Parametric Inference for Stochastic Differential Equations
Author
Summary, in Swedish
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.
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.
Department/s
Publishing year
2012
Language
English
Full text
Document type
Student publication for Master's degree (two years)
Topic
- Mathematics and Statistics
Supervisor
- Umberto Picchini