Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have succeeded in capturing word similarities as well as semantic and syntactic regularities. Instead, we aim at reviving interest in a model based on counts. We pr...

Mixture distributions provide flexibility in modeling data collected from populations having unexplained heterogeneity. While interpretations of regression parameters from traditional finite mixture models are specific to unobserved subpopulations or latent classes, investigators are often interested in making inferences about the marginal mean of a count variable in the overall population. Rec...

This paper explores the relation between non-exponential waiting times between events and the distribution of the number of events in a fixed time interval. It is shown that within this framework the frequently observed phenomenon of overdispersion, i.e. a variance that exceeds the mean, is caused by a decreasing hazard function of the waiting times, while an increasing hazard function leads to...

Bilinear models of count data with Poisson distribution are popular in applications such as matrix factorization for recommendation systems, modeling of receptive fields of sensory neurons, and modeling of neural-spike trains. Bayesian inference in such models remains challenging due to the product term of two Gaussian random vectors. In this paper, we propose new algorithms for such models bas...

Environmental data are spatial, temporal, and often come with many zeros. In this paper, we included space–time random effects in zero-inflated Poisson (ZIP) and ‘hurdle’ models to investigate haulout patterns of harbor seals on glacial ice. The data consisted of counts, for 18 dates on a lattice grid of samples, of harbor seals hauled out on glacial ice in Disenchantment Bay, near Yakutat, Ala...

This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well-known variants of the negative binomial model (the NB1 and NB2 forms). We then analyze some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these mo...

In a recent paper, Levy and Goldberg [2] pointed out an interesting connection between prediction-based word embedding models and count models based on pointwise mutual information. Under certain conditions, they showed that both models end up optimizing equivalent objective functions. This paper explores this connection in more detail and lays out the factors leading to differences between the...

Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and ecology (where the data can represent, for example, children counts associated...

Many cities are developing multiuse urban greenway trails to be used for recreation, exercise, and transportation. Analysts need many kinds of data about these new trails, but especially trail traffic because of its implications for the efficient allocation of resources for trail management. This paper addresses this need by presenting new information about the use of trails. We adapt and test ...

We develop a statistical model of browsing behavior by predicting the number of web pages, in a particular category, that are viewed by a user in a single web session. The purpose of this analysis is to better understand web browsing behavior, and to help predict which sessions are likely to result in retail visits. A single record in our database consists of the number of web pages viewed by a...