ASSESSMENT OF RISK FOR VIOLENT
RECIDIVISM THROUGH MULTIVARIATE
BAYESIAN CLASSIFICATION
Andreas Mokros
University of Regensburg
Cornelis Stadtland
Ludwig-Maximilian University Munich
Michael Osterheider
University of Regensburg
Norbert Nedopil
Ludwig-Maximilian University Munich
Bayesian reasoning has already been applied in the area of assessing recidivism risk.
Based on single predictors for re-offending, various authors have pointed out that
Bayesian analysis was suited to the problem because the base rate of recidivism
could be accounted for in terms of a prior probability. The present paper extends this
argument towards the multivariate case. The result is a case-specific probabilistic
assessment that allows judges and juries to reach informed decisions. The present
paper illustrates the method through the combination of offender’s age with data
from a structured professional risk assessment instrument, the Psychopathy Check-
list-Revised (PCL-R), for a sample of N
393 German convicts. The combination
of these two criteria emerged as optimal from all available subsets of predictors
(including the History Clinical Risk-20 and its components). The effect size for the
Bayesian combination measure with regard to violent offense recidivism was large
and significantly higher than the predictive value for each of its constituents. The
study design was retrospective, average time at risk was 6.5 years.
Keywords: risk assessment, Bayes, PCL-R, HCR-20, violent recidivism
Despite the surge in developing structured or actuarial instruments for risk
assessment over the last decade (Simon, 2005) the use of these instruments for
legal decision making has been met with unease by some authors (e.g., Vrieze &
Grove, 2008; Wollert, 2006). While several scholars have demonstrated superi-
ority of statistical over clinical prediction of offense recidivism in terms of
accuracy (e.g., see the meta-analyses by Grove, Zald, Lebow, Snitz, & Nelson,
2000, and by Hanson and Morton-Bourgon, 2009), concerns have been raised for
various reasons with regard to communicating and utilizing actuarial information
within the legal domain (Amenta, Guy, & Edens, 2002; Hilton, Harris, Rawson,
& Beach, 2005; Prentky, Janus, Barbaree, Schwartz, & Kafka, 2006).
Andreas Mokros and Michael Osterheider, Department of Forensic Psychiatry and Psycho-
therapy, University of Regensburg, Germany; Cornelis Stadtland, and Norbert Nedopil, Department
of Forensic Psychiatry, Ludwig-Maximilian University Munich, Germany.
The authors wish to thank Drs Karl Hanson and Douglas Mossman as well as three reviewers
for valuable comments and suggestions concerning the manuscript.
Correspondence concerning this article should be addressed to Andreas Mokros, University
of Regensburg, Department of Forensic Psychiatry and Psychotherapy, District Hospital,
Universitaetsstrasse 84, D-93053 Regensburg, Germany. E-mail: andreas.mokros@medbo.de
Psychology, Public Policy, and Law
2010, Vol. 16, No. 4, 418–450
© 2010 American Psychological Association
1076-8971/10/$12.00 DOI: 10.1037/a0021312
418

Relevance of Mitigating Factors
There are several factors that may reduce the odds for re-offending. Often-
times, these factors are not fully acknowledged. Among these mitigating factors
are the offender’s age (Wollert, 2006) as well as comparatively low base-rates of
re-offending (Prentky et al., 2006).
Base Rate of Re-Offending
The term base rate denotes the relative frequency with which a relevant
circumstance occurs in a reference set, such as the proportion of left-handed
people in the population. As Koehler (2002) reports courts may deem base rate
information as relevant if the case in question closely matches the features of a
reference class. More specifically, base rates may inform legal decision makers in
terms of a prior probability (Koehler, 2002). Applied to the present question:
Without knowing anything else, what is the relative risk for a released perpetrator
of a given kind to offend again? This is one of the uses of base rates that Koehler
explicitly refers to. The statistical framework for applying base rates or prevalence
estimates is Bayesian reasoning (Mossman & Somoza, 1991) that will be de-
scribed in more detail further below.
As far as prediction outcome is concerned, there is an interplay of the base
rate (in terms of the prior probability for re-offending) with the accuracy of
the risk assessment instrument in question. To put it simply, rare events are more
difficult to detect or to predict than frequent ones. Hence, a test has to achieve
higher levels of sensitivity and specificity the lower a given base rate is.1 As Janus
and Meehl (1997) have shown, the predicted risk of re-offending will be inflated
if the base rate of offense recidivism is below 50% and if this fact is not duly
considered within the assessment procedure. To achieve a rate of at least 50% true
positives (recidivists) within the commitment class through a risk assessment
procedure that has 70% sensitivity and specificity, for example, the corresponding
base rate would have to exceed 30% (Janus & Meehl, 1997, p. 55).
Hence, the inclusion of base rate information into the process of risk assess-
ment is indispensable. Given that some sources question the relevance of statistics
derived from groups for individual cases altogether (e.g., Amenta et al., 2002;
1 Given a particular threshold value, sensitivity denotes the proportion of cases correctly
identified (true positive rate) and specificity refers to the proportion of noncases correctly rejected
(true negative rate). As Meehl and Rosen (1955; cf Janus & Meehl, 1997) demonstrated, a test will
only allow for identifying more cases correctly than causing false alarms (false positive results) if
the ratio of cases to noncases exceeds the ratio of (1 – specificity) divided by sensitivity. The ratio
of cases (recidivists) to noncases (nonrecidivists) in the group with a positive test result is also
termed positive predictive value (PPV; Altman & Bland, 1994) and corresponds to the Bayesian
posterior probability. The relationships between the positive predictive value, sensitivity, specificity
and the base rate can thus be summarized as follows:
PPV
PH
D  .50 N
TPR  PH
FPR  1  PH  1 N
PH
1  PH 
FPR
TPR ,
with PPV
positive predictive value, P(H
D)
posterior probability, TPR
true positive rate (i.e.
sensitivity), FPR
false positive rate (i.e. the complement of the true negative rate [specificity] to
1), P(H)
prior probability (here: base rate of re-offending).
419ASSESSMENT OF RISK