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allowing use of MCFTP: widening technique based on adding two ctitious states and clustering technique based on partitioning the state space in clusters. Usefulness and eciency of our approaches are showed through a sample of Markov Chain Monte Carlo simulations. Keywords: Monte Carlo simulation, Markov chain, stochastic monotonicity, coupling from the past, perfect simulation MSC 2010: 60C05, 60J10, 62G99, 68Q80, 68R10 DOI: 10.1515/mcma-2015-0111 Received July 11, 2015; accepted October 20, 2015 1 Introduction Let X = {Xn , n ≥ 0} be an homogeneous and aperiodic

Abstract

High-throughput sequencing techniques are increasingly affordable and produce massive amounts of data. Together with other high-throughput technologies, such as microarrays, there are an enormous amount of resources in databases. The collection of these valuable data has been routine for more than a decade. Despite different technologies, many experiments share the same goal. For instance, the aims of RNA-seq studies often coincide with those of differential gene expression experiments based on microarrays. As such, it would be logical to utilize all available data. However, there is a lack of biostatistical tools for the integration of results obtained from different technologies. Although diverse technological platforms produce different raw data, one commonality for experiments with the same goal is that all the outcomes can be transformed into a platform-independent data format – rankings – for the same set of items. Here we present the R package TopKLists, which allows for statistical inference on the lengths of informative (top-k) partial lists, for stochastic aggregation of full or partial lists, and for graphical exploration of the input and consolidated output. A graphical user interface has also been implemented for providing access to the underlying algorithms. To illustrate the applicability and usefulness of the package, we integrated microRNA data of non-small cell lung cancer across different measurement techniques and draw conclusions. The package can be obtained from CRAN under a LGPL-3 license.

Abstract

A Bayesian procedure for bandwidth selection in kernel circular density estimation is investigated, when the Markov chain Monte Carlo (MCMC) sampling algorithm is utilized for Bayes estimates. Under the quadratic and entropy loss functions, the proposed method is evaluated through a simulation study and real data sets, which were already discussed in the literature. The proposed Bayesian approach is very competitive in comparison with the existing classical global methods, namely plug-in and cross-validation techniques.

: 62 F 07, 62 G 99 Key words and phrases: Subset selection, locally optimal, locally strongly monotone, joint type II censoring 2 S. S. Gupta, TaChen Liang In practice, it sometimes happens that the actual values of the random variables can only be observed under great cost, or not at all, while their ordering is readily observable. This occurs for instance in life-testing when one only observes the order in which the parts under investigation fail without being able to record the actual time of fail- ure. In problems of this type, one may desire to

we refer to Csörgö and Horvath (1988). A MS 1985 subject classification: Primary 62G10; secondary 62G99 Keywords and phrases: change-point, stochastic process, limit theorems, simulation. *" Research supported in part by NSERC Canada Grant. 72 Ε. Gombay We shall observe Ä», the sequential rank of Xi among X\,..., Xit defined as Ri = l + (i-l)Fi-1(Xi), i> 2, where ί ί - ι ( ί ) = τ—-r#{ l < j < i - 1 : Xj < i } , i > 2. ι — ι The basic properties of Ri, i = 1 , n , were discovered by Parent (1965). Csörgö and Horvath (1987, 1988) utilized their discrete

. Monte Carlo, simulation, Markov chain, steady-state distribution, coupling from the past, importance sampling. AMS classification. 60C05, 60J10, 62G99, 68Q80, 68R10. 1. Introduction The most widely used mathematical tools to model the behavior of fault-tolerant com- puter systems are Markov processes. Many stationary performance measures of such systems can be written in an explicit form of the stationary distribution of a Markov chain. One familiarly form of such measures is θ = ∑ s∈E f(s)πs, where f is a known function of state such that IE[|f(Y)|] = ∑ s∈E |f

(x),A2(x)) = (D^(x)-F(x)"\ D2(x)-F(x)"^) (1.3) 2 = -V log F(x), x € R . 1. Research Partially supported by a Canadian NSERC grant. AMS sub.iect Classification: Primary 62N05, 62G99 , 60F05 Secondary 60F17 Key words and phrases: Hazard gradient function, kemel estimation, Gaussian processes. M.D. Burke In terms of survival analysis (and reliability theory), D^(x) is the instantaneous probability rate that V^ will die (or cease to function) at x^ and V. survives beyond time x. (functions beyond x.)i for i,j = 1,2; i * j. J J J The coordinate A^(x) of the

! " ( ! i * i ^ ' « 1 ! - 0 1 " 2 ' q l + q2 = q ( 1 , 2 ) pxq pxq^ pxq2 AMS Subject C lass i f i ca t ion : 62E7.0, 62J05, 62G99 Key Words and Phrases: Asymptotic power and s i z e , least squares estimators, Linear models, rank s t a t i s t i c s , robustness, sub-hypotheses. 4 5 6 SALEH-SEN We are primarily interested in the test of hypothesis Hg^ : 3^ = 0. A class of l ike l ihood ra t io (LRT) and rank order tests (RPT) of 3̂^ (when 32 may or may not be known) have been studied by Puri and Sen [7 ] . The t es t - s t a t i s t i c s f o r test ing H^^ are d

demjenigen Gerichte zu erheben, welchem die Entscheidung über die bei der Vollstreckung sich etwa erhebenden gtreitigkeiten zustehen würde go: *EK. 10. Jan. 1852 (IMBl. g. 93). A. M ist jedoch *EK. 12. Oft. 1861 (IMBl 62, g. 99), indem dasselbe den beim Friedensgerichte erhobenen KK. als bei der richtigen gtelle angebracht erachtete, obgleich es anerkannte, daß die Exekution deS Urtheils nach Lage der gache nur dem Landgerichte zugestanden haben würde. (In den Motiven wird freilich eine Uebereinstimmung zwischen beiden Erk unterstellt, da eS dort heißt: in Ver