Related papers: Poisson--Gamma Dynamical Systems
Prediction modelling of claim frequency is an important task for pricing and risk management in non-life insurance and needed to be updated frequently with the changes in the insured population, regulatory legislation and technology.…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
This paper presents a novel approach to stochastic mortality modelling by using the Conway--Maxwell--Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of…
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
An important issue in model-based control design is that an accurate dynamic model of the system is generally nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based…
A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed…
We propose a statistical model for networks of event count sequences built on a cascade structure. We assume that each event triggers successor events, whose counts follow additive probability distributions; the ensemble of counts is given…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors, the field of quantitative behavioral research has evolved to increasingly rely upon panel count…
This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…