Bayes-LQAS: classifying the prevalence of global acute malnutrition

The frequentist approach to statistical inference assumes that a parameter of interest is a fixed and unobservable quantity. The goal is to make inference about this fixed value, given an assumed sampling distribution of the data. For example, one might estimate the prevalence of disease in a population and calculate a confidence interval about the estimate to reflect the statistical uncertainty associated with the estimation; or test a hypothesis about the value of the prevalence and report a p-value to determine significance. The attributes of these methods are judged a priori, or before observing any data. For example, a 95% confidence interval will capture the true parameter value on average 95% of the time. Similarly, a hypothesis test is designed to a certain power function, which determines the potential errors. Yet, once the data have been observed, a posteriori the probability that the true parameter lies within that interval is zero or one and the result of the hypothesis test is correct or not- and, unfortunately, we do not know which.It is common for novice statisticians to make such statements as "the probability that the prevalence lies within the confidence interval is 95%", which is, of course, incorrect in the frequentist framework. Indeed, such statements would be attractive and desirable, if only they were correct. There is a vehicle for making probability statements about distributions of unknown parameters: Bayesian inference [1]. In the Bayesian framework, the unknown parameter is treated not as a constant, but as a random quantity, which varies according to some probability distribution. At the core of this theory is Bayes theorem, which states that for two events, A and B, where Pr(B) > 0, the conditional probabilityIn practice, A and B are replaced by the unobservable parameters, ？, and the observable data, X, respectively. Then the expression becomesThe relevant pieces of this expression are the likelihood, Pr(X|？) and the prior distributio