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Analytical approximation of exact Poisson-lognormal likelihood functions
1Los Alamos National Laboratory, Los Alamos, NM 87545, USA. guthrie@lanl.gov
Health Physics
|January 12, 2008
Summary
This study provides simple analytical approximations for Poisson-lognormal likelihood functions, enabling easier data fitting for counting measurements. A free computer program is available for calculating these parameters.
Area of Science:
- Statistical modeling
- Computational statistics
Background:
- The Poisson-lognormal model is used for count data with variable normalization.
- Exact likelihood functions can be computationally intensive.
Purpose of the Study:
- To derive simple analytical approximations of Poisson-lognormal likelihood functions.
- To facilitate maximum likelihood data fitting for these models.
Main Methods:
- Numerical methods were employed to obtain analytical approximations.
- The approximations allow for the use of standard nonlinear-least-squares-minimization algorithms.
Main Results:
- Simple analytical approximations for the Poisson-lognormal likelihood function were successfully obtained.
- These approximations enable efficient data fitting.
Conclusions:
- The developed analytical approximations simplify the analysis of count data modeled by the Poisson-lognormal distribution.
- A publicly available computer program aids in applying these approximations.
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