arXiv subjects

Aafko Boonstra

Publications and source records attributed to Aafko Boonstra.

3 recordsLinked to original sources

arXiv2024

A Bayesian framework for analyzing alleged cheating in sports through hidden codes, with applications to bridge and baseball

We develop a statistical framework to evaluate evidence of alleged cheating involving illegal signaling in sports from a forensic perspective. We explain why, instead of a frequentist procedure, a Bayesian approach is called for. We apply this framework to cases of alleged cheating in professional bridge and professional baseball. The diversity of these applications illustrates the generality of the method.

stat.AP↗

arXiv2024

Reconciling common source, specific source, feature based and score based likelihood ratios

We show that the incorporation of any new piece of information allows for improved decision making in the sense that the expected costs of an optimal decision decrease (or, in boundary cases where no or not enough new information is incorporated, stays the same) whenever this is done by the appropriate update of the probabilities of the hypotheses. Versions of this result have been stated before. However, previous proofs rely on auxiliary constructions with proper scoring rules. We, instead, offer a direct and completely general proof by considering elementary properties of likelihood ratios only. We apply our results to make a contribution to the debates about the use of score based/feature based and common/specific source likelihood ratios. In the literature these are often presented as different ``LR-systems''. We argue that the difference between these is simply a matter which information is processed. There is no therefore no such thing as different ``LR-systems'', there are only differences in the processed information. In particular, despite claims to the contrary, scores can very well be used in forensic practice and we illustrate this with an extensive example in DNA kinship context.

math.ST↗

arXiv2024

Constructions of normal numbers with infinitely many digits

Let $L=(L_d)_{d \in \mathbb N}$ be any ordered probability sequence, i.e., satisfying $0 < L_{d+1} \le L_d$ for each $d \in \mathbb N$ and $\sum_{d \in \mathbb N} L_d =1$. We construct sequences $A = (a_i)_{i \in \mathbb N}$ on the countably infinite alphabet $\mathbb N$ in which each possible block of digits $\alpha_1, \ldots, \alpha_k \in \mathbb N$, $k \in \mathbb N$, occurs with frequency $\prod_{d=1}^k L_{\alpha_d}$. In other words, we construct $L$-normal sequences. These sequences can then be projected to normal numbers in various affine number systems, such as real numbers $x \in [0,1]$ that are normal in GLS number systems that correspond to the sequence $L$ or higher dimensional variants. In particular, this construction provides a family of numbers that have a normal L\"uroth expansion.

math.NT↗