The three results on the PageRank vector are preliminary but shed light on the eigenstructure of a PageRank modified Markov chain and what happens when changing the teleportation parameter in the PageRank model. Computations with the derivative of the PageRank vector with respect to the teleportation parameter show predictive ability and identify an interesting set of pages from Wikipedia.

When the process underlying DNA substitutions varies across evolutionary history, some standard Markov models underlying phylogenetic methods are mathematically inconsistent. The most prominent example is the general time-reversible model (GTR) together with some, but not all, of its submodels. To rectify this deficiency, nonhomogeneous Lie Markov models have been identified as the class of mod...

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for the parameters. Among the tasks typically addressed in the analysis of parametric Markov chains are (1) the computation of closed-form solutions for reachabil...

This paper proposes a software reliability model (SRM) based on a mixed gamma distribution, so-called the mixed gamma SRM. In addition, we develop the parameter estimation method for the mixed gamma SRM. Concretely, the estimation method is based on the Bayesian estimation and the parameter estimation algorithm is described by MCMC (Markov chain Monte Carlo) method with grouped data.

We study parametric Markov decision processes (PMDPs) and their reachability probabilities ”independent” of the parameters. Different to existing work on parameter synthesis (implemented in the tools PARAM and PRISM), our main focus is on describing different types of optimal deterministic memoryless schedulers for the whole parameter range. We implement a simple prototype tool SEA-PARAM that c...

In a full Bayesian probabilistic framework for ‘‘robust’’ system identification, structural response predictions and performance reliability are updated using structural test data D by considering the predictions of a whole set of possible structural models that are weighted by their updated probability. This involves integrating h(u)p(uuD) over the whole parameter space, where u is a parameter...

Parameter dari suatu distribusi biasanya belum diketahui nilainya, untuk mengetahuinya dilakukan estimasi terhadap parameter tersebut. Metode ada dua macam, yaitu metode klasik dan Bayesian. Bayesian merupakan yang menggabungkan sampel dengan prior. Untuk mendapatkan secara acak adalah menggunakan simulasi. Salah satu teknik simulasi digunakan dalam rantai Markov Monte Carlo (RMMC), membangkitk...

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is...

To evaluate and predict component-based software security, a two-dimensional model of software security is proposed by Stochastic Petri Net in this paper. In this approach, the software security is modeled by graphical presentation ability of Petri nets, and the quantitative prediction is provided by the evaluation capability of Stochastic Petri Net and the computing power of Markov chain. Each...

Marginal Data Augmentation and Parameter-Expanded Data Augmentation are related methods for improving the the convergence properties of the two-step Gibbs sampler know as the Data Augmentation sampler. These methods expand the parameter space with a so-callled working parameter that is unidentifiable given the observed data but is identifiable given the so-called augmented data. Although these ...