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We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
Risk assessment algorithms in criminal justice put people's lives at the discretion of a simple statistical tool. This thesis explores how algorithmic decision-making in criminal policy can exhibit feedback effects, where disadvantage…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…
The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses and for its assessment Bayesian methods are widespread in the forensic field. However, the Bayesian `recipe' for the LR…
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
Forensic scientists are often criticised for the lack of quantitative support for the conclusions of their examinations. While scholars advocate for the use of a Bayes factor to quantify the weight of forensic evidence, it is often…
Accurate estimation of the change in crime over time is a critical first step towards better understanding of public safety in large urban environments. Bayesian hierarchical modeling is a natural way to study spatial variation in urban…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
A group of approaches for calculating forensic likelihood ratios first calculates scores which quantify the degree of difference or the degree of similarity between pairs of samples, then converts those scores to likelihood ratios. In order…
The criminalization of poverty has been widely denounced as a collective bias against the most vulnerable. NGOs and international organizations claim that the poor are blamed for their situation, are more often associated with criminal…
As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…
Crime rates per capita are used virtually everywhere to rank and compare cities. However, their usage relies on a strong linear assumption that crime increases at the same pace as the number of people in a region. In this paper, we…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
Modern statisticians are often presented with hundreds or thousands of hypothesis testing problems to evaluate at the same time, generated from new scientific technologies such as microarrays, medical and satellite imaging devices, or flow…
This paper proposes the use of graph pattern matching for investigative graph search, which is the process of searching for and prioritizing persons of interest who may exhibit part or all of a pattern of suspicious behaviors or…
We consider the problem of geographic profiling and offer an approach to choosing a suitable model for each offender. Based on the analysis of the examined dataset, we divide offenders into several types with similar behavior. According to…
We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…
Fairness-aware classification models have gained increasing attention in recent years as concerns grow on discrimination against some demographic groups. Most existing models require full knowledge of the sensitive features, which can be…