Survival Analysis: Techniques for Censored and Truncated Data (2nd ed.) (Book)

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Mathematical Methods Of Statistics

can be formulated in terms of basis functions and discuss the dif culties in posterior simulations due to interdependence of these functions. Such interdependence affects the ef ciency of the sampling algorithms to draw from posterior distribution of the tree structures. Different strategies that are suggested in the literature for dealing with the sampling problem are discussed, and a detailed example using binary classi cation is presented to illustrate the Bayesian analysis. To alleviate the problems that arise in tree models, Chapter 7 introduces partition models. The partition models can be considered a generalization of tree models, and they allow for sampling from the posterior distributions of the tree structure. As noted by the authors, these models suffer from lack of interpretability in high dimensions. The authors present one-dimensional partition models whose analysis provides a general framework for the changepoint problems. Multidimensional partition models, where partitions are de ned by Dirichlet tessellations, are considered, and Bayesian inference for classi cation problems is discussed. Disease mapping models are presented as an application of partition models for spatial problems. Chapter 8 is a short chapter describing Bayesian nearest-neighbor modeling. The nearest-neighbor classi cation algorithm, which is used commonly in pattern recognition, is given a probabilistic formulation by introducing a parameter that controls the degree of association between the neighboring classes. In Chapter 9 the authors generalize the single-response case to multipleresponse models where the observed response is a collection of values. The chapter focuses on regression models and does not consider classi cation models such as the multivariate probit models. Multivariate Bayesian regression framework is introduced where basis functions can be determined from the data using methods of Chapter 3. A generalization is considered using seemingly unrelated regression (SUR) models and their Bayesian analysis is presented. Prior speci cation for basis function matrix are discussed, and computational details of the MCMC methods are given for both models. The book has a comprehensive bibliography, and each chapter (except Chap. 1) has a section on further reading. There are two appendixes at the end. Appendix B gives a summary of posterior inference results that are helpful for some of the development in the text. In summary, this book presents recent developments in Bayesian nonlinear modeling and provides a complete treatment of regression and classi cation problems by emphasizing a data-driven approach in determining appropriate models. Its in-depth coverage of implementation issues and detailed discussion of pros and cons of different modeling strategies make it attractive for many researchers. It de nitely makes my list of recommended texts in Bayesian statistics.

Resampling Methods for Dependent Data

(2007). Stochastic Ageing and Dependence for Reliability. Technometrics: Vol. 49, No. 2, pp. 222-222.

Stochastic Ageing and Dependence for Reliability

http://diposit.ub.edu/dspace/bitstream/2445/129467/1/683944.pdf

Osteocalcin Signaling in Myofibers Is Necessary and Sufficient for Optimum Adaptation to Exercise.

A family of distributions to model load sharing systems

RNA-Seq is increasingly being used for gene expression profiling. In this approach, next-generation sequencing (NGS) platforms are used for sequencing. Due to highly parallel nature, millions of reads are generated in a short time and at low cost. Therefore analysis of the data is a major challenge and development of statistical and computational methods is essential for drawing meaningful conclusions from this huge data. In here, we assessed three different types of normalization (transcript parts per million, trimmed mean of M values, quantile normalization) and evaluated if normalized data reduces technical variability across replicates. In addition, we also proposed two novel methods for detecting differentially expressed genes between two biological conditions: (i) likelihood ratio method, and (ii) Bayesian method. Our proposed methods for finding differentially expressed genes were tested on three real datasets. Our methods performed at least as well as, and often better than, the existing methods for analysis of differential expression.

/pdf/differential-expression-analysis-for-rna-seq-data-li4x980dkz.pdf

Differential Expression Analysis for RNA-Seq Data

Let {X n ;n ≥1} be a sequence of stationary associated random variables having a common marginal density function f (x). Let , be a sequence of Borel-measurable functions defined on R 2. Let be the empirical density function. Here we study a set of sufficient conditions under which the probability at an exponential rate as n → ∞ where the rate possibly depends on ϵ, δ and f and [a, b] is a finite or an infinite interval.

A general method of density estimation for associated random variables

An EM algorithm for estimating the parameter of bivariate Weibull distribution under random censoring

Dependence structures between the failure time and the cause of failure are ex- pressed in terms of the monotonicity properties of the conditional probabilities involving the cause of failure and the failure time. These properties of the conditional probabilities are used for testing four types of departures from the independence of the failure time and the cause of failure and tests based on U-statistics are proposed. In the process, a concept of concordance and discordance between a continuous and a binary variable is introduced to propose a statistical test. The proposed tests are applied to two illustrative applications. Consider a situation where a unit can fail due to one of two competing causes. Let T1 and T2 denote the latent lifetimes of the unit under the two causes. The competing risk data available are the failure time T of the unit, which is the minimum of (T1, T2) and the cause of failure indicator 6, which is equal to 1 if T = T1 and is 0 if T = T2. These data are right censored data where each latent lifetime acts as a censoring variable for the other and, unlike in censoring, the interest lies in both the causes and hence in both the lifetimes. One concentrates on different aspects of the situation by assuming appropriate dependence structures (i) for the two latent lifetimes (T1, T2) and (ii) for the random variables (T, 6). The joint distribution of (T, 6) is defined here by the subsurvival functions, Si(t) = pr(T ? t, 6 i), i = 0, 1. The survival function of T is defined by S(t) = pr(T > t) = So(t) + S,(t). Throughout this paper, we as- sume that the subsurvival functions are continuous with fi(t), i = 0, 1, as the subdensity functions andf(t) = fo(t) + f1(t) as the density of T. The cause-specific hazard rate for cause i is defined as hi(t) =fi(t)/S(t) and the crude hazard rate for cause i is defined as ri(t) = fi(t)l Si(t). The hazard rate of T is h(t) = f(t)/S(t) = h1(t) + ho(t). The problem of identifiability in modelling the competing risks data in terms of the latent lifetimes is well known. The distributions of the latent lifetimes are identifiable under the assumption of independence of the competing causes and also under some weaker conditions of non-informative censoring, see Kalbfleisch & Prentice (2002). There has been an ongoing debate for many years about the use of the models in terms of latent lifetimes and the models in terms of (T, 6), see Prentice et al. (1978), Larson & Dinse (1985), Davis & Lawrance (1989), Deshpande (1990), Aras & Deshpande (1992), Gasbarra & Karia (2000), Crowder (2001),

Isha Dewan

Papers

A family of distributions to model load sharing systems

Differential Expression Analysis for RNA-Seq Data

A general method of density estimation for associated random variables

An EM algorithm for estimating the parameter of bivariate Weibull distribution under random censoring

On Testing Dependence between Time to Failure and Cause of Failure via Conditional Probabilities