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

Hemoglobin enhances the biological activity of synthetic and natural bacterial (endotoxic) virulence factors: a general principle.

Although hemoglobin (Hb) is mainly present in the cytoplasm of erythrocytes (red blood cells), lower concentrations of pure, cell-free Hb are released permanently into the circulation due to an inherent intravascular hemolytic disruption of erythrocytes. Previously it was shown that the interaction of Hb with bacterial endotoxins (lipopolysaccharides, LPS) results in a significant increase of the biological activity of LPS. There is clear evidence that the enhancement of the biological activity of LPS by Hb is connected with a disaggregation of LPS. From these findings one questions whether the property to enhance the biological activity of endotoxin, in most cases proven by the ability to increase the cytokine (tumor-necrosis-factor-alpha, interleukins) production in human mononuclear cells, is restricted to bacterial endotoxin or is a more general principle in nature. To elucidate this question, we investigated the interaction of various synthetic and natural virulence (pathogenicity) factors with hemoglobin of human or sheep origin. In addition to enterobacterial R-type LPS a synthetic bacterial lipopeptide and synthetic phospholipid-like structures mimicking the lipid A portion of LPS were analysed. Furthermore, we also tested endotoxically inactive LPS and lipid A compounds such as those from Chlamydia trachomatis. We found that the observations made for endotoxically active form of LPS can be generalized for the other synthetic and natural virulence factors: In every case, the cytokine-production induced by them is increased by the addition of Hb. This biological property of Hb is connected with its physical property to convert the aggregate structures of the virulence factors into one with cubic symmetry, accompanied with a considerable reduction of the size and number of the original aggregates.

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