Conferencias: Una perspectiva general sobre algunos modelos estocásticos de crecimiento
Seminario 1: Growths equations and their stochastic generalizations: modeling and
inference.
14 de enero de 2025. Seminario 1 del IMAG. 9:00 horas
In this seminar the introduction of stochasticity in growth equations is developed. In
particular, the introduction of noise within the growth equations is discussed, distinguishing
between multiplicative and additive noises. The resulting stochastic diffusion processes
and their parametric inference procedures are discussed. Results for a general growth
curve including a wide family of growth phenomena are shown. Maximum likelihood
method is discussed, and its solution is obtained by means of metaheuristic techniques.
Several simulation studies and an application to real data are performed. The discussion of
the topics will be approached from an informal and not analytic point of view, to provide
students with the basic idea of these topics, favoring the intuitive aspect over
methodological rigor.
Seminario 2: Stochastic SIR model including growths: modeling and inference.
15 de enero de 2025. Seminario 1 del IMAG. 9:00 horas
In this talk the focus is on epidemiological models. In particular, the background of
Susceptible-Infected- Removed model is discussed, emphasizing the role of the
contribution of each subpopulation. The role of stochasticity in such models is also
addressed. However, the main contribution is made to the inference for SIR models. For a
SIR stochastic model, able to include the natural growth of the Susceptible population, the
inference is addressed by means of a quasi-maximum likelihood method. Numerical
procedures for determining the local maxima of the likelihood function are discussed.
Emphasis is placed on the problems associated with the use of such techniques and some
insights are provided.
