This thesis tests novel methods of creating advice to assist police with behavioural aspects of investigations. Using a sample of 361 serial stranger sexual offenses, simulated samples, and a sample of 84 serial burglary offences, the paper predicts behavioural characteristics using frequency information and a cross-validation approach. Experiment 1 predicts dichotomous offender characteristics from dichotomous and categorical crime scene characteristics. Experiment 2 predicts continuous behavioural variables from point estimates. Novel Bayesian algorithms are compared to base rate, mean, and point estimate prediction methods. In Experiment 1, Bayes’ Theorem (74.6% accurate) predicts with 11.1% more accuracy than base rates (63.5% accurate), and provides improved advising estimates. In Experiment 2, Bayesian algorithms predict more accurately than mean and point estimate methods (this improvement is not always statistically significant). These tests suggest that Bayesian approaches increase predictive power. Advising statements are considered, and suggestions regarding future research for police decision support are discussed.