The Akaike Information Criterion (AIC) is a powerful and highly principled method of model selection. When working with probabilistic models it is typical to fit them to the data by maximum likelihood, using Markov Chain Monte Carlo or Belief Propagation. The maximum likelihood value obtained in this way gives an indication of how good a fit the model is to the data. Unfortunately, models with ...

Recently, Azari et al (2006) showed that (AIC) criterion and its corrected versions cannot be directly applied to model selection for longitudinal data with correlated errors. They proposed two model selection criteria, AICc and RICc, by applying likelihood and residual likelihood approaches. These two criteria are estimators of the Kullback-Leibler’s divergence distance which is asymmetric. In...

Sometimes the maximum likelihood estimation procedure for the probit model fails. There may be two reasons: the maximum likelihood estimate (MLE) just does not exist or computer overflow error occurs during the computation of the cumulative distribution function (cdf). For example, the approximation explosive effect due to an inaccurate computation of the cdf for a large value of the argument o...

A fast and efficient estimation method is proposed that compensates the distortion in nonlinear transformation models. A likelihood-based estimator is developed that can be computed by an EM-type algorithm. The consistency of the estimator is shown and its limit distribution is provided. The new estimator is particularly well suited for fluorescence lifetime measurements, where only the shortes...

Computing all critical points of a monomial on very affine variety is fundamental task in algebraic statistics, particle physics and other fields. The number known as the maximum likelihood (ML) degree. When smooth, it coincides with Euler characteristic. We introduce degeneration techniques that are inspired by soft limits CEGM theory, we answer several questions raised literature. These perta...

The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates ...

Background: Photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of SPECT images and results to errors in accuracy of quantitative measurements. This can be corrected via different physical or mathematical approaches. As the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘Piece ...