Pixel Likelihood Calculation#

Reference/API#

ctapipe.image.pixel_likelihood Module#

Class for calculation of likelihood of a pixel expectation, given the pixel amplitude, the level of noise in the pixel and the photoelectron resolution. This calculation is taken from [DNR09].

The likelihood is essentially a poissonian convolved with a gaussian, at low signal a full possonian approach must be adopted, which requires the sum of contributions over a number of potential contributing photoelectrons (which is slow). At high signal this simplifies to a gaussian approximation.

The full and gaussian approximations are implemented, in addition to a general purpose implementation, which tries to intellegently switch between the two. Speed tests are below:

neg_log_likelihood_approx(image, prediction, spe, ped) 29.8 µs per loop

neg_log_likelihood_numeric(image, prediction, spe, ped) 93.4 µs per loop

neg_log_likelihood(image, prediction, spe, ped) 59.9 µs per loop

TODO:#

Need to implement more tests, particularly checking for error states
Additional terms may be useful to add to the likelihood

Functions#

`neg_log_likelihood_approx`(image, prediction, ...)	Calculate negative log likelihood for telescope.
`neg_log_likelihood_numeric`(image, ...[, ...])	Calculate likelihood of prediction given the measured signal, full numerical integration from [DNR09].
`neg_log_likelihood`(image, prediction, ...[, ...])	Safe implementation of the poissonian likelihood implementation, adaptively switches between the full solution and the gaussian approx depending on the prediction.
`mean_poisson_likelihood_gaussian`(prediction, ...)	Calculation of the mean of twice the negative log likelihood for a give expectation value of pixel intensity in the gaussian approximation.
`mean_poisson_likelihood_full`(prediction, ...)	Calculation of the mean of twice the negative log likelihood for a give expectation value of pixel intensity using the full numerical integration.
`chi_squared`(image, prediction, pedestal[, ...])	Simple chi-squared statistic from Le Bohec et al 2008

Classes#

PixelLikelihoodError