Estimating the number of classes

Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one-sided. Confidence intervals for the number of classes are also necessarily one-sided. A sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes.Comment: Published at http://dx.doi.org/10.1214/009053606000001280 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Empirical Bayesian Method for Detecting Differentially Expressed Genes Using EST Data

Detection of differentially expressed genes from expressed sequence tags (ESTs) data has received much attention. An empirical Bayesian method is introduced in which gene expression patterns are estimated and used to define detection statistics. Significantly differentially expressed genes can be declared given detection statistics. Simulation is done to evaluate the performance of proposed method. Two real applications are studied

Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages

Aims: In ecology and conservation biology, the number of species counted in a biodiversity study is a key metric but is usually a biased underestimate of total species richness because many rare species are not detected. Moreover, comparing species richness among sites or samples is a statistical challenge because the observed number of species is sensitive to the number of individuals counted or the area sampled. For individual-based data, we treat a single, empirical sample of species abundances from an investigator-defined species assemblage or community as a reference point for two estimation objectives under two sampling models: estimating the expected number of species (and its unconditional variance) in a random sample of (i) a smaller number of individuals (multinomial model) or a smaller area sampled (Poisson model) and (ii) a larger number of individuals or a larger area sampled. For sample-based incidence (presence-absence) data, under a Bernoulli product model, we treat a single set of species incidence frequencies as the reference point to estimate richness for smaller and larger numbers of sampling units. Methods: The first objective is a problem in interpolation that we address with classical rarefaction (multinomial model) and Coleman rarefaction (Poisson model) for individual-based data and with sample-based rarefaction (Bernoulli product model) for incidence frequencies. The second is a problem in extrapolation that we address with sampling-theoretic predictors for the number of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number of sampling units (Bernoulli product model), based on an estimate of asymptotic species richness. Although published methods exist for many of these objectives, we bring them together here with some new estimators under a unified statistical and notational framework. This novel integration of mathematically distinct approaches allowed us to link interpolated (rarefaction) curves and extrapolated curves to plot a unified species accumulation curve for empirical examples. We provide new, unconditional variance estimators for classical, individual-based rarefaction and for Coleman rarefaction, long missing from the toolkit of biodiversity measurement. We illustrate these methods with datasets for tropical beetles, tropical trees and tropical ants. Important Findings: Surprisingly, for all datasets we examined, the interpolation (rarefaction) curve and the extrapolation curve meet smoothly at the reference sample, yielding a single curve. Moreover, curves representing 95% confidence intervals for interpolated and extrapolated richness estimates also meet smoothly, allowing rigorous statistical comparison of samples not only for rarefaction but also for extrapolated richness values. The confidence intervals widen as the extrapolation moves further beyond the reference sample, but the method gives reasonable results for extrapolations up to about double or triple the original abundance or area of the reference sample. We found that the multinomial and Poisson models produced indistinguishable results, in units of estimated species, for all estimators and datasets. For sample-based abundance data, which allows the comparison of all three models, the Bernoulli product model generally yields lower richness estimates for rarefied data than either the multinomial or the Poisson models because of the ubiquity of non-random spatial distributions in nature. © 2012 The Author. Published by Oxford University Press on behalf of the Institute of Botany, Chinese Academy of Sciences and the Botanical Society of China. All rights reserved

Experimental and Numerical Analysis of High-Resolution Injection Technique for Capillary Electrophoresis Microchip

This study presents an experimental and numerical investigation on the use of high-resolution injection techniques to deliver sample plugs within a capillary electrophoresis (CE) microchip. The CE microfluidic device was integrated into a U-shaped injection system and an expansion chamber located at the inlet of the separation channel, which can miniize the sample leakage effect and deliver a high-quality sample plug into the separation channel so that the detection performance of the device is enhanced. The proposed 45° U-shaped injection system was investigated using a sample of Rhodamine B dye. Meanwhile, the analysis of the current CE microfluidic chip was studied by considering the separation of Hae III digested ϕx-174 DNA samples. The experimental and numerical results indicate that the included 45° U-shaped injector completely eliminates the sample leakage and an expansion separation channel with an expansion ratio of 2.5 delivers a sample plug with a perfect detection shape and highest concentration intensity, hence enabling an optimal injection and separation performance

AAV-Mediated Cone Rescue in a Naturally Occurring Mouse Model of CNGA3-Achromatopsia

Achromatopsia is a rare autosomal recessive disorder which shows color blindness, severely impaired visual acuity, and extreme sensitivity to bright light. Mutations in the alpha subunits of the cone cyclic nucleotide-gated channels (CNGA3) are responsible for about 1/4 of achromatopsia in the U.S. and Europe. Here, we test whether gene replacement therapy using an AAV5 vector could restore cone-mediated function and arrest cone degeneration in the cpfl5 mouse, a naturally occurring mouse model of achromatopsia with a CNGA3 mutation. We show that gene therapy leads to significant rescue of cone-mediated ERGs, normal visual acuities and contrast sensitivities. Normal expression and outer segment localization of both M- and S-opsins were maintained in treated retinas. The therapeutic effect of treatment lasted for at least 5 months post-injection. This study is the first demonstration of substantial, relatively long-term restoration of cone-mediated light responsiveness and visual behavior in a naturally occurring mouse model of CNGA3 achromatopsia. The results provide the foundation for development of an AAV5-based gene therapy trial for human CNGA3 achromatopsia