Calculate Qn
Qn calculates Q_n, the posterior probability that λ
came from the first component of the mixture, given N = n (Eq. 6,
DuMouchel 1999). Q_n is the mixture fraction for the posterior
distribution.
Qn(theta_hat, N, E)
theta_hat |
A numeric vector of hyperparameter estimates (likely from
|
N |
A whole number vector of actual counts from
|
E |
A numeric vector of expected counts from |
The hyperparameter estimates (theta_hat) are:
α_1, β_1: Parameter estimates of the first component of the prior distribution
α_2, β_2: Parameter estimates of the second component
P: Mixture fraction estimate of the prior distribution
A numeric vector of probabilities.
DuMouchel W (1999). "Bayesian Data Mining in Large Frequency Tables, With an Application to the FDA Spontaneous Reporting System." The American Statistician, 53(3), 177-190.
autoHyper, exploreHypers,
negLLsquash, negLL,
negLLzero, and negLLzeroSquash for
hyperparameter estimation.
processRaw for finding counts.
Other posterior distribution functions:
ebgm(),
quantBisect()
theta_init <- data.frame( alpha1 = c(0.2, 0.1), beta1 = c(0.1, 0.1), alpha2 = c(2, 10), beta2 = c(4, 10), p = c(1/3, 0.2) ) data(caers) proc <- processRaw(caers) squashed <- squashData(proc, bin_size = 100, keep_pts = 100) squashed <- squashData(squashed, count = 2, bin_size = 10, keep_pts = 20) suppressWarnings( theta_hat <- autoHyper(data = squashed, theta_init = theta_init)$estimates ) qn <- Qn(theta_hat, N = proc$N, E = proc$E) head(qn)
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