Reception data for different sentence categories are projected separately for adults and young offenders and then converted into populations. Female prisoner numbers are not projected separately as the number of women in custody is too small to be modelled statistically. The data used are derived from the Scottish Prison Service management information system.
Some groups of prisoners are treated differently from the direct sentenced group for the projections (details shown in Table 4 in Annex):
- Remand receptions are projected as a proportion of direct sentenced receptions during 2008.
- Part of the prison population consists of persons who have been previously released under licence or supervision but subsequently recalled into custody. This population has been projected as a proportion of the long-term population.
- Receptions of fine defaulters are held constant at 2008 levels. This group spends very short periods in custody (around three days) and so any change in the number of receptions makes very little difference to the resulting projected population.
- The population of other types of prisoners is also very low and held constant at 2008 levels.
Projected receptions are converted into populations using the average time spent in custody, or time served factor, for each sentence band (see Table 5 in Annex for more detail on time served factors).
The projection model was run during December 2009 using the most recent available reception data to October 2009. The underlying trends assumed for all categories of sentenced receptions are trends in receptions since 1972, but the projected trends are based on a range of time periods in order to model more accurately changes of different magnitudes over different time scales.
Sensitivity of population projections: high and low variants
A range of methods are required to compensate for the inherent volatility of the population over time, particularly for the smaller groups. Three time periods are used to take account of short (past 10 years), medium (past 25 years) and long (since 1972) term trends. Two different approaches are used: exponential smoothing models the seasonal variation over the year using monthly data, while linear regression models underlying trends using annual data. This gives six projection variants for each sentence category.
The main projection is derived by combining the most likely projection variant for each sentence category. The sensitivity of the projection to the choice of variant is shown by the upper and lower limits for all possible projections, based on the highest and lowest variant for each sentence category (Chart 3).
Chart 3 Prison population projections: 2009-10 to 2018-19
At present, 10 years is the shortest time period used to establish a trend. This makes the projections less volatile in relation to potential short lived spikes in the figures. However, in periods of rapid change such as the ones observed over the past few years, it is difficult to predict to what extent an initial spike may turn out to be the leading edge of a change in trend.
For example, the high variant for the October 2008 projections gave the best fit at that point. The next highest projection substantially under projected the population for 2008, confirming to some extent that recent developments were driving the increases at that point in time.
However, for the 2009 projections, the volatility of the population appears to have stabilised to some degree. It is still showing an overall upward trend, although the rate of increase seems to have eased off somewhat. The choice of main variant reflects this in that it is relatively high (in line with the consistently upward trend over the past 10 years), but not the highest variant (Table 3).
Table 3 Prison population projection variants: October 2008 and October 2009
Main (high) variant