Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm

Two Avenues of Inference: The Evidential Paradigm and Relative Belief Theory

This thesis focuses on two inferential theories, the Evidential paradigm (Royall, 1997) and (Bayesian) relative belief inferences (Evans, 1997), both of which are concerned with characterizing statistical evidence. We investigate the success of these theories in quantifying the strength of statistical evidence in a number of statistical problems. We contribute evidential methodology for the analysis of genetic association in family data using the ratio of composite likelihoods as our evidence function. We show that composite likelihoods, with a robust adjustment, have the two crucial performance properties of the Evidential paradigm: (1) The evidence function will support the true value over the false value by an arbitrarily large factor as the sample size increases, and (2) for large samples, the probability of misleading evidence, is approximated by the bump function which has a small upper bound. Thus, in the Evidential paradigm, composite likelihood ratios can be used as a surrogate for the likelihood ratios constructed from true likelihoods when evaluating the full likelihood is not convenient.We illustrate an approach to Bayesian point null hypothesis assessment based on relative belief inferences. We develop a methodology to assess possible bias inherent in the relative belief ratio, the evidence function, which measures the change in belief after seeing the data. We then present the application of these inferences to independent binary data in a logistic regression setting. We derive a goodness-of-fit test for logistic regression based on a weakly informative prior. When no lack of fit is detected, we show how to use these priors to induce priors on model parameters. These priors do not have the issues that the more commonly used priors have on the model parameters, e.g. a common approach is to assign diffuse priors on the model coefficients s to reflect little information, which in fact induces an informative prior on thePh.D

Goodness of fit for the logistic regression model using relative belief

Abstract A logistic regression model is a specialized model for product-binomial data. When a proper, noninformative prior is placed on the unrestricted model for the product-binomial model, the hypothesis H 0 of a logistic regression model holding can then be assessed by comparing the concentration of the posterior distribution about H 0 with the concentration of the prior about H 0. This comparison is effected via a relative belief ratio, a measure of the evidence that H 0 is true, together with a measure of the strength of the evidence that H 0 is either true or false. This gives an effective goodness of fit test for logistic regression

Assessing the potential impact of nonnative fish on native fish by relative condition

Nonnative species (NNS) pose one of the most common threats to the conservation of biodiversity. Given the difficulty in measuring and documenting the specific impacts of introduced species on native species, indices of condition may provide an easy and inexpensive alternative. The aim of this study was to understand the impact of NNS on some common and endemic freshwater fishes, examining their relative conditions in the absence (allopatry) and presence (sympatry) of nonnative fish species from 3 different regions in the western part of Turkey. Data from 19 sites, a total of 1672 fish of 11 cyprinid species, were used for calculation of condition indices. Relative condition was significantly higher in allopatry than sympatry for Capoeta sieboldii, Gobio gobio, Ladigesocypris ghigii, Leucaspius delineatus, and Phoxinus phoxinus; however, it was higher in sympatry only for Rhodeus amarus, whereas Barbus tauricus, Cyprinus carpio, Rutilus rutilus, Squalius fellowesii, and S. pursakensis showed no significant differences in relative condition between allopatry and sympatry. Results suggest that there was a possible impact of NNS on native species and that relative condition would provide an easy and useful alternative to get a preliminary evaluation of the impact of nonnative fish species as long as sampling follows proper methodology

Length-weight relationships of freshwater fishes from the western part of Anatolia, Turkey

Lengthweight relationships were calculated for nine freshwater fish species belonging to two families using 1020 specimens from 15 water sources in the western part of Anatolia, Turkey. This study is the first reference on lengthparameters for these species, eight of which are endemic, and with new maximum length records for three of the species

Acute and long-term effects of hyperbaric oxygen therapy on hemorheological parameters in patients with various disorders

Inhalation of 100% oxygen in a hyperbaric chamber has been accepted as a useful treatment for patients with various pathologies who suffer from hypoxia. The oxidative effects of hyperbaric oxygen (HBO) on RBCs have been investigated in animals but there is not enough data on hemorheological parameters in patients following HBO treatment (HBOT)

Development of empirical standard weight equation for Pursak chub Squalius pursakensis, an endemic cyprinid species of Northwest Anatolia

Indices of condition enable the evaluation of the well-being of fish, with the assumption that heavier fish of a given length are in a better condition. Relative weight (W-r) is one of these indices; it is calculated by comparing the actual weight of a specimen with the ideal weight of a specimen in good physiological condition of the same length from the same species, i.e. standard weight (W-s). In this research, length and weight data over the distribution range for Pursak chub Squalius pursakensis, an endemic species distributed in the Sakarya and Porsuk drainages in Northwest Anatolia (Turkey), were used to compute a W-s equation by means of the empirical percentile (EmP) method. The W-s equation obtained was log(10) W-s = -4.657 + 2.614 log(10) TL + 0.127 (log(10) TL)(2), and the total length range of application was 80-340 mm. Since the EmP W-s equation was not influenced by length variation, the use of this equation to compute the relative weight (W-r) for S. pursakensis throughout its area of distribution is suggested

The Genetics of Reading Disability in an Often Excluded Sample: Novel Loci Suggested for Reading Disability in Rolandic Epilepsy

Reading disability (RD) is a common neurodevelopmental disorder with genetic basis established in families segregating "pure" dyslexia. RD commonly occurs in neurodevelopmental disorders including Rolandic Epilepsy (RE), a complex genetic disorder. We performed genomewide linkage analysis of RD in RE families, testing the hypotheses that RD in RE families is genetically heterogenenous to pure dyslexia, and shares genetic influences with other sub-phenotypes of RE.We initially performed genome-wide linkage analysis using 1000 STR markers in 38 US families ascertained through a RE proband; most of these families were multiplex for RD. We analyzed the data by two-point and multipoint parametric LOD score methods. We then confirmed the linkage evidence in a second US dataset of 20 RE families. We also resequenced the SEMA3C gene at the 7q21 linkage locus in members of one multiplex RE/RD pedigree and the DISC1 gene in affected pedigrees at the 1q42 locus.In the discovery dataset there was suggestive evidence of linkage for RD to chromosome 7q21 (two-point LOD score 3.05, multipoint LOD 3.08) and at 1q42 (two-point LOD 2.87, multipoint LOD 3.03). Much of the linkage evidence at 7q21 derived from families of French-Canadian origin, whereas the linkage evidence at 1q42 was well distributed across all the families. There was little evidence for linkage at known dyslexia loci. Combining the discovery and confirmation datasets increased the evidence at 1q42 (two-point LOD = 3.49, multipoint HLOD = 4.70), but decreased evidence at 7q21 (two-point LOD = 2.28, multipoint HLOD  = 1.81), possibly because the replication sample did not have French Canadian representation.Reading disability in rolandic epilepsy has a genetic basis and may be influenced by loci at 1q42 and, in some populations, at 7q21; there is little evidence of a role for known DYX loci discovered in "pure" dyslexia pedigrees. 1q42 and 7q21 are candidate novel dyslexia loci