Rediscovery of Good-Turing estimators via Bayesian nonparametrics.

The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics, linguistics, designs of experiments, machine learning, etc. A full range of statistical approaches, parametric and nonparametric as well as frequentist and Bayesian, has been proposed for estimating discovery probabilities. In this article, we investigate the relationships between the celebrated Good-Turing approach, which is a frequentist nonparametric approach developed in the 1940s, and a Bayesian nonparametric approach recently introduced in the literature. Specifically, under the assumption of a two parameter Poisson-Dirichlet prior, we show that Bayesian nonparametric estimators of discovery probabilities are asymptotically equivalent, for a large sample size, to suitably smoothed Good-Turing estimators. As a by-product of this result, we introduce and investigate a methodology for deriving exact and asymptotic credible intervals to be associated with the Bayesian nonparametric estimators of discovery probabilities. The proposed methodology is illustrated through a comprehensive simulation study and the analysis of Expressed Sequence Tags data generated by sequencing a benchmark complementary DNA library.

The Impact of Type 2 Diabetes on Peripheral and Cerebral Hemodynamic Responses to Active Stand.

BACKGROUND: Although type 2 diabetes mellitus (T2DM) is an established risk factor for cognitive impairment, the underlying mechanisms remain poorly explored. One potential mechanism may be through effects of T2DM on cerebral perfusion. The current study hypothesized that T2DM is associated with altered peripheral and central hemodynamic responses to orthostasis, which may in turn be associated with cognitive impairment in T2DM. METHODS: A novel use of function-on-scalar regression, which allows the entire hemodynamic response curve to be modeled, was employed to assess the association between T2DM and hemodynamic responses to orthostasis. Logistic regression was used to assess the relationship between tissue saturation index (TSI), T2DM, and cognitive impairment. All analyses used cross-sectional data from Wave 3 of The Irish Longitudinal Study on Ageing (TILDA). RESULTS: Of 2 984 older adults (aged 64.3 ±â€…8.0; 55% female), 189 (6.3%) had T2DM. T2DM was associated with many features that are indicative of autonomic dysfunction including a blunted peak heart rate and lower diastolic blood pressure. T2DM was associated with reduced TSI and also with greater odds of impaired performance on the Montreal Cognitive Assessment (odds ratio [OR]: 1.62; confidence interval [CI: 1.07, 2.56]; p = .019). Greater TSI was associated with lower odds of impaired performance (OR: 0.90, CI [0.81-0.99]; p = .047). CONCLUSIONS: T2DM was associated with impaired peripheral and cerebral hemodynamic responses to active stand. Both T2DM and reduced cerebral perfusion were associated with impaired cognitive performance. Altered cerebral perfusion may represent an important mechanism linking T2DM and adverse brain health outcomes in older adults.