Inverse problem approach to regularized regression models with application to predicting recovery after stroke.

Regression modelling is a powerful statistical tool often used in biomedical and clinical research. It could be formulated as an inverse problem that measures the discrepancy between the target outcome and the data produced by representation of the modelled predictors. This approach could simultaneously perform variable selection and coefficient estimation.

On the final size of epidemics in random environment.

This paper extends the final size result of the classical SIR epidemic model in constant and periodic environments to random environment. Conditionally on the basic reproduction number R0 recently defined for random environment and the initial infected population fraction, we prove a final size result of an epidemic governed by the SIR model with time-depending parameters. The parameters are driven by an ergodic inhomogeneous time-periodic Markov process with finite state space.

On the basic reproduction number in a random environment.

The concept of basic reproduction number R0 in population dynamics is studied in the case of random environments. For simplicity the dependence between successive environments is supposed to follow a Markov chain. R0 is the spectral radius of a next-generation operator.

The evolution of dispersal in random environment.

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.