Parametric Inference for Stochastic Differential Equations
Angela Ciliberti · Lund University Publications Student Papers (Lund University) · 2012
Stochastic dierential equations (SDEs) proved a fundamental mathematical tool to model dynamics subject to randomness and are nowadays a necessary instrument in e.g. nancial mathematics, neuronal modelling, population growth and physiological modelling. In realistic applications SDEs parameters are unknown quantities that have to be estimated from available data. However inference for SDEs is non-trivial and a considerable amount of research eort has been devoted to such problem in the last 20 years. In this work we implement and compare several parameter estimation methods for SDEs based on (approximated) likelihood maximization using data collected at discrete times. The comparison has proved useful to select the most convenient likelihood approximation methodology for estimating the parameters of mixed-eects models based on SDEs. Such mixed-eect models are characterized by the introduction of random parameters into SDEs: this allow to model the inter-subjects variability characterising repeated-measurement experiments while simultaneously accounting for individual stochastic dynamics, thus providing a more precise estimation for population parameters. Finally a pharmacokinetic application considering real data from the time-course of theophilline concentrations when measured on several subjects is presented.