Credibility Theory and Generalized Linear Models

Signal Detection Theory and Generalized Linear Models

Generalized linear models are a general class of regressionlike models for continuous and categorical response variables. Signal detection models can be formulated as a subclass of generalized linear models, and the result is a rich class of signal detection models based on different underlying distributions. An example is a signal detection model based on the extreme value distribution. The ex...

Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Basic Theory for Generalized Linear Solid Viscoelastic Models

In this paper, we consider the generalized linear solid model of viscoelastic wave propagation, which is modeled by a system of integro-differential equations. We show the existence and uniqueness of a weak solution to the initial-boundary value problem; we show that the solution has finite propagation speed; and we prove regularity results for the solution, depending on the regularity of the d...

Generalized Linear Mixed Models

Generalized linear models (GLMs) represent a class of fixed effects regression models for several types of dependent variables (i.e., continuous, dichotomous, counts). McCullagh and Nelder [32] describe these in great detail and indicate that the term ‘generalized linear model’ is due to Nelder and Wedderburn [35] who described how a collection of seemingly disparate statistical techniques coul...

Generalized Linear Models