Decision-theoretic analysis of forensic sampling criteria using Bayesian decision networks

Sampling issues represent a topic of ongoing interest to the forensic science community essentially because of their crucial role in laboratory planning and working protocols. For this purpose, forensic literature described thorough (Bayesian) probabilistic sampling approaches. These are now widely implemented in practice. They allow, for instance, to obtain probability statements that parameters of interest (e.g., the proportion of a seizure of items that present particular features, such as an illegal substance) satisfy particular criteria (e.g., a threshold or an otherwise limiting value). Currently, there are many approaches that allow one to derive probability statements relating to a population proportion, but questions on how a forensic decision maker - typically a client of a forensic examination or a scientist acting on behalf of a client - ought actually to decide about a proportion or a sample size, remained largely unexplored to date. The research presented here intends to address methodology from decision theory that may help to cope usefully with the wide range of sampling issues typically encountered in forensic science applications. The procedures explored in this paper enable scientists to address a variety of concepts such as the (net) value of sample information, the (expected) value of sample information or the (expected) decision loss. All of these aspects directly relate to questions that are regularly encountered in casework. Besides probability theory and Bayesian inference, the proposed approach requires some additional elements from decision theory that may increase the efforts needed for practical implementation. In view of this challenge, the present paper will emphasise the merits of graphical modelling concepts, such as decision trees and Bayesian decision networks. These can support forensic scientists in applying the methodology in practice. How this may be achieved is illustrated with several examples. The graphical devices invoked here also serve the purpose of supporting the discussion of the similarities, differences and complementary aspects of existing Bayesian probabilistic sampling criteria and the decision-theoretic approach proposed throughout this paper.

Large multi-gene phylogenetic trees of the grasses (Poaceae): progress towards complete tribal and generic level sampling.

In this paper we included a very broad representation of grass family diversity (84% of tribes and 42% of genera). Phylogenetic inference was based on three plastid DNA regions rbcL, matK and trnL-F, using maximum parsimony and Bayesian methods. Our results resolved most of the subfamily relationships within the major clades (BEP and PACCMAD), which had previously been unclear, such as, among others the: (i) BEP and PACCMAD sister relationship, (ii) composition of clades and the sister-relationship of Ehrhartoideae and Bambusoideae + Pooideae, (iii) paraphyly of tribe Bambuseae, (iv) position of Gynerium as sister to Panicoideae, (v) phylogenetic position of Micrairoideae. With the presence of a relatively large amount of missing data, we were able to increase taxon sampling substantially in our analyses from 107 to 295 taxa. However, bootstrap support and to a lesser extent Bayesian inference posterior probabilities were generally lower in analyses involving missing data than those not including them. We produced a fully resolved phylogenetic summary tree for the grass family at subfamily level and indicated the most likely relationships of all included tribes in our analysis.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.