Natural statistics for spectral samples

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1107 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

Terminalia bentzoë, a Mascarene Endemic Plant, Inhibits Human Hepatocellular Carcinoma Cells Growth In Vitro via G0/G1 Phase Cell Cycle Arrest

Tropical forests constitute a prolific sanctuary of unique floral diversity and potential medicinal sources, however, many of them remain unexplored. The scarcity of rigorous scientific data on the surviving Mascarene endemic taxa renders bioprospecting of this untapped resource of utmost importance. Thus, in view of valorizing the native resource, this study has as its objective to investigate the bioactivities of endemic leaf extracts. Herein, seven Mascarene endemic plants leaves were extracted and evaluated for their in vitro antioxidant properties and antiproliferative effects on a panel of cancer cell lines, using methyl thiazolyl diphenyl-tetrazolium bromide (MTT) and clonogenic cell survival assays. Flow cytometry and comet assay were used to investigate the cell cycle and DNA damaging effects, respectively. Bioassay guided-fractionation coupled with liquid chromatography mass spectrometry (MS), gas chromatography-MS, and nuclear magnetic resonance spectroscopic analysis were used to identify the bioactive compounds. Among the seven plants tested, Terminaliabentzoë was comparatively the most potent antioxidant extract, with significantly (p < 0.05) higher cytotoxic activities. T. bentzoë extract further selectively suppressed the growth of human hepatocellular carcinoma cells and significantly halted the cell cycle progression in the G0/G1 phase, decreased the cells’ replicative potential and induced significant DNA damage. In total, 10 phenolic compounds, including punicalagin and ellagic acid, were identified and likely contributed to the extract’s potent antioxidant and cytotoxic activities. These results established a promising basis for further in-depth investigations into the potential use of T. bentzoë as a supportive therapy in cancer management

Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.Comment: 16 page

Spatial Variation of Extreme Rainfall Observed From Two Century‐Long Datasets

This paper presents the spatial variation of area‐orientated annual maximum daily rainfall (AMDR), represented by well‐fitted generalized extreme value (GEV) distributions, over the last century in Great Britain (GB) and Australia (AU) with respect to three spatial properties: geographic locations, sizes, and shapes of the region‐of‐interest (ROI). The results show that the spatial variation of GEV location‐scale parameters is dominated by geographic locations and area sizes. In GB, there is an eastward‐decreasing banded pattern compared with a concentrically increasing pattern from the middle to coasts in AU. The parameters tend to decrease with increased area sizes in both studied regions. Although the impact of the ROI shapes is insignificant, the round‐shaped regions usually have higher‐valued parameters than the elongated ones. These findings provide a new perspective to understand the heterogeneity of extreme rainfall distribution over space driven by the complex interactions between climate, geographical features, and the practical sampling approaches

Fast stable direct fitting and smoothness selection for Generalized Additive Models

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models

Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case

In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers . We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum