Symmetric coding region

The quantised coding region in the previous subsection was $R=[\theta-a(\theta), \theta+b(\theta)]$. This coding region is not symmetric as $\theta$ does not lie in the middle of the interval. Although an asymmetric coding region (section ) can be used, Wallace and Freeman [#!Wallace.Freeman:1987!#] decided upon a symmetric coding region, whereby $\theta$ lies in the middle of the coding region. The values of $a(\theta)$ and $b(\theta)$ chosen were

$$a(\theta) = b(\theta) = \frac{s(\theta)}{2}$$ (6)

where $s(\theta)$ is the spacing parameter and the coding region is now the interval $R=[\theta-\frac{s(\theta)}{2}, \theta+\frac{s(\theta)}{2}]$. Therefore, the message length equation can be simplified to -

$$\textrm{MesgLen~} = -\log_e \int_ {\theta - \frac{s(\theta)}... ...c{s(\theta)}{2}} -\log_e f(x\vert\theta^\prime) d\theta^\prime$$ (7)