Non-Gaussian Statistical Models for Individualised Predictions

05/12/2018, 14:00 - 15:00 in MAP/0G/005

Asar, Özgür (Istanbul)


Abstract:

This talk is on statistical modelling for predicting concurrent and future events; called nowcasting and forecasting, respectively. We consider these problems using data-sets that exhibit departures from Gaussian distribution. The talk will be two- fold.

In the first, the interest is on modelling long series of repeated measures from large number of study units. The modelling framework postulates that observed outcomes can be de-composed into fixed-effects, random-effects, a continuous-time stochastic process, and random noise. Distributions of random-effects coefficients, stochastic process and noise are specified using Normal variance-mean mixtures. Likelihood- based inference is implemented by a computationally efficient stochastic gradient algorithm. Random components are predicted by either of filtering or smoothing distributions. The R package ngme provides functions to implement the methodology.

In the second, the interest is on joint modelling of repeated measures and time- to-event outcomes. The framework combines linear mixed models for repeated measures and Cox modelling with time-varying frailty for time-to-event outcome. Random-effects and noise terms are assumed to be t-distributed. We take the Bayesian paradigm for inference, and sample from the joint posterior density using Markov Chain Monte Carlo methods. Individualised dynamic predictions for both repeated measures and survival outcome are obtained. Methods are implemented in the R package robjm.