Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties
- Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics
The fitting of data by {chi}{sup 2}-minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimates for the fit parameters. They compare this method with a {chi}{sup 2}-minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than {approximately}20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers.
- Research Organization:
- Wisconsin Univ., Madison, WI (United States). Plasma Physics Research
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG02-85ER53198
- OSTI ID:
- 266730
- Report Number(s):
- DOE/ER/53198-274; CONF-960543-26; ON: DE96012000; TRN: 96:017025
- Resource Relation:
- Journal Volume: 68; Journal Issue: 1; Conference: 11. annual high-temperature plasma diagnostics conference, Monterey, CA (United States), 12-16 May 1996; Other Information: PBD: Jun 1996
- Country of Publication:
- United States
- Language:
- English
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