An 18th-century theory used by sports-bettors, gamblers and even weather forecasters could help criminologists and policymakers uncover the so-called “dark figure” of crime, according to a British researcher.
The study by Refat Aljumily, published this month in the Journal of Quantitative Criminology, argues that Bayesian probability theory can fill the “gap” in crime statistics between officially reported crimes and those that are either never reported to police or not disclosed by law enforcement.
The gap, long acknowledged by criminologists as the “dark figure” of crime, has led to fierce policy debates over crime rates and the prevalence of crimes such as domestic abuse that often are lost in official figures, Aljumily says.
“The fact [is] that many, if not most, minor and some serious crimes remain unknown to the police and other law and justice enforcement authorities, and that crime statistics [do] not provide the true rate of crimes occurring in society,” he wrote in a paper first presented earlier this month to a conference held at Sheffield Hallam University in the United Kingdom.
The Bayesian theorem, originally developed by an 18th century mathematician and theologian named Thomas Bayes, uses both probability formulas and informed judgment to estimate the likelihood of certain events.
One example often used is a gambler trying to guess the outcome of rolling a set of dice. Traditional probability thinking suggests that after six rolls of the dice, a “six” will come up at least once, on average. But a Bayesian might notice that sixes are turning up more often than expected, and he might conclude that other factors are at play—such as the possibility the dice are loaded. So he adjusts his expectations—even deciding that he should leave the game.
Some mathematicians have used Bayesian probability as well to predict the likelihood of adverse weather events or even the success of new drugs.
Applying the approach to crime, a statistician would combine both prior assumptions and evidence about the crime’s known prevalence in a given locality to try to estimate the “real” crime figure.
Aljumily concedes that the approach isn’t perfect, but he argues that Bayesian formulas can help reveal the true incidence of crimes that often are under-reported in official statistics such as sexual violence (crimes against women), and driving while intoxicated.
The full study, including examples of the formulas Aljumily suggests using, can be downloaded here.