Doubly stochastic model

In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling

The basic idea for a doubly stochastic model is that an observed random variable is modelled in two stages. In one stage, the distribution of the observed outcome is represented in a fairly standard way using one or more parameters. At a second stage, some of these parameters (often only one) are treated as being themselves random variables. In a univariate context this is essentially the same as the well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series or stochastic model are simultaneously affected by the underlying parameters, either by using a single parameter affecting many outcome variates, or by treating the underlying parameter as a time-series or stochastic process in its own right.

The basic idea here is essentially similar to that broadly used in

An example of a doubly stochastic model is the following.

• Cox process

References