# likelihood_calculations¶

This module provides several functions for calculating likelihood values.

A ‘likelihood’ is an un-normalized probability, calculated from the pdf of a distribution. In this module, the pdf that is used is the Gaussian pdf.

The main function is cum_corr_loglikelihood() in that it can stand in for any of the other functions, in particular by setting the correlation coefficient to zero and possibly giving only a single point.

`likelihood_calculations.``aicc`(logLikelihood, n, k)

Akaike information criterion corrected for small sample size n = number of samples k = number of degrees of freedom

`likelihood_calculations.``likelihood`(y, m, sigma)

calculates likelihood given Gaussian statistics

Args:
y (float): measured value m (float): mean (expected model value) sigma (float): stdev of measurements
Returns:
un-normalized probability based on Gaussian distribution
`likelihood_calculations.``loglikelihood`(y, m, sigma)

calculate ln(likelihood) given Gaussian statistics

Args:
y (float): measured value m (float): mean (expected model value) sigma (float): stdev of measurements
Returns:
natural logarithm of un-normalized probability based on Gaussian distribution
`likelihood_calculations.``logLikelihoodLine`(y, sigmaB=None, left=None, right=None)

log likelihood of a straight line through the readings

`likelihood_calculations.``cum_loglikelihood`(y, m, sigma, left, right)

numpy accelerated sum of loglikelihoods

ARGS:
y (ndarray): measured values m (ndarray): associated mean values (the ‘model’) sigma (ndarray): associated stdev values left index of first y to include right index of last y to include
`likelihood_calculations.``conditional_likelihood`(rho, y1, m1, sigma1, y0, m0, sigma0)

Computes the conditional likelihood p(y1|y0) which should be read as: ...the probability of y1, given y0, when the values are partially correlated.

All arguments are standard floats

Args:
rho: correlation coefficient (0 <= rho < 1) y1: measured value at position 1 y0: measured value at position 0 m1: model value at position 1 m0: model value at position 0 sigma1: noise at position 1 sigma0: noise at position 0
`likelihood_calculations.``cum_corr_loglikelihood`(rho, y, m, sigma)

calculates the sum of correlated loglikelihoods of a measurement array using numpy acceleration

Args:
rho (float): average nearest neighbor correlation coeffiecient y (ndarray): measurements m (ndarray): means (model values) sigma (ndarray): stdev associated with each y
Returns:
sum of natural logarithms of nearest neighbor correlated measurements assuming measurements have Gaussian distributions