Binomial Likelihood and Noninformative Priors Sample Clauses

Binomial Likelihood and Noninformative Priors. The Poisson distribution was assumed previously for cancer death count.The Poisson distri- bution with parameter λ = np can be used as an approximation to the Binomial distribution B(n, p) if n is sufficiently large and p is sufficiently small. In the Bayesian framework for the Armitage-Doll model, we can also assume a Binomial observation model for cancer death count y with an unknown cancer mortality rate p. In other words, y ∼ Bin(n, p) where n is the total persons at risk and p denotes the probability of persons at risk will die from cancer. We decompose the log-odds π = log(p/(1 − p)) of these probabilities into a linear combination of constant and a multiplication of number of stage (s) and log transformation of age t. More specifically, the logit model will be written as p log 1 − p = α + (s − 1)logt so eα+(s—1)logt p = 1 + eα+(s—1)logt .
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