4 research outputs found
A non-Markovian model for cell population growth: speed of convergence and central limit theorem
No full textAbstractIn De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data
Bayesian mixture regression analysis for regulation of Pluripotency in ES cells
No full textBackground: Observed levels of gene expression strongly depend on both activity of DNA binding transcription factors (TFs) and chromatin state through different histone modifications (HMs). In order to recover the functional relationship between local chromatin state, TF binding and observed levels of gene expression, regression methods have proven to be useful tools. They have been successfully applied to predict mRNA levels from genome-wide experimental data and they provide insight into context-dependent gene regulatory mechanisms. However, heterogeneity arising from gene-set specific regulatory interactions is often overlooked. Results: We show that regression models that predict gene expression by using experimentally derived ChIP-seq profiles of TFs can be significantly improved by mixture modelling. In order to find biologically relevant gene clusters, we employ a Bayesian allocation procedure which allows us to integrate additional biological information such as three-dimensional nuclear organization of chromosomes and gene function. The data integration procedure involves transforming the additional data into gene similarity values. We propose a generic similarity measure that is especially suitable for situations where the additional data are of both continuous and discrete type, and compare its performance with similar measures in the context of mixture modelling. Conclusions: We applied the proposed method on a data from mouse embryonic stem cells (ESC). We find that including additional data results in mixture components that exhibit biologically meaningful gene clusters, and provides valuable insight into the heterogeneity of the regulatory interactions
Wild bootstrap for counting process-based statistics:a martingale theory-based approach
No full textThe wild bootstrap is a popular resampling method in the context of time-to-event data analysis. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper provides a general framework for establishing large sample properties in a unified way by using martingale structures. This framework includes most of the well-known parametric, semiparametric and nonparametric statistical methods in time-to-event analysis. Along the way of proving the validity of the wild bootstrap, a new variant of Rebolledo’s martingale central limit theorem for counting process-based martingales is developed as well.</p
Gene Network Reconstruction using Global-Local Shrinkage Priors
No full textReconstructing a gene network from high-throughput molecular data is an important but challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model likelihood. In network models, this is often done in the neighborhood of each node or gene. However, estimation of the many regularization parameters is often difficult and can result in large statistical uncertainties. In this paper we propose to combine local regularization with shrinkage of the regularization parameters to borrow strength between genes and improve inference. We employ a simple Bayesian model with nonsparse, conjugate priors to facilitate the use of fast variational approximations to posteriors. We discuss empirical Bayes estimation of hyperparameters of the priors, and propose a novel approach to rank-based posterior thresholding. Using extensive model- and data-based simulations, we demonstrate that the proposed inference strategy outperforms popular (sparse) methods, yields more stable edges, and is more reproducible. The proposed method, termed , is then applied to Glioblastoma to investigate the interactions between genes associated with patient survival
