
Gjermund Henriksen ◽  
Till Sprenger ◽  
Michael Valet ◽  
Isabelle Stangier ◽  
...  
Keyword(s):  
Bayesian Methods

Pierre D. Thionet. Quelques problemes concemtlnt les sondages. Goettingen : Vandenhoeck & Ruprecht. 1978. 137pp.

1982 ◽  
Vol 21 (1) ◽  
pp. 83-84
Author(s):  
Karol J. Krotki
Keyword(s):  
Information Theory ◽  
Developing Countries ◽  
Experimental Design ◽  
Bayesian Methods ◽  
English Language ◽  
Applied Statistics ◽  
A Posteriori ◽  
Journal Articles ◽  
Multi Stage ◽  
Theoretical Issues

The publication reviewed is number 9 in the series" Applied Statistics and Econometrics" edited by Gerhard Tintner, Pierre Desire Truonet, and Heinrich Strecker. The purpose of the series is to publish papers " too long for ordinary journal articles, but not long enough for books . ... . . Upon acceptance, speedy publication can be promised". The abstracts in English, French, and German, usual in this series, are missing from the copy reviewed. The book consists of ten chapters: sampling theory; multi -stage sampling and other fundamental problems; optimum stratification; variances; sampling with replacement and other theoretical issues; experimental design; information theory; a posteriori raising factors ; order statistics; Bayesian methods. Such an ambitious content within 130 pages requires parsimonious presentation. One chapter has been squeezed into hardly more than four pages. The chapter on a posteriori raising factors will be useful in developing countries and particularly when samples do not work out as designed. It will also be refreshing to those limited to the literature in the English language.

The Spirit of Cromwell’s Rule

2018 ◽  
Author(s):  
Timothy McGrew
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
Bayesian Probability ◽  
Standard Textbook ◽  
Per Se

One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods have responded by adding restrictions motivated by broader epistemic concerns about the possibility of changing one’s mind. This chapter explores some cases where, intuitively, a straightforward Bayesian model yields unreasonable results. Problems arise in these cases not because there is something wrong with the Bayesian formalism per se but because standard textbook illustrations teach us to represent our inferences in simplified ways that break down in extreme cases. It also explores some interesting limitations on the extent to which successive items of evidence ought to induce us to change our minds when certain screening conditions obtain.

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