Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Work-related training and the probability of transitioning from non-permanent to permanent employment

It is widely believed that work-related training increases a worker’s probability of moving up the job-quality ladder. This is usually couched in terms of effects on wages, but it has also been argued that training increases the probability of moving from non-permanent forms of employment to more permanent employment. This hypothesis is tested using nationally representative panel data for Australia, a country where the incidence of non-permanent employment, and especially casual employment, is high by international standards. While a positive association between participation in work-related training and the subsequent probability of moving from either casual or fixed-term contract employment to permanent employment is observed among men, this is shown to be driven not by a causal impact of training on transitions but by differences between those who do and do not receive training; i.e., selection bias.

Learning about probability from text and tables: Do color coding and labeling through an interactive-user interface help?

Learning from visual representations is enhanced when learners appropriately integrate corresponding visual and verbal information. This study examined the effects of two methods of promoting integration, color coding and labeling, on learning about probabilistic reasoning from a table and text. Undergraduate students (N = 98) were randomly assigned to learn about probabilistic reasoning from one of 4 computer-based lessons generated from a 2 (color coding/no color coding) by 2 (labeling/no labeling) between-subjects design. Learners added the labels or color coding at their own pace by clicking buttons in a computer-based lesson. Participants' eye movements were recorded while viewing the lesson. Labeling was beneficial for learning, but color coding was not. In addition, labeling, but not color coding, increased attention to important information in the table and time with the lesson. Both labeling and color coding increased looks between the text and corresponding information in the table. The findings provide support for the multimedia principle, and they suggest that providing labeling enhances learning about probabilistic reasoning from text and tables

Increase of the delivered energy probability in DES using a fuzzy probabilistic modeling

The paper proposes a methodology to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The proposed methodology is based on statistical failure and repair data of distribution components and it uses a fuzzy-probabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A mixed integer nonlinear programming optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Conditional probability applied to the definition of limestone geochemical facies: A new Methodological Approach

A new method, based on linear correlation and phase diagrams was successfully developed for processes like the sedimentary process, where the deposition phase can have different time duration - represented by repeated values in a series - and where the erosion can play an important rule deleting values of a series. The sampling process itself can be the cause of repeated values - large strata twice sampled - or deleted values: tiny strata fitted between two consecutive samples. What we developed was a mathematical procedure which, based upon the depth chemical composition evolution, allows the establishment of frontiers as well as the periodicity of different sedimentary environments. The basic tool isn't more than a linear correlation analysis which allow us to detect the existence of eventual evolution rules, connected with cyclical phenomena within time series (considering the space assimilated to time), with the final objective of prevision. A very interesting discovery was the phenomenon of repeated sliding windows that represent quasi-cycles of a series of quasi-periods. An accurate forecast can be obtained if we are inside a quasi-cycle (it is possible to predict the other elements of the cycle with the probability related with the number of repeated and deleted points). We deal with an innovator methodology, reason why it's efficiency is being tested in some case studies, with remarkable results that shows it's efficacy. Keywords: sedimentary environments, sequence stratigraphy, data analysis, time-series, conditional probability.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.