Estimating the number of neurons in multi-neuronal spike trains

A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains spikes generated by multiple neurons. A natural question that arises is "what is the number of neurons $\nu$ generating the spike train?"; This article proposes a method-of-moments technique for estimating $\nu$. This technique estimates the noise nonparametrically using data from the silent region of the spike train and it applies to isolated spikes with a possibly small, but nonnegligible, presence of overlapping spikes. Conditions are established in which the resulting estimator for $\nu$ is shown to be strongly consistent. To gauge its finite sample performance, the technique is applied to simulated spike trains as well as to actual neuronal spike train data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS371 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Some theoretical results on neural spike train probability models

This article contains two main theoretical results on neural spike train models. The first assumes that the spike train is modeled as a counting or point process on the real line where the conditional intensity function is a product of a free firing rate function s, which depends only on the stimulus, and a recovery function r, which depends only on the time since the last spike. If s and r belong to a q-smooth class of functions, it is proved that sieve maximum likelihood estimators for s and r achieve essentially the optimal convergence rate (except for a logarithmic factor) under L_1 loss. The second part of this article considers template matching of multiple spike trains. P-values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system. By identifying the pattern with an experimental stimulus, multiple spike trains can be deciphered to provide useful information.Comment: 55 page

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS429 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Published by Blackwell Publishers Ltd, 108 Cowley Road Oxford OX4 UF, UK and 350 Main Street

ABSTRCT. Ths paper is concerned with estiatig a mixing density using a random sample from the mitue distrbutionj(x) = Jj(x 0)g(0) dO wherej(' 0) is a known discrete exponential famiy of density functions. Recently two teclmques for estiatig have been proposed. The fist uses Fourier analysis and the method of kernels and the seond uses orthogonal polynomials. It is known that the fit teclmque is capable of yieldig estiators that achieve (or alost achieve) the miax convergence rate. We show that this is tre for the teclmque base on orthogonal polynomials as well. The practical implementation of thes estiators is also addresd. Computer experiments indicate that the kernel estiators give somewhat disappointing fite sample results. However, the orthogonal polynomial estiators appear to do much better. To improve on the finite sample performance of the orthogonal polynomial estiators, a way of estiatig the optial trncation parameter is propose. The resuJtant estiators retai the convergence rates of the previous estiators and a Monte Carlo fite sample study reveals that they perform well relative to the ones based on the optial truncation parameter

Comprehensive profiling of DNA methylation in colorectal cancer reveals subgroups with distinct clinicopathological and molecular features

<p>Abstract</p> <p>Background</p> <p>Most previous studies of the CpG island methylator phenotype (CIMP) in colorectal cancer (CRC) have been conducted on a relatively small numbers of CpG sites. In the present study we performed comprehensive DNA methylation profiling of CRC with the aim of characterizing CIMP subgroups.</p> <p>Methods</p> <p>DNA methylation at 1,505 CpG sites in 807 cancer-related genes was evaluated using the Illumina GoldenGate^®methylation array in 28 normal colonic mucosa and 91 consecutive CRC samples. Methylation data was analyzed using unsupervised hierarchical clustering. CIMP subgroups were compared for various clinicopathological and molecular features including patient age, tumor site, microsatellite instability (MSI), methylation at a consensus panel of CpG islands and mutations in <it>BRAF </it>and <it>KRAS</it>.</p> <p>Results</p> <p>A total of 202 CpG sites were differentially methylated between tumor and normal tissue. Unsupervised hierarchical clustering of methylation data from these sites revealed the existence of three CRC subgroups referred to as CIMP-low (CIMP-L, 21% of cases), CIMP-mid (CIMP-M, 14%) and CIMP-high (CIMP-H, 65%). In comparison to CIMP-L tumors, CIMP-H tumors were more often located in the proximal colon and showed more frequent mutation of <it>KRAS </it>and <it>BRAF </it>(<it>P </it>< 0.001).</p> <p>Conclusions</p> <p>Comprehensive DNA methylation profiling identified three CRC subgroups with distinctive clinicopathological and molecular features. This study suggests that both <it>KRAS </it>and <it>BRAF </it>mutations are involved with the CIMP-H pathway of CRC rather than with distinct CIMP subgroups.</p

DNA methylation subgroups and the CpG island methylator phenotype in gastric cancer: A comprehensive profiling approach

10.1186/1471-230X-14-55BMC Gastroenterology141-BGMA

ON CLOSED SUBALGEBRAS OF CERTAIN HOMOGENEOUS BANACH ALGEBRAS

Master'sMASTER OF SCIENC

Estimating covariance matrices II

Let S1 and S2 be two independent p - p Wishart matrices with S1 ~ Wp([Sigma]1, n1) and S2 ~ Wp([Sigma]2, n2). We wish to estimate [zeta] = [Sigma]2[Sigma]1-1 under the loss function L1 = tr([zeta] - [zeta])' [Sigma]2-1([zeta] - [zeta]) [Sigma]1/tr [zeta]. By extending the techniques of Berger, Haff, and Stein for the one sample problem, alternative estimators to the usual estimators for [zeta] are obtained. However, the risks of these estimators are not available in closed form. A Monte Carlo study is used instead to evaluate their risk performances. The results indicate that the alternative estimators have excellent risk properties with respect to the usual estimators. In particular, dramatic savings in risk are obtained when the eigenvalues of [Sigma]2[Sigma]1-1 are close together.covariance matrices equivariant estimation unbiased estimate of risk Wishart distribution