Limiting Behaviour of Poisson-Dirichlet and Generalised Poisson-Dirichlet Distributions

We derive large-sample and other limiting distributions of the ``frequency of frequencies'' vector, ${\bf M_n}$, together with the number of species, $K_n$, in a Poisson-Dirichlet or generalised Poisson-Dirichlet gene or species sampling model. Models analysed include those constructed from gamma and $\alpha$-stable subordinators by Kingman, the two-parameter extension by Pitman and Yor, and another two-parameter version constructed by omitting large jumps from an $\alpha$-stable subordinator. In the Poisson-Dirichlet case ${\bf M_n}$ and $K_n$ turn out to be asymptotically independent, and notable, especially for statistical applications, is that in other cases the conditional limiting distribution of ${\bf M_n}$, given $K_n$, is normal, after certain centering and norming

Limiting Distributions of Generalised Poisson-Dirichlet Distributions Based on Negative Binomial Processes

The \text {PD}_\alpha ^{(r)} distribution, a two-parameter distribution for random vectors on the infinite simplex, generalises the \text {PD}_\alpha distribution introduced by Kingman, to which it reduces when r=0. The parameter \alpha \in (0,1) arises from its construction based on ratios of ordered jumps of an \alpha -stable subordinator, and the parameter r>0 signifies its connection with an underlying negative binomial process. Herein, it is shown that other distributions on the simplex, including the Poisson-Dirichlet distribution \text {PD}(\theta ), occur as limiting cases of \text {PD}_\alpha ^{(r)}, as r\rightarrow \infty . As a result, a variety of connections with species and gene sampling models, and many other areas of probability and statistics, are made

Reciprocal and Self-Aging Effects of Power Components on Reliability of DC-DC Boost Converter With Coupled and Decoupled Thermal Structures

WOS:000502852100019International audienc

Fluid biomarkers in cerebral amyloid angiopathy

Cerebral amyloid angiopathy (CAA) is a type of cerebrovascular disorder characterised by the accumulation of amyloid within the leptomeninges and small/medium-sized cerebral blood vessels. Typically, cerebral haemorrhages are one of the first clinical manifestations of CAA, posing a considerable challenge to the timely diagnosis of CAA as the bleedings only occur during the later disease stages. Fluid biomarkers may change prior to imaging biomarkers, and therefore, they could be the future of CAA diagnosis. Additionally, they can be used as primary outcome markers in prospective clinical trials. Among fluid biomarkers, blood-based biomarkers offer a distinct advantage over cerebrospinal fluid biomarkers as they do not require a procedure as invasive as a lumbar puncture. This article aimed to provide an overview of the present clinical data concerning fluid biomarkers associated with CAA and point out the direction of future studies. Among all the biomarkers discussed, amyloid β, neurofilament light chain, matrix metalloproteinases, complement 3, uric acid, and lactadherin demonstrated the most promising evidence. However, the field of fluid biomarkers for CAA is an under-researched area, and in most cases, there are only one or two studies on each of the biomarkers mentioned in this review. Additionally, a small sample size is a common limitation of the discussed studies. Hence, it is hard to reach a solid conclusion on the clinical significance of each biomarker at different stages of the disease or in various subpopulations of CAA. In order to overcome this issue, larger longitudinal and multicentered studies are needed.</p