Fabio Corradi

Probabilistic Classification of Age by Third Molar Development: The Use of Soft Evidence

Abstract:  This study introduces a method to classify individuals according to an age threshold, given sex and third molars’ dental maturity measured on the Demirjian scale by expressing uncertainty on dental evidence (soft evidence). We introduced a procedure to learn the parameters of the Naïve Bayes model, and we discussed two classification rules. The model was estimated and tested on 559 Italians aged 16–22. Two experts provided the dental evaluations, and the model was estimated for each of them. We evaluated the coherence of the evidence provided by the experts. Some indexes have been proposed to evaluate the effectiveness of the models, emphasizing how the experts’ ability and the technology affect the results. We introduced two benchmarks, one based on the sample distribution per sex and age: in this case, probability of correct classification increases 22% and the proportion of false adults impressively decreases 80.2%; the other benchmark, obtained by simulating hard evidence, shows how the use of soft evidence increases the proportion of correct classification 3.1% and decreases the crucial proportion of false adults about 20%. Similarly, the proportion of false minors decreases about 5.3%.

The evaluation of DNA evidence in pedigrees requiring population inference

The evaluation of nuclear DNA evidence for identification purposes is performed here taking account of the uncertainty about population parameters. Graphical models are used to detail the hypotheses being debated in a trial with the aim of obtaining a directed acyclic graph. Graphs also clarify the set of evidence that contributes to population inferences and they also describe the conditional independence structure of DNA evidence. Numerical illustrations are provided by re-examining three case-studies taken from the literature. Our calculations of the weight of evidence differ from those given by the authors of case-studies in that they reveal more conservative values. Copyright 2003 Royal Statistical Society.

Missing data and forecasting in multivariate time series: An application of the common components dynamic linear model

The paper deals with missing data and forecasting problems in multivariate time series making use of the Common Components Dynamic Linear Model (DLMCC), presented in Quintana (1985), and West and Harrison (1989).

Searching secrets rationally

We study quantitative information flow, from the perspective of an analyst who is interested in maximizing its expected gain in the process of learning a secret, or settling a hypothesis, represented by an unobservable X, after observing some Y related to X. In our framework, learning the secret has an associated reward, while the investigation of the set of possibilities prompted by the observation has a cost, proportional to the sets size. Approaches based on probability coverage, or on trying a fixed number of guesses, are sub-optimal in this framework. Inspired by Bayesian decision theory, we characterize the optimal behavior for the analyst and the corresponding expected gain (payoff) in a variety of situations. We argue about the importance of advantage, defined as the increment in expected gain after the observation if the analyst acts optimally, and representing the value of the information conveyed by Y. We characterize advantage precisely in a number of special but important instances of the framework. Applications to cryptographic systems and to familial DNA searching are examined. Quantitative information flow with a cost proportional to the number of possible guesses.The proposed strategy to choose the guess is demonstrated to be a Bayes Action.The advantage on discovering the secret is meaningfully decomposed.Examples concerning cryptographic systems and familial DNA searching are provided.Capacity is investigated for deterministic channels.