A random walk in the literature on criminality: A partial and critical view on some statistical analyses and modelling approaches

Abstract

We are interested in the possible contributions of mathematical modelling of crime. We refer to numerous and quite recent papers that analyse and discuss empirical data in an attempt to discover stylised trends worthy of being understood through simple models. We summarise part of this literature and try to understand the reasons of important discrepancies in their conclusions. Then we present some recent modelling attempts that may help to understand the large variance in the statistical-based conclusions.

A dynamic economic model of criminal activity in the criminal law

“…Let denotes death speed, denotes the rate of the flow from the non-impoverished class N to the impoverished class P. 2 indicates transmission probability (for example, probability speed of transferring poor people to criminals or recovered people to criminals), 3 denotes speed of jailing of criminals, 4 is releasing of jailed from jail, 5 denotes speed of recovery of impoverished without committing crime, 0 ≤ 6 ≤ 1 is transmission coefficient of recovered people to criminal people and is probability of criminals to total people in society. As shown in Figure (1), in order that recovered or healthy people commit crime, it depends upon the fact that healthy person visits the criminal on which probability and it is regarding the ratio of criminal to total people, the probability of criminals and probability of transferring healthy people to commit crime.…”

“…Thus, those living in poverty can commit the crime than public population [1,2]. Delinquency is defined as theft, stealing [1][2][3]. In the paper of Becker, statistical and economic analysis is used to determine optimal control of crime [1].…”

Life and Death in a Gang-A Mathematical Model of Gang Membership

“…It must be emphasized at the onset that estimating the parameters in this model was extremely difficult due to the difficulty in quantifying parameters as well as difficulties in obtaining police and sociological records due to the sensitive nature of the research. Since some of the parameters can only be roughly estimated, the model is used not "to predict actual data but to explain stylized facts and understand the consequences of different hypothesis" (Gordon, 2010), as well as to suggest further data-gathering. In addition to estimating the parameters, the initial conditions N(0), S (0), G(0), R(0) must be estimated for use as initial values in the numerical ODE solvers.…”

Geographical influences of an emerging network of gang rivalries

“…Various models have been created to address criminal activity [23,48,46,9,56]. One such work uses an agent-based model to understand the formation of crime hot spots [55].…”