Linguistic Bayesian Networks for reasoning with subjective probabilities in forensic statistics

Recent work in forensic statistics has shown how Bayesian Networks (BNs) can be used to infer the probability of defence and prosecution statements based on forensic evidence. This is an important development as it helps to quantify the meaning of forensic expert testimony during court proceedings, for example, that there is "strong support" for the defence or prosecution position. Due to the lack of experimental data, inferred probabilities often rely on subjective probabilities provided by experts. Because these are based on informed guesses, it is very difficult to express them accurately with precise numbers. Yet, conventional BNs can only employ probabilities expressed as real numbers. To address this issue, this paper presents a novel extension of probability theory. This allow the expression of subjective probabilities as fuzzy numbers, which more faithfully reflect expert opinion. By means of practical a example, it will be shown that the accurate representation of this lack of precision in reasoning with subjective probabilities has important implications for the overall result.