Aim/Purpose: The study examined how the developed mobile courseware can be used as instructional material to improve senior high school statistics and probability learning, particularly during distance learning caused by the COVID-19 pandemic. The study also aims to assess the gamified mobile courseware’s engagement, functionality, aesthetics, and information quality using the Mobile App Rating Scale (MARS) and a researcher-made Gamified Mobile Courseware Assessment Tool (GMCET). Background: The need to investigate the effectiveness of incorporating game-based elements into mathematics courses through innovative instructional materials inspired the study. The COVID-19 pandemic has made distance learning a necessity, and gamified mobile courseware is a potential solution to improve learning outcomes and engagement in mathematics courses. Methodology: The study employed a descriptive-evaluative method with quantitative and qualitative data to achieve its objectives. Five IT practitioners assessed the developed courseware using the MARS regarding engagement, functionality, aesthetics, and information. A researcher-made GMCET was also used to evaluate the app’s content quality, learning objectives, content presentation, learning assessment, and usability. Five math experts and 12 math teachers rated the app using the GMCET. The study used weighted mean to analyze the quantitative data and content analysis for the qualitative data. Contribution: The study provides insights into the strengths and weaknesses of gamified mobile courseware from the perspective of IT practitioners, math experts, and math teachers. The study’s findings can inform improvements in future iterations of courseware, and the study provides a valuable guide for practitioners looking to develop gamified mobile courseware for mathematics courses. Findings: The quantitative results based on the weighted mean indicate that the IT practitioners had a moderately positive perception of the developed courseware across all categories. At the same time, the math teachers and math experts showed highly positive perceptions of the gamified mobile courseware in Statistics and Probability, rating it highly across all categories. The qualitative data analysis through content analysis highlights the need for improving the user interface, usability, user experience design, user control, flexibility in interaction, data quality, reliability, and user privacy of the developed app. Recommendations for Practitioners: Practitioners can use the study’s findings to improve the design of gamified mobile courseware for mathematics courses and other content areas. The study recommends that practitioners focus on improving the user interface, usability, user experience design, user control, flexibility in interaction, data quality, reliability, and user privacy of gamified mobile courseware. Recommendation for Researchers: Future research can build on this study’s findings by exploring the use of gamified mobile courseware in other mathematical courses and other subject areas. Further research can also examine how gamified mobile courseware can improve learning outcomes for students with different learning needs. Impact on Society: The study’s findings could improve the effectiveness of gamified mobile courseware in enhancing student learning outcomes in mathematics courses. This can lead to better student performance, improved engagement, and increased interest in mathematics courses, positively impacting society. Future Research: Future research can explore using gamified mobile courseware in other mathematics courses and other subject areas. Additionally, future studies can examine how gamified mobile courseware can improve learning outcomes for students with different learning needs. Further research can also investigate the impact of gamified mobile courseware on student motivation, interest, and performance in mathematics courses.

Hendrickson & Lattman [Acta Cryst. (1970), B26, 136–143] introduced a method for representing crystallographic phase probabilities defined on the unit circle. Their approach could model the bimodal phase probability distributions that can result from experimental phase determination procedures. It also provided simple and highly effective means to combine independent sources of phase information. The present work discusses the equivalence of the Hendrickson–Lattman distribution and the generalized von Mises distribution of order two, which has been studied in the statistical literature. Recognizing this connection allows the Hendrickson–Lattman distribution to be expressed in an alternative form which is easier to interpret, as it involves the location and concentration parameters of the component von Mises distributions. It also allows clarification of the conditions for bimodality and access to a simplified analytical method for evaluating the trigonometric moments of the distribution, the first of which is required for computing the best Fourier synthesis in the presence of phase, but not amplitude, uncertainty.

There’s some confusion regarding jumps in election forecasts. New information is coming in every day, so it makes sense that forecasts change too. But they don’t change very much. Each new piece of information tells you only a little bit. … Continue reading →

Marcelo Campos, Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe
J. Amer. Math. Soc. 38 (), 179-224.
Abstract, references and article information

Christian Weiss
Theor. Probability and Math. Statist. 111 (), 199-209.
Abstract, references and article information

Probability of operating an alarm clock

National Bureau of Economic Research

Boca Raton : Chapman & Hall/CRC Press, 2021

Boca Raton, FL : CRC Press, 2022.

New York : Springer, [2005]

New York : Springer, ©2006

What? William Hill has entered into preliminary talks about a purchase of Probability, the mobile gambling company. So what? An acquisition of Probability would add to William Hill’s offering for users of smartphones and tablet computers. Pr...

(The Paypers) Consumer expectations for convenience have increased significantly across a variety of markets, and quick-service restaurants (QSRs) are no...

New research on climate-driven reductions in Arctic sea ice has predicted that, by 2040 to 2059, new shipping routes will become passable across the Arctic, linking the Atlantic and Pacific oceans. An increase in traffic has implications for the ecosystems of this fragile area.

New research on climate-driven reductions in Arctic sea ice has predicted that, by 2040 to 2059, new shipping routes will become passable across the Arctic, linking the Atlantic and Pacific oceans. An increase in traffic has implications for the ecosystems of this fragile area.

In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical L'evy process but by the mixed fractional Brownian motion.

