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. Central notations 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 understood easily 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 weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces 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 functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Making Multiple Decisions Adaptively

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptive procedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition for the existence of such a procedure is derived. Several examples are investigated in detail, and possible lack of adaptation of the traditional overall maximum likelihood rule is discussed.

A genome wide linkage scan for dizygotic twinning in 525 families of mothers of dizygotic twins

BACKGROUND: The tendency to conceive dizygotic (DZ) twins is a complex trait influenced by genetic and environmental factors. To search for new candidate loci for twinning, we conducted a genome-wide linkage scan in 525 families using microsatellite and single nucleotide polymorphism marker panels. METHODS AND RESULTS: Non-parametric linkage analyses, including 523 families containing a total of 1115 mothers of DZ twins (MODZT) from Australia and New Zealand (ANZ) and The Netherlands (NL), produced four linkage peaks above the threshold for suggestive linkage, including a highly suggestive peak at the extreme telomeric end of chromosome 6 with an exponential logarithm of odds \[(exp)LOD] score of 2.813 (P = 0.0002). Since the DZ twinning rate increases steeply with maternal age independent of genetic effects, we also investigated linkage including only families where at least one MODZT gave birth to her first set of twins before the age of 30. These analyses produced a maximum expLOD score of 2.718 (P = 0.0002), largely due to linkage signal from the ANZ cohort, however, ordered subset analyses indicated this result is most likely a chance finding in the combined dataset. Linkage analyses were also performed for two large DZ twinning families from the USA, one of which produced a peak on chromosome 2 in the region of two potential candidate genes. Sequencing of FSHR and FIGLA, along with INHBB in MODZTs from two large NL families with family specific linkage peaks directly over this gene, revealed a potentially functional variant in the 5' untranslated region of FSHR that segregated with the DZ twinning phenotype in the Utah family. CONCLUSION: Our data provide further evidence for complex inheritance of familial DZ twinning.

Towards self-authorship in child care students : implications for working with children and their families

Using self authorship as a theoretical framework, this chapter examines the relationship between personal epistemology and beliefs about children’s learning for students studying to be child care workers in Australia. Scenario-based interviews were used to investigate how students’ views of knowledge, identity and relationships with others were related to beliefs about how children learn. Implications for vocational education are discussed.

Burden of care and general health in families of patients with schizophrenia

Background: De-institutionalization of psychiatric patients has led to a greater emphasis on family management in the community, and family members are often overwhelmed by the demands that caring for a patient with schizophrenia involves. Most studies of family burden in schizophrenia have taken place in developed countries. The current study examined family burden and its correlates in a regional area of a medium income country in South America. Method: Sixty-five relatives of patients with schizophrenia who were attending a public mental health out-patient service in the province of Arica, Chile, were assessed on Spanish versions of the Zarit Caregiver Burden Scale and SF-36 Health Survey (SF-36). Results: Average levels of burden were very high, particularly for mothers, carers with less education, carers of younger patients and carers of patients with more hospitalisations in the previous 3 years. Kinship and number of recent hospitalisations retained unique predictive variance in a multiple regression. Burden was the strongest predictor of SF-36 subscales, and the prediction from burden remained significant after entry of other potential predictors. Conclusions: In common with families in developed countries, family members of schizophrenia patients in regional Chile reported high levels of burden and related functional and health impact. The study highlighted the support needs of carers in contexts with high rates of poverty and limited health and community resources.

The family attitude scale : reliability and validity of a new scale for measuring the emotional climate of families

Research on outcomes from psychiatric disorders has highlighted the importance of expressed emotion (EE), but its cost-effective measurement remains a challenge. This article describes development of the Family Attitude Scale (FAS), a 30-item instrument that can be completed by any informant. Its psychometric characteristics are reported in parents of undergraduate students and in 70 families with a schizophrenic member. The total FAS had high internal consistency in all samples, and reports of angry behaviour in FAS items showed acceptable inter-rater agreement. The FAS was associated with the reported anger, anger expression and anxiety of respondents. Substantial associations between the parents' FAS and the anger and anger expression of students was also observed. Parents of schizophrenic patients had higher FAS scores than parents of students, and the FAS was higher if disorder duration was longer or patient functioning was poorer. Hostility, high criticism and low warmth on the Camberwell Family Interview (CFI) were associated with a more negative FAS. The highest FAS in the family was a good predictor of a highly critical environment on the CFI. The FAS is a reliable and valid indicator of relationship stress and expressed anger that has wide applicability.