Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Valtioneuvos K.-A.Fagerholm 8/6 1970

Kirje 8.6.1970

Statsrådet K.-A. Fagerholm 8.6.1970

Kirje

Mutation identification by direct comparison of whole-genome sequencing data from mutant and wild-type individuals using k-mers.

Genes underlying mutant phenotypes can be isolated by combining marker discovery, genetic mapping and resequencing, but a more straightforward strategy for mapping mutations would be the direct comparison of mutant and wild-type genomes. Applying such an approach, however, is hampered by the need for reference sequences and by mutational loads that confound the unambiguous identification of causal mutations. Here we introduce NIKS (needle in the k-stack), a reference-free algorithm based on comparing k-mers in whole-genome sequencing data for precise discovery of homozygous mutations. We applied NIKS to eight mutants induced in nonreference rice cultivars and to two mutants of the nonmodel species Arabis alpina. In both species, comparing pooled F2 individuals selected for mutant phenotypes revealed small sets of mutations including the causal changes. Moreover, comparing M3 seedlings of two allelic mutants unambiguously identified the causal gene. Thus, for any species amenable to mutagenesis, NIKS enables forward genetics without requiring segregating populations, genetic maps and reference sequences.

Osastopäällikkö, tohtori A.K. Kivivuori 4/9 1972

Kirje 4.9.1972

Tal till K. J. Ståhlberg i mässhallen den 28.1.1945

Puhe

Frequent users of emergency departments present very high prevalence of mental health and substance use disorders, which are largery underdiagnosed by clinicians.

Background: The objective of this study was to determine if mental health and substance use diagnoses were equally detected in frequent users (FUs) compared to infrequent users (IUs) of emergency departments (EDs). Methods: In a sample of 399 adult patients (>= 18 years old) admitted to a teaching hospital ED, we compared the mental health and substance use disorders diagnoses established clinically and consigned in the medical files by the ED physicians to data obtained in face-to-face research interviews using the Primary Care Evaluation of Mental Disorders (PRIME-MD) and the Alcohol, Smoking and Involvement Screening Test (ASSIST). Between November 2009 and June 2010, 226 FUs (>4 visits within a year) who attended the ED were included, and 173 IUs (<= 4 visits within a year) were randomly selected from a pool of identified patients to comprise the comparison group. Results: For mental health disorders identified by the PRIME-MD, FUs were more likely than IUs to have an anxiety (34 vs. 16%, Chi2(1) = 16.74, p <0.001), depressive (47 vs. 25%, Chi2(1) = 19.11, p <0.001) or posttraumatic stress (PTSD) disorder (11 vs. 5%, Chi2(1) = 4.87, p = 0.027). Only 3/76 FUs (4%) with an anxiety disorder, 16/104 FUs (15%) with a depressive disorder and none of the 24 FUs with PTSD were detected by the ED medical staff. None of the 27 IUs with an anxiety disorder, 6/43 IUs (14%) with a depressive disorder and none of the 8 IUs with PTSD were detected. For substance use disorders identified by the ASSIST, FUs were more at risk than IUs for alcohol (24 vs. 7%, Chi2(1) = 21.12, p <0.001) and drug abuse/dependence (36 vs. 25%, Chi2(1) = 5.52, p = 0.019). Of the FUs, 14/54 (26%) using alcohol and 8/81 (10%) using drugs were detected by the ED physicians. Of the IUs, 5/12 (41%) using alcohol and none of the 43 using drugs were detected. Overall, there was no significant difference in the rate of detection of mental health and substance use disorders between FUs and IUs (Fisher's Exact Test: anxiety, p = 0.567; depression, p = 1.000; PTSD, p = 1.000; alcohol, p = 0.517; and drugs, p = 0.053). Conclusions: While the prevalence of mental health and substance use disorders was higher among FUs, the rates of detection were not significantly different for FUs vs. IUs. However, it may be that drug disorders among FUs were more likely to be detected.