In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several real-world datasets, such as recidivism records and medical expenditure surveys. If unaccounted for, such shifts can cause the predictions of a classifier to become unfair towards specific population subgroups. While the fairness notion called Proportional Equality (PE) accounts for such shifts, a procedure to ensure PE-fairness was unknown.

In this work, we propose a method, called CAPE, which provides a comprehensive solution to the aforementioned problem. CAPE makes novel use of prevalence estimation techniques, sampling and an ensemble of classifiers to ensure fair predictions under prior probability shifts. We introduce a metric, called prevalence difference (PD), which CAPE attempts to minimize in order to ensure PE-fairness. We theoretically establish that this metric exhibits several desirable properties.

We evaluate the efficacy of CAPE via a thorough empirical evaluation on synthetic datasets. We also compare the performance of CAPE with several popular fair classifiers on real-world datasets like COMPAS (criminal risk assessment) and MEPS (medical expenditure panel survey). The results indicate that CAPE ensures PE-fair predictions, while performing well on other performance metrics.

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Sigma$ and a stochastic memoryless map $Psi$. After that, we extend the result to the class of large scale systems in which: $Sigma$ consists of many sub-systems; and $Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.

In this paper, we present a novel MaxSAT-based technique to compute Maximum Probability Minimal Cut Sets (MPMCSs) in fault trees. We model the MPMCS problem as a Weighted Partial MaxSAT problem and solve it using a parallel SAT-solving architecture. The results obtained with our open source tool indicate that the approach is effective and efficient.

Each play of a base game increases the likelihood of winning a bonus award. A display provides a graphical indication of the change in likelihood of winning the bonus award. In one aspect, the bonus award comprises the opportunity to play a secondary game.

London : printed by W. Wilson, for E. Brewster, and George Sawbridge, at the Bible on Ludgate-Hill, neere Fleet-bridge, 1653.

Daniela Bertacchi, Fabio Zucca.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 426--438.

Abstract:
Given a branching random walk on a set $X$, we study its extinction probability vectors $mathbf{q}(cdot,A)$. Their components are the probability that the process goes extinct in a fixed $Asubseteq X$, when starting from a vertex $xin X$. The set of extinction probability vectors (obtained letting $A$ vary among all subsets of $X$) is a subset of the set of the fixed points of the generating function of the branching random walk. In particular here we are interested in the cardinality of the set of extinction probability vectors. We prove results which allow to understand whether the probability of extinction in a set $A$ is different from the one of extinction in another set $B$. In many cases there are only two possible extinction probability vectors and so far, in more complicated examples, only a finite number of distinct extinction probability vectors had been explicitly found. Whether a branching random walk could have an infinite number of distinct extinction probability vectors was not known. We apply our results to construct examples of branching random walks with uncountably many distinct extinction probability vectors.

Kamran Kalbasi, Thomas Mountford.

Source: Bernoulli, Volume 26, Number 2, 1504--1534.

Abstract:
In this paper, we study the local times of vector-valued Gaussian fields that are ‘diagonally operator-self-similar’ and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the temporal unit hypercube by $Z$, we show that there exists $lambdain(0,1)$ such that under some quite weak conditions, $lim_{n ightarrow+infty}frac{sqrt[n]{mathbb{E}(Z^{n})}}{n^{lambda}}$ and $lim_{x ightarrow+infty}frac{-logmathbb{P}(Z>x)}{x^{frac{1}{lambda}}}$ both exist and are strictly positive (possibly $+infty$). Moreover, we show that if the underlying Gaussian field is ‘strongly locally nondeterministic’, the above limits will be finite as well. These results are then applied to establish similar statements for the intersection local times of diagonally operator-self-similar Gaussian fields with stationary increments.

Yating Liu, Gilles Pagès.

Source: Bernoulli, Volume 26, Number 2, 1171--1204.

Abstract:
We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic (convergence for the $L^{p}$-Wasserstein distance). We first propose a criterion on the quantization level $N$, valid for any norm on $mathbb{R}^{d}$ and any order $p$ based on a geometrical approach involving the Voronoï diagram. Then, we prove that in the $L^{2}$-case on a (separable) Hilbert space, the condition on the level $N$ can be reduced to $N=2$, which is optimal. More quantization based characterization cases in dimension 1 and a discussion of the completeness of a distance defined by the quantization error function can be found at the end of this paper.

Ioannis Ntzoufras, Claudia Tarantola, Monia Lupparelli.

Source: Bayesian Analysis, Volume 14, Number 3, 797--823.

Abstract:
We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

Hyundai aims to make the Aura the sub-compact king of sedans in India and dethrone the Maruti Suzuki Dzire with BS6 petrol and diesel engines. But does the Aura have what it takes to beat the Dzire? Watch this video and find out.

Cham : Birkhäuser, [2019]

Ugarte, María Dolores, author

Johnson, Richard Arnold

Schweder, Tore, author

Hogg, Robert V., author

Walpole, Ronald E., author

Akritas, Michael G., author

Roe, Byron P., author

Montgomery, Douglas C., author

Dewey Library - QA273.S6875 2019

Dewey Library - QA273.M38495 2020

Barker Library - QA273.2.T55 2018

Cham : Springer International Publishing : Imprint: Springer, 2014

Cham : Springer International Publishing : Imprint: Springer, 2014

Seattle : University of Washington, 1996-

[Seattle, Wash.] : Electronic Journal of Probability and Electronic Communications in Probability, 1995-