In this Bachelor’s thesis we describe the use of probability and statistics in criminal justice. Statistical methods are base of criminal justice and criminology, not only for research based on statistical data and analysis, but also for evaluating hypotheses and evidence in the judicial process. Increasingly, a significant portion of the conclusion of legal proceedings is based on probabilistic calculations of the impact of evidence on initial and intermediate hypotheses. The concept of probability relies on comparing the probability of evidence based on two competing propositions, namely the prosecution's proposition and the defence's proposition, and it is very important in assessing evidence
as it provides an objective evaluation of their impact on the probability of a particular assumption or hypothesis. In this Bachelor’s thesis we also describe methods that are used in the evidence assessment.
The most frequently used method, and also one of the most developed ones, is based on Bayesian statistics. Bayesian statistics is a statistical branch that employs mathematical approaches to update prior probabilities of evidence into posterior probabilities. Challenges arise in determining prior probabilities, as there is a divided opinion on who should establish these probabilities and in what manner. Different methods of determination can yield different results, which is problematic since the entire Bayesian theory relies on these initial calculations. Due to the probabilistic nature of the Bayesian theorem, the measure of the evidential value uses the likelihood ratio.
As statistics in criminal law is still evolving and the knowledge and understanding of probability are quite limited among lawyers, judges, and juries, numerous fallacies arise. The most well-known examples of such fallacies are the Prosecutor's Fallacy, which is a well-known statistical problem, and a more significant fallacy stemming from it, known as the Defence Attorney's Fallacy. Because these fallacies often go unrecognized, their consequence can be an incorrect conclusion in the judicial process. The Prosecutor's Fallacy is based on the confusion of two different conditional probabilities with vastly different values. In the Defence Attorney's Fallacy, evidence presented by the accused that matches evidence of the criminal act is considered insignificant. Most other fallacies also arise from a misunderstanding of conditional probability.
Because fallacies are a significant issue, I also describe some appropriate approaches to avoid them. In my opinion, the most effective approach is the use of Bayesian networks, as they help us determine appropriate probability formulas within graphical models without displaying their complete algebraic form. They significantly enhance the evaluation of likelihood ratios used for evidence assessment and enable more complex analyses. Constructing them requires a consistent framework, as inconsistent approaches can yield different results. However, since the computation of hypotheses and evidence probabilities once again relies on Bayesian theory, the imperfections of Bayesian statistics are also transferred to Bayesian networks.
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