Posts tagged ‘Rostislav Protassov’

Likelihood Ratio Test Statistic [Equation of the Week]

From Protassov et al. (2002, ApJ, 571, 545), here is a formal expression for the Likelihood Ratio Test Statistic,

TLRT = -2 ln R(D,Θ0,Θ)

R(D,Θ0,Θ) = [ supθεΘ0 p(D|Θ0) ] / [ supθεΘ p(D|Θ) ]

where D are an independent data sample, Θ are model parameters {θi, i=1,..M,M+1,..N}, and Θ0 form a subset of the model where θi = θi0, i=1..M are held fixed at their nominal values. That is, Θ represents the full model and Θ0 represents the simpler model, which is a subset of Θ. R(D,Θ0,Θ) is the ratio of the maximal (technically, supremal) likelihoods of the simpler model to that of the full model.
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