R: Likelihood with zero counts

negLLzero {openEBGM}

R Documentation

Likelihood with zero counts

Description

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 recommended (negLLsquash is typically more efficient).

Usage

negLLzero(theta, N, E)

Arguments

`theta`	A numeric vector of hyperparameters ordered as: `\alpha_1, \beta_1, \alpha_2, \beta_2, P`.
`N`	A whole number vector of actual counts from `processRaw`.
`E`	A numeric vector of expected counts from `processRaw`.

Details

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:

\alpha_1, \beta_1: Parameters of the first component of the marginal distribution of the counts (also the prior distribution)
\alpha_2, \beta_2: Parameters of the second component
P: Mixture fraction

This function will not need to be called directly if using exploreHypers or autoHyper.

Value

A scalar negative log-likelihood value.

Warnings

Make sure N actually contains zeroes before using this function. You should have used the zeroes = TRUE option when calling the processRaw function.

Make sure the data were not squashed before using this function.

References

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.