negLL computes the negative log-likelihood based on the conditional
marginal distribution of the counts, N, given that N >= N*,
where N* is the smallest count used for estimating the hyperparameters
(DuMouchel et al. 2001). This function is minimized to estimate the
hyperparameters of the prior distribution. Use this function when neither
zero counts nor data squashing are being used. Generally this function is not
recommended unless using a small data set since data squashing (see
negLLsquash) can increase
efficiency (DuMouchel et al. 2001).
negLL(theta, N, E, N_star = 1)
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
A scalar whole number for the minimum count size used.
The conditional marginal distribution for the counts, N,
given that N >= N*, is based on 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
conditional marginal distribution. It is recommended to use
1 when practical.
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_star matches the smallest actual count in N before using this function. Filter N and E if needed.
Make sure the data were not squashed before using this function.
DuMouchel W, Pregibon D (2001). "Empirical Bayes Screening for Multi-item Associations." In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '01, pp. 67-76. ACM, New York, NY, USA. ISBN 1-58113-391-X.
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