Chapter 6 Point Source Problems

Recall from Section 3.3 that a commonly-used model for spatial variation in risk is that:

• •

  $\lambda (x)=\alpha {\lambda }_0(x)\rho (x)$ where

  • –

    $\lambda (x)$ is the intensity of the Poisson process forming the cases

  • –

    ${\lambda }_0(x)$ is the intensity of the Poisson process forming the controls

  • –

    $\alpha$ is determined by the number of controls in the design

  • –

    $\rho (x)$ represents spatial variation in risk

Conditional on both case and control locations, case/control labels are determined by a series of independent Bernoulli trials with success probabilities

In Section 3.3 we looked at non-parametric models for $\rho$ that could be used when no information other than the case and control locations was available. In this section we consider scenarios in which there is a hypothesised model for the spatial variation in risk $\rho$.