By Umberto Picchini
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Extra resources for Stochastic Differential Models With Applications To Physiology (Ph.D. dissertation)
Example text
We choose to employ the transition density approximation method suggested in Aït-Sahalia (2001, 2002b) for time-homogeneous SDE, since it is the fastest and the most accurate among the available methods (Durham and Gallant (2002), Jensen and Poulsen (2002)). This is a desirable condition to make the parameter estimation procedure proposed here effective and reliable. We thus derive an approximation to the likelihood function and estimate the parameters of a SDME model by (approximated) maximum likelihood.
2005, 2006a), the former being Paper 1 of this dissertation, that concerns of purely deterministic modelization, which has also been considered in Paper 2. Therefore, in this section we only summarize the Paper 2 contents. 2. 4 to validate our model. 3 we focus our attention on the mathematical and statistical part of our application. The present application has two main goals: on one hand it purports to determine whether, in a particular physiological situation, system error (or “system noise”) is identifiable and necessary to explain observations, above and beyond commonly accepted levels of measurement error.
7, where the residuals are plotted against percentiles from the U (0, 1) distribution. 05 the simulated residuals do not conform to the hypothesis of U (0, 1) distribution at a 5% confidence level. The tests have not been subjected to correction for simultaneous inference (Bonferroni or similar) in order to be more conservative. 05, except for the glycemia residuals for subject 6. 4 Conclusions In the present application, a (simple) deterministic model of the clamp procedure is studied first. 07) commonly accepted levels of measurement error in in vitro repeated testing of the same laboratory preparation.