214 research outputs found
Generalized Species Sampling Priors with Latent Beta reinforcements
Many popular Bayesian nonparametric priors can be characterized in terms of
exchangeable species sampling sequences. However, in some applications,
exchangeability may not be appropriate. We introduce a {novel and
probabilistically coherent family of non-exchangeable species sampling
sequences characterized by a tractable predictive probability function with
weights driven by a sequence of independent Beta random variables. We compare
their theoretical clustering properties with those of the Dirichlet Process and
the two parameters Poisson-Dirichlet process. The proposed construction
provides a complete characterization of the joint process, differently from
existing work. We then propose the use of such process as prior distribution in
a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte
Carlo sampler for posterior inference. We evaluate the performance of the prior
and the robustness of the resulting inference in a simulation study, providing
a comparison with popular Dirichlet Processes mixtures and Hidden Markov
Models. Finally, we develop an application to the detection of chromosomal
aberrations in breast cancer by leveraging array CGH data.Comment: For correspondence purposes, Edoardo M. Airoldi's email is
[email protected]; Federico Bassetti's email is
[email protected]; Michele Guindani's email is
[email protected] ; Fabrizo Leisen's email is
[email protected]. To appear in the Journal of the American
Statistical Associatio
Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance
We measure the influence of individual observations on the sequence of the
hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler
distance (KLD). Namely, we consider the KLD between the conditional
distribution of the hidden states' chain given the complete sequence of
observations and the conditional distribution of the hidden chain given all the
observations but the one under consideration. We introduce a linear complexity
algorithm for computing the influence of all the observations. As an
illustration, we investigate the application of our algorithm to the problem of
detecting outliers in HMM data series
S-estimation of hidden Markov models
A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step
with high breakdown S-estimation of location and scatter, performed by using the
bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on
robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved
and its finite sample behavior is investigated by means of a brief simulation study and
n application to a multivariate time series of daily returns for seven stock markets
Functional characterization and annotation of trait-associated genomic regions by transcriptome analysis
In this work, two novel implementations have been presented, which could assist in the design and data analysis of high-throughput genomic experiments. An efficient and flexible tiling probe selection pipeline utilizing the penalized uniqueness score has been implemented, which could be employed in the design of various types and scales of genome tiling task. A novel hidden semi-Markov model (HSMM) implementation is made available within the Bioconductor project, which provides a unified interface for segmenting genomic data in a wide range of research subjects.In dieser Arbeit werden zwei neuartige Implementierungen präsentiert, die im Design und in der Datenanalyse von genomischen Hochdurchsatz-Experiment hilfreich sein könnten. Die erste Implementierung bildet eine effiziente und flexible Auswahl-Pipeline für Tiling-Proben, basierend auf einem Eindeutigkeitsmaß mit einer Maluswertung. Als zweite Implementierung wurde ein neuartiges Hidden-Semi-Markov-Modell (HSMM) im Bioconductor Projekt verfügbar gemacht
Hidden Markov Models
Hidden Markov Models (HMMs), although known for decades, have made a big career nowadays and are still in state of development. This book presents theoretical issues and a variety of HMMs applications in speech recognition and synthesis, medicine, neurosciences, computational biology, bioinformatics, seismology, environment protection and engineering. I hope that the reader will find this book useful and helpful for their own research
Robust unmixing of tumor states in array comparative genomic hybridization data
Motivation: Tumorigenesis is an evolutionary process by which tumor cells acquire sequences of mutations leading to increased growth, invasiveness and eventually metastasis. It is hoped that by identifying the common patterns of mutations underlying major cancer sub-types, we can better understand the molecular basis of tumor development and identify new diagnostics and therapeutic targets. This goal has motivated several attempts to apply evolutionary tree reconstruction methods to assays of tumor state. Inference of tumor evolution is in principle aided by the fact that tumors are heterogeneous, retaining remnant populations of different stages along their development along with contaminating healthy cell populations. In practice, though, this heterogeneity complicates interpretation of tumor data because distinct cell types are conflated by common methods for assaying the tumor state. We previously proposed a method to computationally infer cell populations from measures of tumor-wide gene expression through a geometric interpretation of mixture type separation, but this approach deals poorly with noisy and outlier data
Gene Copy Number Analysis for Family Data Using Semiparametric Copula Model
Gene copy number changes are common characteristics of many genetic disorders. A new technology, array comparative genomic hybridization (a-CGH), is widely used today to screen for gains and losses in cancers and other genetic diseases with high resolution at the genome level or for specific chromosomal region. Statistical methods for analyzing such a-CGH data have been developed. However, most of the existing methods are for unrelated individual data and the results from them provide explanation for horizontal variations in copy number changes. It is potentially meaningful to develop a statistical method that will allow for the analysis of family data to investigate the vertical kinship effects as well. Here we consider a semiparametric model based on clustering method in which the marginal distributions are estimated nonparametrically, and the familial dependence structure is modeled by copula. The model is illustrated and evaluated using simulated data. Our results show that the proposed method is more robust than the commonly used multivariate normal model. Finally, we demonstrated the utility of our method using a real dataset
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