Proper likelihood function of the ratio of two spectra

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SUMMARY

The discussion focuses on conducting an unbinned likelihood analysis of the ratio of two spectra, represented as \( \frac{S_{1}(E)}{S_{2}(E)} = F(E) \). The user seeks guidance on how to input their data for this analysis, particularly in the absence of binning, which complicates the process. Key concepts mentioned include likelihood analysis, probability models, and the distinction between binned and unbinned data. The conversation emphasizes the necessity of defining a probability model for the data to proceed effectively.

PREREQUISITES
  • Understanding of unbinned likelihood analysis
  • Familiarity with probability models in statistical analysis
  • Knowledge of maximum likelihood estimation
  • Experience with spectral data analysis
NEXT STEPS
  • Research methods for defining probability models for unbinned data
  • Learn about maximum likelihood estimation techniques in unbinned contexts
  • Explore likelihood ratio tests and their applications
  • Investigate software tools for spectral data analysis, such as ROOT or MATLAB
USEFUL FOR

Researchers and analysts in fields such as astrophysics, particle physics, or any domain involving spectral data analysis, particularly those working with unbinned likelihood methods.

QuantumDefect
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Hello PF'ers,

I am doing an unbinned likelihood analysis where I am analyzing the ratio of two spectra:
\[ \frac{S_{1}(E)}{S_{2}(E)} = F(E) \]

and each spectra,

\[ S_{1}, S_{2} \]

has its own data set. My first idea was to take the function, \[ F(E) \] and divide by the integral of the function to get a probability distribution but I am unsure how to input my data. If this was binned, it would be straight forward but in the unbinned case, it has stumped me. Anyone have any ideas? Thanks a bunch!
 
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QuantumDefect said:
Hello PF'ers,

I am doing an unbinned likelihood analysis

What is a likelihood analysis? (I've heard of maximum likelihood estimation and likelihood ratio tests.)

Things dealing with likelihood require a probability model. What is the probability model for you data?
 

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