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 presented in most of the literature consists of plugging‐in Bayesian estimates of the involved nuisance parameters into a frequentist‐defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LRs for the ‘rare type match problem’, the situation in which the expert wants to evaluate a match between the DNA profile of a suspect and that of a trace from the crime scene, and this profile has never been observed before in the database of reference. LR assessment using the two most popular Bayesian models (beta‐binomial and Dirichlet‐multinomial) is discussed and compared with corresponding plug‐in versions.

The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the true one, and its parameters are estimated through a limited database. Moreover, it may be wise to discard part of data, especially that only indirectly related to the hypotheses. Different reductions define different LRs. Therefore, it is more sensible to talk about 'a' LR instead of 'the' LR, and the error involved in the estimation should be quantified. Two frequentist methods are proposed in the light of these points for the 'rare type match problem', that is, when a match between the perpetrator's and the suspect's DNA profile, never observed before in the database of reference, is to be evaluated.

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The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) is based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles, that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions, and discards the information about the names of the different DNA profiles. This fits very well the data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes approach.

Screening plans for prevention and containment of SARS-CoV-2 infection should take into account the epidemic context, the fact that undetected infected individuals may transmit the disease, and that the infection spreads through outbreaks, creating clusters in the population. In this paper, we compare the performance of six screening plans based on poorly sensitive individual tests, in detecting infection outbreaks at the level of single classes in a school context. The performance evaluation is done by simulating different epidemic dynamics within the class during the five weeks following the day of the first infection. The plans have different costs in terms of number of individual tests required for the screening and are based on recurrent evaluations on all students or subgroups of students in rotation. Especially in scenarios where the rate of contagion is high, at an equal cost, testing half of the class in rotation every week appears to be better in terms of sensitivity than testing all students every two weeks. Similarly, testing one-fourth of the students every week is comparable with testing all students every two weeks, despite the first one is a much cheaper strategy. In the presence of natural clusters in the population, testing subgroups of individuals belonging to the same cluster in rotation may have a better performance than testing all the individuals less frequently. The proposed simulations approach can be extended to evaluate more complex screening plans than those presented in the paper.

The emergence of hyper-transmissible SARS-CoV-2 variants that rapidly became prevalent throughout the world in 2022 made it clear that extensive vaccination campaigns cannot represent the sole measure to stop COVID-19. However, the effectiveness of control and mitigation strategies, such as the closure of non-essential businesses and services, is debated. To assess the individual behaviours mostly associated with SARS-CoV-2 infection, a questionnaire-based case-control study was carried out in Tuscany, Central Italy, from May to October 2021. At the testing sites, individuals were invited to answer an online questionnaire after being notified regarding the test result. The questionnaire collected information about test result, general characteristics of the respondents, and behaviours and places attended in the week prior to the test/symptoms onset. We analysed 440 questionnaires. Behavioural differences between positive and negative subjects were assessed through logistic regression models, adjusting for a fixed set of confounders. A ridge regression model was also specified. Attending nightclubs, open-air bars or restaurants and crowded clubs, outdoor sporting events, crowded public transportation, and working in healthcare were associated with an increased infection risk. A negative association with infection, besides face mask use, was observed for attending open-air shows and sporting events in indoor spaces, visiting and hosting friends, attending courses in indoor spaces, performing sport activities (both indoor and outdoor), attending private parties, religious ceremonies, libraries, and indoor restaurants. These results might suggest that during the study period people maintained a particularly responsible and prudent approach when engaging in everyday activities to avoid spreading the virus.