How to solve posterior odds in Bayes assignments?
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in Bayes theorem, the posterior odds are the posterior probability of an event happening. Let’s assume that there are three possible events, say a, b, and c. The posterior odds are calculated using the given formula: P(c) = P(c|a)P(a) + P(c|b)P(b) + P(c|not-a)P(not-a) Here, P(c) is the prior probability of c, P(a) is the prior probability of a and P(b)
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In essence, posterior odds are those odds based on the posterior, that is, the probability distribution of the outcomes after the first batch of observations has been made. It is the probability that the next batch will lead to the occurrence of the next event, divided by the probability that the next batch will not lead to that event, when considering all the events in the initial batch. Get the facts I. Constructing a posterior distribution Posterior distribution is a probability distribution that reflects the posterior estimates, or the model. It is typically constructed by making the assumption that
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In the recent years, Bayesian statistics have been gaining popularity among students and researchers. Bayesian statistics is based on the principle that every observation can be assigned with a prior probability. One of the most critical Bayesian statistics problems is Bayes assignment, in which we predict the posterior probability distribution of a parameter based on observations and the prior distribution. The posterior probability is the posterior probability distribution obtained after Bayes’s formula. There are two ways to solve posterior odds in Bayes assignments: 1) Gibbs Sampling: In Gib
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In Bayes theory, we are trying to answer questions like ‘what is the probability that a patient’s blood tests are positive for COVID-19 when there is no information on whether the patient had COVID-19 or not?’, or ‘what is the probability that a student’s exam score is higher than the average student in the class if the student has a higher score than the average student?’, or ‘what is the probability that a woman in her 30s gets pregnant if she is taking contraception with progesterone?’.
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in the first chapter, I used the “posterior odds” method to solve Bayes assignments. The “posterior odds” method is another way of finding the probability distribution of a probability of a random variable. The “posterior odds” formula was derived from the Bayes formula in 18th century by John Bayes. It’s important to note that Bayes’s formula gives us a very important and practical tool for analyzing the data that we collect and that is Bayes factor. It’s a method to compare