Hasil untuk "Probabilities. Mathematical statistics"

L. Shepp, Y. Vardi

D. Brockmann, L. Hufnagel, T. Geisel

The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools. Human travel, for example, is responsible for the geographical spread of human infectious disease. In the light of increasing international trade, intensified human mobility and the imminent threat of an influenza A epidemic, the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive, and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Using a comprehensive data set of over a million individual displacements, we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale-free random walks known as Lévy flights. Second, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and conclude that human travel on geographical scales is an ambivalent and effectively superdiffusive process.

André I. Khuri

This book is the little brother to Moore and McCabe (1999), which recently had its third edition, as reported by Ziegel (2001). Previously the Ž rst edition (1E) of the book was reviewed for Technometrics by Moore (1996). It received a solid endorsement in the reviewer’s summary: “ I believe that all introductory students would beneŽ t from this style of presentation, which minimizes the distraction of the mathematics of probability and statistics, emphasizing exploratory data analysis, sampling, and experimental design concepts, and encouraging the development of insight and understanding afforded by the use of statistical inference” (p. 404). The review described the content of the book in equally imposing sentences. As the quote indicates, this book is classical statistics presented as gently as possible. The author is widely renowned for this approach. Moore and McCabe (1999) gave an even bigger dose of the same type of stuff. The book is intended to be suitable for use in two-year colleges, so this version of this approach is very basic. Computing within the book is at the level of the “two-variable statistics calculator,” Excel, and Minitab. Using the “classical approach,” it certainly involves less statistical computing than I would present. As a second edition (2E), there are not many changes from the Ž rst edition. Some probability material was separated from the chapter on probability and sampling distributions, made into a following chapter on probability theory, and labeled as optional. It is not hard to agree with that decision. There is a new chapter on nonparametric statistics tacked on at the end of the book. There also is a nice shiny CD-ROM packaged with the 2E that includes an encyclopedia of examples, datasets, quizzes, a Web link for updates, and some additional text sections that are not in the book. The book has been reformatted in a four-color layout. It now includes new chapter introductions and adds chapter summary sections.

M. Kendall

Tai L. Chow

The field of “probability theory” is a branch of mathematics that is concerned with describing the likelihood of different outcomes from uncertain processes. Probability theory is the cornerstone of the field of Statistics, which is concerned with assessing the uncertainty of inferences drawn from random samples of data. Thus, we need to understand basics of probability theory to comprehend some of the basic principles used in inferential statistics. Before defining what the word “probability” means, I will introduce some terminology to motivate the need for thinking probabilistically.

M. Modarres, M. Kaminskiy, Vasiliy V. Krivtsov

Kawthar ELHAYANI, Mourad ZENASNI

This study examines the role of local financial capacity in promoting the territorial implementation of the Sustainable Development Goals (SDGs) in Morocco, where the localization of the 2030 Agenda remains insufficiently documented. It aims to analyze the determinants of local financing capacity for sustainable territorial development and to assess their influence on the local appropriation of the SDGs. An exploratory qualitative approach was adopted, based on semi-structured interviews with a purposive sample of ten Moroccan experts in local finance and a content analysis of the collected data. The study proposes and validates a conceptual model that links local financial capacity to the territorialization of the SDGs. The results identify financial autonomy, fiscal potential, and budgetary balance as the main determinants of local financial capacity and as key levers for strengthening the effective implementation of the SDGs at the territorial level in Morocco.

Toha Saifudin, Marisa Rifada, Karina Rubita Makhbubah et al.

Leprosy, a highly contagious disease caused by the bacterium Mycobacterium leprae, can result in permanent disability if left untreated. It remains a significant public health issue in many regions, particularly tropical countries like Indonesia. Despite ongoing control efforts, incidence rates are still high in some areas. In 2023, East Java had the highest number of leprosy cases in Indonesia, with 2,124 out of 7,166. To understand the factors contributing to these cases, this study explores various influences and offers policy recommendations to reduce leprosy in East Java. The study uses spatial modeling with a weighting scheme based on queen contiguity, selected because leprosy spreads through human interactions and movement, creating spatial dependencies. It examines spatial, social, economic, educational, and environmental factors based on cross-sectional data from 38 regencies/cities in East Java for 2023. Among the regression models tested, the spatial error regression model proved most effective, showing an R-Square value of 67.14% and an AIC of 213.023. Key findings identified () average years of schooling and () healthcare worker ratios as significant factors influencing leprosy cases. These results aim to guide policymakers in developing stronger leprosy control strategies and offer a basis for further research in East Java.

