Abstract
Problem statement: Studies on apnea patients are often carried out based on data obtained from the sleep study. This data is quite scarce since high cost is required for conducting the study. Bayesian method is particularly suitable for analyzing limited data as it allows for updating of information by combining the current information with the prior belief. Approach: In this study we demonstrated the use of Bayesian methods to rank the severity of apnea for 14 patients, based on the posterior mean of the rate of occurrence of apnea. Results: The results indicated from the comparison using three different prior distribution for the underlying rate of occurrence of apnea, that is improper, gamma and log-normal priors, the ranking of patients in terms of severity of apnea are the same, regardless of the choice for the prior distributions. Conclusion: In conclusion the model fitting was found to be slightly better when based on gamma prior.
Highlights
The problem of apnea is a matter of concern since it can cause daytime sleepiness, where in some cases it may contribute to automobile accident
Improper prior: For comparison of results based on gamma and log-normal priors, we assume another prior, which is represented by an improper prior distribution indicating our vague prior knowledge, given by: g(λ) = 1 λ; λ > 0 (10)
By implementing the EM algorithm the estimated prior parameters for μ and σ are-1.051 and Bayesian approach is quite flexible making it as a suitable tool to be used for analyzing the apnea data, which is often find to be quite scarce
Summary
The problem of apnea is a matter of concern since it can cause daytime sleepiness, where in some cases it may contribute to automobile accident. Assume that λ1, λ2,...,λn represent a random sample which follows a gamma distribution probability density function (pdf) given by: The data on apnea is obtained from a polysomnography which was originated from Rigney et al (1994). Process, we can say that Yi follows a Poisson distribution with parameter λiti which can be written as: The prior parameter of α and β can be estimated using the empirical Bayes method by fitting the p(yi
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