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In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values. [1] [2]Given a set of N i.i.d. observations = {, …,}, a new value ~ will be drawn from a distribution that depends on a parameter , where is the parameter space.
Posterior distribution is the summary of uncertainties about the parameter. Predictive distribution has not only the uncertainty about parameter but also the uncertainty about estimating parameter using data. Posterior distribution and predictive distribution have same mean, but former has smaller variance.
So after receiving a positive test result, the posterior odds of having the disease becomes 1:1, which means that the posterior probability of having the disease is 50%. If a second test is performed in serial testing, and that also turns out to be positive, then the posterior odds of having the disease becomes 10:1, which means a posterior ...
In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest ...
For example, in an experiment that determines the distribution of possible values of the parameter , if the probability that lies between 35 and 45 is =, then is a 95% credible interval. Credible intervals are typically used to characterize posterior probability distributions or predictive probability distributions. [ 1 ]
Integrated nested Laplace approximations (INLA) is a method for approximate Bayesian inference based on Laplace's method. [1] It is designed for a class of models called latent Gaussian models (LGMs), for which it can be a fast and accurate alternative for Markov chain Monte Carlo methods to compute posterior marginal distributions.
Coronary artery disease (CAD), also called coronary heart disease (CHD), or ischemic heart disease (IHD), [13] is a type of heart disease involving the reduction of blood flow to the cardiac muscle due to a build-up of atheromatous plaque in the arteries of the heart. [5] [6] [14] It is the most common of the cardiovascular diseases. [15]
Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences. For example, the Trauma and Injury Severity Score (), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. [6]
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