We answer positively a question of Kaimanovich and Vershik from 1979, showing that the final configuration of lamps for simple random walk on the lamplighter group over Z (d ≥ 3) is the Poisson boundary. For d ≥ 5, this had been shown earlier by Erschler (2011). We extend this to walks of more general types on more general groups.

We present a novel phoneme-based student model for spelling training. Our model is data driven, adapts to the user and provides information for, e.g., optimal word selection. We describe spelling errors using a set of features accounting for phonemic, capitalization, typo, and other error categories. We compute the influence of individual features on the error expectation values based on previo...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...