Luis E. Nieto-Barajas

Markov Beta and Gamma Processes for Modelling Hazard Rates

This paper generalizes the discrete time independent increment beta process of Hjort (1990), for modelling discrete failure times, and also generalizes the independent gamma process for modelling piecewise constant hazard rates (Walker and Mallick, 1997). The generalizations are from independent increment to Markov increment prior processes allowing the modelling of smoothness. We derive posterior distributions and undertake a full Bayesian analysis.

Bayesian Random Segmentation Models to Identify Shared Copy Number Aberrations for Array CGH Data

Array-based comparative genomic hybridization (aCGH) is a high-resolution, high-throughput technique for studying the genetic basis of cancer. The resulting data consist of log fluorescence ratios as a function of the genomic DNA location and provide a cytogenetic representation of the relative DNA copy number variation. Analysis of such data typically involves estimating the underlying copy number state at each location and segmenting regions of DNA with similar copy number states. Most current methods proceed by modeling a single sample / array at a time, and thus fail to borrow strength across multiple samples to infer shared regions of copy number aberrations. We propose a hierarchical Bayesian random segmentation approach for modeling aCGH data that uses information across arrays from a common population to yield segments of shared copy number changes. These changes characterize the underlying population and allow us to compare different population aCGH profiles to assess which regions of the genome have differential alterations. Our method, which we term Bayesian detection of shared aberrations in aCGH (BDSAScgh), is based on a unified Bayesian hierarchical model that allows us to obtain probabilities of alteration states as well as probabilities of differential alterations that correspond to local false discovery rates for both single and multiple groups. We evaluate the operating characteristics of our method via simulations and an application using a lung cancer aCGH data set. This article has supplementary material online.

A Bayesian Nonparametric Approach for Time Series Clustering

In this work we propose a model-based clustering method for time series. The model uses an almost surely discrete Bayesian nonparametric prior to induce clustering of the series. Specifically we propose a general Poisson-Dirichlet process mixture model, which includes the Dirichlet process mixture model as particular case. The model accounts for typical features present in a time series like trends, seasonal and temporal components. All or only part of these features can be used for clustering according to the user. Posterior inference is obtained via an easy to implement Markov chain Monte Carlo (MCMC) scheme. The best cluster is chosen according to a heterogeneity measure as well as the model selection criteria LPML (logarithm of the pseudo marginal likelihood). We illustrate our approach with a dataset of time series of shares prices in the Mexican stock exchange.

A Time Series Model for Responses on the Unit Interval

We introduce an autoregressive model for responses that are restricted to lie on the unit interval, with beta-distributed marginals. The model includes strict stationarity as a special case, and is based on the introduction of a series of latent random variables with a simple hierarchical specication that achieves the desired dependence while being amenable to posterior simulation schemes. We discuss the construction, study some of the main properties, and compare it with alternative models using simulated data. We

Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates

A full Bayesian analysis is developed for an extension to the short-term and long-term hazard ratios model that has been previously introduced. This model is specified by two parameters, short- and long-term hazard ratios respectively, and an unspecified baseline function. Furthermore, the model also allows for crossing hazards in two groups and includes the proportional hazards, and the proportional odds models as particular cases. The model is extended to include covariates in both, the short- and long-term parameters, and uses a Bayesian nonparametric prior, based on increasing additive processes mixtures, to model the baseline function. Posterior distributions are characterized via their full conditionals. Latent variables are introduced wherever needed to simplify computations. The algorithm is tested with a simulation study and posterior inference is illustrated with a survival study of ovarian cancer patients who have undergone a treatment with erythropoietin stimulating agents.

A Time‐Series DDP for Functional Proteomics Profiles

Using a new type of array technology, the reverse phase protein array (RPPA), we measure time-course protein expression for a set of selected markers that are known to coregulate biological functions in a pathway structure. To accommodate the complex dependent nature of the data, including temporal correlation and pathway dependence for the protein markers, we propose a mixed effects model with temporal and protein-specific components. We develop a sequence of random probability measures (RPM) to account for the dependence in time of the protein expression measurements. Marginally, for each RPM we assume a Dirichlet process model. The dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick-breaking representation. We also acknowledge the pathway dependence among proteins via a conditionally autoregressive model. Applying our model to the RPPA data, we reveal a pathway-dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers.

Bayesian interpolation of unequally spaced time series

A comparative analysis of time series is not feasible if the observation times are different. Not even a simple dispersion diagram is possible. In this article we propose a Gaussian process model to interpolate an unequally spaced time series and produce predictions for equally spaced observation times. The dependence between two observations is assumed a function of the time differences. The novelty of the proposal relies on parametrizing the correlation function in terms of Weibull and Log-logistic survival functions. We further allow the correlation to be positive or negative. Inference on the model is made under a Bayesian approach and interpolation is done via the posterior predictive conditional distributions given the closest

A Bayesian semi-parametric bivariate failure time model

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