Optimal covariance estimation of discrete-time locally self-similar processes in time-scale and ambiguity domains

This paper investigates the optimal estimate of the covariance function in the sense of mean-square of errors, for the class of discrete-time locally self-similar processes. The covariance function is estimated in time-scale and ambiguity domains. Since the class of estimators is completely characterized in terms of kernels, the problem is reduced to finding the optimal kernel, which is obtained in time-scale domain. Also, the optimal kernel is computed for two classes of discrete-time locally self-similar and locally self-similar chirp processes. Furthermore, it is shown that the proposed method gives more accurate estimate than the ordinary methods for non stationary processes.     

A stochastic graph process for epidemic modelling

A stochastic graph process with a Markov property is introduced to model the flow of an infectious disease over a known contact network. The model provides a probability distribution over unobserved infectious pathways. The basic reproductive number in compartmental models is generalized to a dynamic reproductive number based on the sequence of outdegrees in the graph process. The cumulative resistance and threat associated with each individual is also measured based on the cumulative indegree and outdegree of the graph process. The model is applied to the outbreak data from the 2001 foot‐and‐mouth (FMD) outbreak in the United Kingdom. The Canadian Journal of Statistics 40: 55–67; 2012 © 2012 Statistical Society of Canada