This paper documents the performance of a Bayesian Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM). This distribution was originally developed as an extension of the Poisson distribution in 1962 and has a unique characteristic, in that it can handle both under-dispersed and over-dispersed count data. Previous work by the authors lead to the development of a dual-link GLM bas...

In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: 1) collinearity of regressors is a factor of estimation instability, and 2) as predictive dimensions may lean on noise, bo...

We introduce the Recurrent Generalized Linear Model (R-GLM), an extension of GLMs based on a compact representation of the spiking history through a linear recurrent neural network. R-GLMs match the predictive likelihood of Linear Dynamical Systems (LDS) with linear-Gaussian observations. We also address a disadvantage of GLMs, including the R-GLM, that they cannot model instantaneous correlati...

Recruitment estimates for yellowfin tuna (Thunnus albacares) in the western and central Pacific Ocean (WCPO), derived from a stock assessment model, are highly variable seasonally, interannually, and over decadal periods. A generalized linear model (GLM) was developed that predicts the variation in yellowfin tuna recruitment in response to a range of oceanographic variables. The GLM model accou...

Dandekar S, Privitera C, Carney T, Klein SA. Neural saccadic response estimation during natural viewing. J Neurophysiol 107: 1776–1790, 2012. First published December 14, 2011; doi:10.1152/jn.00237.2011.— Studying neural activity during natural viewing conditions is not often attempted. Isolating the neural response of a single saccade is necessary to study neural activity during natural viewin...

Studying neural activity during natural viewing conditions is not often attempted. Isolating the neural response of a single saccade is necessary to study neural activity during natural viewing; however, the close temporal spacing of saccades that occurs during natural viewing makes it difficult to determine the response to a single saccade. Herein, a general linear model (GLM) approach is appl...

We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincaré (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then state the EP Averaging Lemma – that GLM averaged equations arise from GLM averaged Lagrangians in the EP framework. Next, we derive a set of approximate small amplitude GLM equations (glm ...

Running title GLM with natural sounds 2 2 ABSTRACT In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimul...