Estimating total drug offending in Victoria using statistical methodologies. Richard Watkins Craig Darragh Victoria Police

Aim of this presentation To present two types of statistical methodologies based on estimating unknown populations which we have been piloting. These statistical methodologies can be used to assist with interpreting trends in certain types of crimes. Traditional approaches such as triangulating with other data sources (i.e. surveys, hospital data) are useful but have limitations. Before discussing the methodologies, we’ll first go through the factors behind crime statistics to help better understand trends. Then show some current and long term trends in Drug offences. Run through the mechanics of the statistical methodologies and show some of the results. Finish up the presentation with how we intend to use them.

What are Crime Statistics? Crime statistics are a combination of:  Reported Crime  Detected crimes Crime Statistics are:  an indication of community safety.  tied to factors such as resourcing, strategies and policy changes.  are used by management to make decisions and to task & coordinate resources and police performance. They are not the “complete picture” of all crime.

Snapshot of current Drug offences in Victoria In 2011/12 the no. of drug offences recorded in Victoria increased by 23% compared to 2010/11 financial year. Drug (Cult., Manuf., Traff.) offences increased by 11% compared to 2010/11. Drug (Possess, Use) offences increased by 27% compared to 2010/11. Drug offences in 2011/12 comprised approximately 5% of Victoria’s total recorded crime. The use of drugs are associated with proportion of crimes against the person and property offending.

What does drug offences comprise of? Detected Drug Crimes is a function of the following factors:  No. of police members available to detecting drug crimes.  Productivity of those police members (strategies and targeting)  True extent of drug offending (detected crimes + dark figure) Offender Sworn Member Detected Offender

Victoria Police Capacity In 2011/12 sworn police members increased by 5% compared to the previous financial year. 1700/940 project will increase the force by 1700 sworn members and 940 Protective Security Officers (PSO’s) over a five year period which began in Building Operational Capacity & Capability (BOCC) project (~ 150 members back on the front line).

Long Term Drug Trends and current increases 13% increase in 2011/12 compared to 2010/11. 66% increase in 2011/12 compared to 2010/11. 9% increase in 2011/12 compared to 2010/11 Is this increased drug offending or increased police productivity?

Estimating unknown population sizes There are many statistical techniques in literature that have been proposed to estimate unknown population sizes. This presentation will focus on the following two techniques:  Good-Turing Estimation (GTE).  Zelterman Estimators (GTE with heterogeneous assumptions). Both techniques use the frequency count distributions of offenders to extrapolate a population estimate.

Good–Turing Estimation (GTE) Good-Turing was developed during World War II. It is based on the following principles:  The population is drawn from a Poisson Distribution.  Each offender is equally likely to be detected. The Good-Turing (1953) estimator uses the following equation: P 0 = f 1 / N the proportion of things you have not sampled = the number of things that you have sampled just only once divided by the total number of samples taken all together. Estimate unknown population using Horvtiz-Thompson Estimator GTE = n / (1 - P 0 ) Good, I.J. (1953). "The population frequencies of species and the estimation of population parameters". Biometrika 40 (3–4): 237–264. doi: /biomet/ JSTOR MR

Good–Turing Estimation (cont.) fifi CannabisHeroinATS Total Distinct Offenders (n) Total Samples 2011/12 (N) Good Turing Estimator Good-Turing estimation for selected drug types (2011/12) Cannabis: P0 = 5435 / 6417 = 85% GTE = 5888 / (1 – 0.85) = Heroin: P0 = 797 / 1023 = 78% GTE = 896 / (1 – 0.78) = 4056 ATS: P0 = 2717 / 3420 = 79% GTE = 3039 / (1 – 0.79) = 14784

Limitations of Good-Turing Estimation Based on homogenous assumptions (every offender has the same probability of being detected). Real data is heterogeneous (offenders have different probabilities of being detected). Due to the above Good-Turing underestimates population sizes. To help overcome this the use of Zelterman Estimator can be used instead.

Zelterman Estimator Zelterman (Zelterman, 1988) argued that the Poisson assumption might not be valid over the whole range but might be valid for small ranges of the data (say f i = 0,1,2) λ = 2f 2 / f 1 Lambda is the estimate for the Poisson distribution in the range of (f i = 0,1,2) P 0 = e – λ Zelterman, D.: Robust estimation in truncated discrete distributions with application to capture recapture experiments. Journal of Statistical Planning and Inference 18, (1988)

Zelterman Estimator (cont.) Zelterman estimation for selected drug types (2011/12) fifi CannabisHeroinATS Lambda Zelterman Estimator Good Turing Estimator

Population trend estimates - Cannabis

Population trend estimates - Heroin

Population trend estimates - ATS

Where to from here This is what we are experimenting with and what we have shown is only a subset of the results we have obtained. We haven’t officially implemented these techniques. We have found these techniques are designed for offender based crimes and not victim reported crimes. We have run these techniques for other offence categories like Drugs (Cult., manuf., Traff.), Weapons / Explosives, Handle Stolen Goods. Overall we believe it is a useful technique to help understand movements in selected offence categories.