negLLzero computes the negative log-likelihood based on the
unconditional marginal distribution of N (equation 12 in DuMouchel
1999, except taking negative natural log). This function is minimized to
estimate the hyperparameters of the prior distribution. Use this function if
including zero counts but not squashing data. Generally this function is not
negLLsquash is typically more efficient).
negLLzero(theta, N, E)
A numeric vector of hyperparameters ordered as: α_1, β_1, α_2, β_2, P.
A whole number vector of actual counts from
A numeric vector of expected counts from
The marginal distribution of the counts, N, is a mixture of two negative binomial distributions. The hyperparameters for the prior distribution (mixture of gammas) are estimated by optimizing the likelihood equation from this marginal distribution.
The hyperparameters are:
α_1, β_1: Parameters of the first component of the marginal distribution of the counts (also the prior distribution)
α_2, β_2: Parameters of the second component
P: Mixture fraction
This function will not need to be called directly if using
A scalar negative log-likelihood value.
Make sure N actually contains zeroes before using this function. You
should have used the
zeroes = TRUE option when calling the
Make sure the data were not squashed before using this function.
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.
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