A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an e...

Stochastic differential equation (SDE) models have shown useful to describe continuous time processes, e.g. a physiological process evolving in an individual. Biomedical experiments often imply repeated measurements on a series of individuals or experimental units and individual differences can be represented by incorporating random effects into the model. When both system noise and individual ...

Markov Logic Networks (MLNs) combine Markov networks and first-order logic by attaching weights to first-order formulas and viewing these as templates for features of Markov networks. Learning the structure of MLNs is performed by state-of-the-art methods by maximizing the likelihood of a relational database. This can lead to suboptimal results given prediction tasks. On the other hand better r...

Conditional Poisson models have been used to analyze vaccine safety data from self-controlled case series (SCCS) design. In this paper, we derived the likelihood function of fixed effects models in analyzing SCCS data and showed that the likelihoods from fixed effects models and conditional Poisson models were proportional. Thus, the maximum likelihood estimates (MLEs) of time-varying variables...

We propose a general approach for estimating the parameters of latent variable probability models to maximize conditional likelihood and discriminant criteria. Unlike joint likelihood, these objectives are better suited for classiication and regression. The approach utilizes and extends the previously introduced CEM framework (Conditional Expectation Maximization), which reformulates EM to hand...

We introduce Multi-Conditional Learning, a framework for optimizing graphical models based not on joint likelihood, or on conditional likelihood, but based on a product of several marginal conditional likelihoods each relying on common sets of parameters from an underlying joint model and predicting different subsets of variables conditioned on other subsets. When applied to undirected models w...

We consider regression models in which covariates and responses jointly form a higher order Markov chain. A quasi-likelihood model speciies parametric models for the conditional means and variances of the responses given the past observations. A simple estimator for the parameter is the maximum quasi-likelihood estimator. We show that it does not use the information in the model for the conditi...

This paper presents a new approach to conditional inference, based on the simulation of samples conditioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of long runs of the sample given the observed statistics is provided. It is shown that when the conditioning statistics is sufficient for a given parameter, the approximating densi...

Recently, we proposed an autoregressive linear mixed effects model for the analysis of longitudinal data in which the current response is regressed on the previous response, fixed effects, and random effects (Funatogawa et al., Statist. Med. 2007; 26:2113-2130). The model represents profiles approaching random equilibriums. Because intermittent missing is an inherent problem of the autoregressi...