相关论文: Interval Computations and their Categorification

Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…

In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…

When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…

Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

Forecasts for uncertain future events should be probabilistic. Probabilistic forecasts are commonly issued as prediction intervals, which provide a measure of uncertainty in the unknown outcome whilst being easier to understand and…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we…

Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…

Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements…

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…

Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions…

The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…

Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is…

To analyse the significance of the digits used for interval bounds, we clarify the philosophical presuppositions of various interval notations. We use information theory to determine the information content of the last digit of the numeral…

System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely…

In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting…

We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…

There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of…