The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks.

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings.

Meta-analysis of 32 genome-wide linkage studies of schizophrenia

A genome scan meta-analysis (GSMA) was carried out on 32 independent genome-wide linkage scan analyses that included 3255 pedigrees with 7413 genotyped cases affected with schizophrenia (SCZ) or related disorders. The primary GSMA divided the autosomes into 120 bins, rank-ordered the bins within each study according to the most positive linkage result in each bin, summed these ranks (weighted for study size) for each bin across studies and determined the empirical probability of a given summed rank (P-SR) by simulation. Suggestive evidence for linkage was observed in two single bins, on chromosomes 5q (142-168 Mb) and 2q (103-134 Mb). Genome-wide evidence for linkage was detected on chromosome 2q (119-152 Mb) when bin boundaries were shifted to the middle of the previous bins. The primary analysis met empirical criteria for 'aggregate' genome-wide significance, indicating that some or all of 10 bins are likely to contain loci linked to SCZ, including regions of chromosomes 1, 2q, 3q, 4q, 5q, 8p and 10q. In a secondary analysis of 22 studies of European-ancestry samples, suggestive evidence for linkage was observed on chromosome 8p (16-33 Mb). Although the newer genome-wide association methodology has greater power to detect weak associations to single common DNA sequence variants, linkage analysis can detect diverse genetic effects that segregate in families, including multiple rare variants within one locus or several weakly associated loci in the same region. Therefore, the regions supported by this meta-analysis deserve close attention in future studies. Molecular Psychiatry (2009) 14, 774-785; doi:10.1038/mp.2008.135; published online 30 December 2008

An Update of the Rules for Pyranoside Sulfonate Displacement

The original 1967 Richardson–Hough rules for predicting SN2 displacement viability in carbohydrate sulfonate derivatives with external nucleophiles have now been updated. Not only do the original rules still hold, but the newly updated rules rationalize why O-triflates (trifluoromethanesulfonate esters) frequently allow many seemingly “disallowed” pyranosidic nucleophilic substitutions to proceed. The new guidelines, which are based on three decades of experimental evidence, allow the feasibility of many pyranosidic O-triflate SN2 displacements to be gauged beforehand.