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

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.

scholarly journals Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

INFERENCE OF BIOMEDICAL DATA SETS USING BAYESIAN MACHINE LEARNING

2019 ◽  
Vol 31 (04) ◽  
pp. 1950030
Author(s):  
Ayesha Sohail
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Methods ◽  
Relevant Information ◽  
Data Sets ◽  
Hybrid Technique ◽  
Biomedical Data ◽  
Bayesian Techniques ◽  
Clinical Databases ◽  
The Individual ◽  
Available Information

Due to the advancement in data collection and maintenance strategies, the current clinical databases around the globe are rich in a sense that these contain detailed information not only about the individual’s medical conditions, but also about the environmental features, associated with the individual. Classification within this data could provide new medical insights. Data mining technology has become an attraction for researchers due to its affectivity and efficacy in the field of biomedicine research. Due to the diverse structure of such data sets, only few successful techniques and easy to use softwares, are available in literature. A Bayesian analysis provides a more intuitive statement of probability that hypothesis is true. Bayesian approach uses all available information and can give answers to complex questions more accurately. This means that Bayesian methods include prior information. In Bayesian analysis, no relevant information is excluded as prior represents all the available information apart from data itself. Bayesian techniques are specifically used for decision making. Uncertainty is the main hurdle in making decisions. Due to lack of information about relevant parameters, there is uncertainty about given decision. Bayesian methods measure these uncertainties by using probability. In this study, selected techniques of biostatistical Bayesian inference (the probability based inferencing approach, to identify uncertainty in databases) are discussed. To show the efficiency of a Hybrid technique, its application on two distinct data sets is presented in a novel way.

scholarly journals HIV/AIDS Clinical Trials: A Statistical Review

2006 ◽  
Vol 5 (2) ◽  
pp. 71-85
Author(s):  
Annie Sumithri Soans ◽  
Nagaraja Rao Chillale ◽  
T. Srivenkataramana
Keyword(s):  
Infectious Disease ◽  
Clinical Trials ◽  
Bayesian Analysis ◽  
Incomplete Data ◽  
Meta Analysis ◽  
Economic Stability ◽  
Statistical Review ◽  
The World ◽  
Aids Clinical Trials ◽  
Hiv Aids

The HIV pandemic has grown to become one of the greatest infectious disease threats, to human health and to socio-economic stability that the world has ever encountered.It is imperative that the epidemic is controlled as rapidly as possible through prevention of new infections.Carefully conducted clinical trials are the fastest and safest way to find treatments that work in people to improve health.When the objectives or the endpoints of clinical trials for HIV/AIDS are carefully defined then Statistics will be very useful not only in designing the trial and formulating hypothesis but also in providing guidance in the analysis of the data on completion of the trial and to enhance the credibility of the results.This article mainly reviews the analysis of HIV/AIDS clinical trials.Concepts such as meta-analysis,analysis in the case of incomplete data and Bayesian analysis in the context of HIV/AIDS have also been covered.

scholarly journals Determination of the Tolerant Concentration of Eisenia fetida to Chrome Solid Residues from Tannery

2020 ◽  
Vol 20 (4) ◽  
pp. 345-352
Author(s):  
Robert BULEJE DEL CARPIO ◽  
Liliana MARRUFO SALDAÑA
Keyword(s):  
Experimental Design ◽  
Mortality Rate ◽  
Biological Treatment ◽  
Eisenia Fetida ◽  
Statistical Treatment ◽  
Dry Weight ◽  
Negative Control ◽  
Response Variable ◽  
Tanning Industry

The tanning industry, although it is characterized by the use of the skin waste originated by the cattle raising, in contrast, produces huge volumes of waste, among which chrome shavings stand out due to their high percentage of chromium. The objective of this research was to determine the concentration where earthworms (Eisenia fetida) could tolerate chrome shavings, in order to evaluate the potential for degradation of these wastes through biological treatment. To determine the tolerant concentration, an experimental design was established that included as factors, the time of exposure in weeks (0-11) and the concentrations of exposure: 0.01, 0.02, 0.04, 0.08, 0.12 and 0.16 grams of shavings per grams of substrate. The response variable was the mortality rate. Each treatment was performed in triplicate and a negative control was included. Statistical treatment was performed using ANOVA and multiple comparison tests at 95% confidence with the statistical complement Real Statistics, Statgraphics and Yupana software. The tolerant concentration established in the study was 0.04 g/g (grams of shavings per grams of substrate) which is equivalent to 636 mg/kg (based on dry weight) expressed in weight of chrome per weight of compost.

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