In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced p...

Covariate shift correction allows one to perform supervised learning even when the distribution of the covariates on the training set does not match that on the test set. This is achieved by re-weighting observations. Such a strategy removes bias, potentially at the expense of greatly increased variance. We propose a simple strategy for removing bias while retaining small variance. It uses a bi...

We propose covariate adjustment methodology for a situation where one wishes to study the dependency of a generalized response on predictors while both predictors and response are distorted by an observable covariate. The distorting covariate is thought of as a size measurement that affects predictors in a multiplicative fashion. The generalized response is modeled by means of a random threshol...

Probabilistic modelling and statistical analysis of environmental conditions is important for the design assessment ships other marine structures. It will give a necessary input to structural reliability assessments risk provides means identify that structures are expected withstand in their lifetime. In this paper, recent developments relevant metocean variables describing environment at sea b...

To the Editor: Paloyelis et al. (1) raise two concerns about the statistical ethods used in the original article by Scheres et al. (2): first, they ndicate that analysis of covariance (ANCOVA) is inappropriate hen groups differ on the covariate; and second, they suggest that he results from the regression analysis might be an artifact resulting rom pooling heterogeneous populations. To remedy t...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discret...