  We develop a Bayesian modeling framework to address a pressing real-life
problem faced by the police in tackling insurgent gangs. Unlike criminals
associated with common crimes such as robbery, theft or street crime, insurgent
gangs are trained in sophisticated arms and strategise against the government
to weaken its resolve. They are constantly on the move, operating over large
areas causing damage to national properties and terrorizing ordinary citizens.
Different from the more commonly addressed problem of modeling crime-events,
our context requires that an approach be formulated to model the movement of
insurgent gangs, which is more valuable to the police forces in preempting
their activities and nabbing them. This paper evolved as a collaborative work
with the Indian police to help augment their tactics with a systematic method,
by integrating past data on observed gang-locations with the expert knowledge
of the police officers. A methodological challenge in modeling the movement of
insurgent gangs is that the data on their locations is incomplete, since they
are observable only at some irregularly separated time-points. Based on a
weighted kernel density formulation for temporal data, we analytically derive
the closed form of the likelihood, conditional on incomplete past observed
data. Building on the current tactics used by the police, we device an approach
for constructing an expert-prior on gang-locations, along with a sequential
Bayesian procedure for estimation and prediction. We also propose a new metric
for predictive assessment that complements another known metric used in similar
problems.
