Table 2 Procedural comparisons based on a (highly simplified) investigative advising example

   Given: Two homicide cases in which knives and strangle wires were used (i.e., a knife and strangle wire were used in case 1 and a knife and strangle wire were used in case 2).

   Task: Assess whether

   a) the two cases are linked (i.e., they have a common offender), and

   b) the offender was known or a stranger to the victims.

a) Case linkage

b) Offender characteristic

Dimensional frequentist approach

1) “Crunch” all data from a relevant database into a minimal number of fundamental dimensions

1) The dimensional scores of the cases (obtained for “a”) point vaguely to certain offender characteristics that belong to or have similar dimensional scores as the cases themselves (e.g., given the offender used both a knife and a strangle wire, this may yield a higher score on a “sadism” dimension. Assume being a stranger offender is associated with sadism: If the offender is a stranger, then the evidence is more likely than the evidence would be if the offender were not a stranger).

2) Link the cases based on the similarity of their scores along these dimensions such that, if the cases have uncommonly similar dimensional scores based on the frequencies of such scores (according to some predetermined rule), it is predicted that they are linked.

2) Use more specific base rate analysis to obtain pared-down (quantified) likelihood estimates of the offender being a stranger by seeing what percentage of homicide cases involving a knife and strangle wire also involved a stranger offender (this number, the pared-down base rate, would constitute the likelihood estimate).

Note that this analysis estimates how probable the scores are assuming they occur by chance only, which is a different question than whether they are indeed linked.

3) Narratively combine the above to obtain 1) an argument, and 2) a quantification.

Bayesian approach

1) Keep each behavioural variable (in both the database and the cases themselves) as an individual unit of information, and evaluate the case information using Bayesian reasoning. For this, iteratively train a model with the cases of a relevant database to predict the random variable: linkage.

1) Obtain the prior likelihood of the offender being a stranger to the victim (this could be the simple base percentage of stranger homicides among all homicides, or an investigator’s initial opinion).

2) Produce a probability estimate of whether the cases are linked given their behavioural variable values. That is, combine using Bayes’ theorem the case information and the trained model developed from the database, into a posterior estimate. This approach treats the conditional likelihood (from “a 2” above) as only one element of the linkage estimate.

2) Produce a conditional likelihood, based on the database, of an offender using a knife and wire given the offender is a stranger to the victim.

3) Combine the prior, likelihood, and the case data using Bayes’ theorem. In this way, the probability that the offender is a stranger to the victim, based on the fact that the offender used a knife and wire, can be explicitly assessed within the context of the (specific) pertinent data, and a singular value can be obtained.