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Full-Text Articles in Physical Sciences and Mathematics
Task Interrupted By A Poisson Process, Jarrett Christopher Nantais
Task Interrupted By A Poisson Process, Jarrett Christopher Nantais
Major Papers
We consider a task which has a completion time T (if not interrupted), which is a random variable with probability density function (pdf) f(t), t>0. Before it is complete, the task may be interrupted by a Poisson process with rate lambda. If that happens, then the task must begin again, with the same completion time random variable T, but with a potentially different realization. These interruptions can reoccur, until eventually the task is finished, with a total time of W. In this paper, we will find the Laplace Transform of W in several special cases.
On Variable Selections In High-Dimensional Incomplete Data, Tao Sun
On Variable Selections In High-Dimensional Incomplete Data, Tao Sun
Major Papers
Modern Statistics has entered the era of Big Data, wherein data sets are too large, high-dimensional, incomplete and complex for most classical statistical methods. This analysis of Big data firstly focuses on missing data. We compare different multiple imputation methods. Combining the characteristics of medical high-throughput experiments, we compared multivariate imputation by chained equations (MICE), missing forest (missForest), as well as self-training selection (STS) methods. A phenotypic data set of common lung disease was assessed. Moreover, in terms of improving the interpretability and predictability of the model, variable selection plays a pivotal role in the following analysis. Taking the Lasso-Poisson …
Extension Of First Passage Probability, Yiping Zhang
Extension Of First Passage Probability, Yiping Zhang
Major Papers
In this paper, we consider the extension of first passage probability. First, we present the first, second, third, and generally k-th passage probability of a Markov Chain moving from one state to another state through step-by-step calculation and two other matrix-version methods. Similarly, we compute the first passage probability of a Markov Chain moving from one state to multiple states. In all discussions, we take into account the situations that one state moves to a different state and returns to itself. Also, we find the mean number of steps needed from one state to another state in a Markov Chain …