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Using exact Poisson likelihood functions in Bayesian interpretation of counting measurements
Guthrie Miller1, Harry F Martz, Tom T Little
1Los Alamos National Laboratory, NM 87545, USA. guthrie@lanl.gov
Health Physics
|September 21, 2002
Summary
This study introduces an exact method for calculating Poisson likelihood in background-subtracted measurements. This approach offers practical advantages over Gaussian approximations, especially for small count data in scientific research.
Area of Science:
- Statistical methods
- Scientific measurement
- Dosimetry
Background:
- Background subtraction is common in counting measurements.
- Gaussian approximations are often used for Poisson likelihood.
- Accurate likelihood functions are crucial for reliable data analysis.
Purpose of the Study:
- To describe a technique for computing the exact marginalized Poisson likelihood function.
- To introduce an empirical Bayesian method for determining prior probability distributions.
- To implement exact likelihood functions in Bayesian internal dosimetry codes.
Main Methods:
- Developed a technique for exact marginalized Poisson likelihood computation.
- Recommended an empirical Bayesian method for background rate priors.
- Implemented exact likelihoods using an interpolation-table approach.
Main Results:
- The exact marginalized Poisson likelihood function can be computed.
- Empirical Bayesian method offers practical advantages for background priors.
- Differences between exact and Gaussian methods are observed with small counts.
Conclusions:
- The exact marginalized Poisson likelihood provides a more accurate alternative to Gaussian approximations.
- The empirical Bayesian method is advantageous for determining background priors.
- Exact likelihood functions can be used in dosimetry codes without computational penalty.