Modelling preferential sampling in time

Abstract

Preferential sampling in time occurs when there is stochastic dependence between the process being modeled and the times of the observations. Examples occur in fisheries if the data are observed when the resource is available, in sensoring when sensors keep only some records in order to save memory and in clinical studies, when a worse clinical condition leads to more frequent observations of the patient. In all such situations the observation times are informative on the underlying process. To make inference in time series observed under Preferential Sampling we propose, in this work, a numerical method based on a Laplace approach to optimize the likelihood and to approximate the underlying process we adopt a technique based on stochastic partial differential equation. Numerical studies with simulated and real data sets are performed to illustrate the benefits of the proposed approach.