Y.A. Sharifov, A.R. Mammadli

Local boundary value problems for hyperbolic differential equations have been studied in considerable detail. However, the mathematical modeling of a number of real-world processes leads to nonlocal boundary value problems involving nonlinear hyperbolic differential equations, which remain poorly understood. In this paper, we consider a system of hyperbolic equations defined by both point and integral boundary conditions in a rectangular domain. To the best of our knowledge, such a problem is studied here for the first time. We note that this formulation is quite general and encompasses several special cases. The classical Goursat-Darboux problem-a problem with integral boundary conditions in which some boundary conditions are specified as point conditions and others as integral conditions-is derived from this formulation as a particular case. Under natural conditions on the initial data, the necessary conditions for the solvability of a nonlocal boundary value problem are established. A corresponding Green‘s function for the boundary value problem is constructed and the problem is reduced to an equivalent integral equation. Using the principle of contracting Banach maps, conditions for the existence and uniqueness of a solution to the boundary value problem are established. An example is given illustrating the validity of the obtained results.

Paul N Zivich, Bonnie E Shook-Sa, Stephen R Cole et al.

Introduction: Accounting for missing data by imputing or weighting conditional on covariates relies on the variable with missingness being observed at least some of the time for all unique covariate values. This requirement is referred to as positivity and positivity violations can result in bias. Here, we review a novel approach to addressing positivity violations in the context of systolic blood pressure. Methods: To illustrate the proposed approach, we estimate the mean systolic blood pressure among children and adolescents aged 2-17 years old in the United States using data from the 2017-2018 National Health and Nutrition Examination Survey (NHANES). As blood pressure was not measured for those aged 2-7, there exists a positivity violation by design. Using a recently proposed synthesis of statistical and mathematical models, we integrate external information with NHANES to address our motivating question. Results: With the synthesis model, the estimated mean systolic blood pressure was 100.5 (95% confidence interval: 99.9, 101.0), which is notably lower than either a complete-case analysis or extrapolation from a statistical model. The synthesis results were supported by a diagnostic comparing the performance of the mathematical model in the positive region. Discussion: Positivity violations pose a threat to quantitative medical research, and standard approaches to addressing nonpositivity rely on restrictive untestable assumptions. Using a synthesis model, like the one detailed here, offers a viable alternative.

Dina Novita, Teguh Herlambang, Vaizal Asy’ari et al.

Tourism is one of the government's priority sectors for economic growth. East Java is one of Indonesia's provinces and is attractive to international visitors. International visitors will appreciate the natural beauty and multiculturalism offered by East Java. In this study, predictions of international visitor visits in East Java from the entrance of Juanda International Airport were carried out using k-NN (k-Nearest Neighbor) and a neural network. The dataset used is based on BPS statistics of Jawa Timur Province in the form of the number of international visitor arrivals from January 2000 to February 2024. The datasets were distributed by dividing the data into 70% for training data and 30% for testing data. The creation of the k-NN model is carried out using k-values 2 to 7. The creation of a modern neural network using hidden layers 1 to 3. The prediction results that were made using k-NN obtained optimal RMSE at k-values 2, resulting in an RMSE of 1594,674 or an error of 3,98%. Meanwhile, the prediction results that have been made using neural networks obtained optimal RMSE at two hidden layers, which resulted in an RMSE of 1873, 355 or an error of 4,68%. So, it is recommended that the k-NN algorithm be used to predict the number of international visitors in East Java. The results of this study can be used to provide quantitative information for the government and stakeholders in adjusting the program to the development of international visitors visiting East Java.

Hikmah Hikmah, Nur Hilal A Syahrir, Putri Indi Rahayu

Indonesian medicinal plants, such as turmeric and soursop, have shown promising anticancer properties through their bioactive compounds, like curcumin and extracts from soursop. Despite many extensive studies on medicinal plants in Indonesia, research revealing the activity of natural products in West Sulawesi is still limited, and the studies focus mainly on ethnobotanical research. In this work, we propose a machine-learning approach to predict the anticancer activity of compounds in medicinal plants in West Sulawesi by leveraging high throughput-screening data, especially molecular information from a public database. We applied Support Vector Machine (SVM) with five sampling techniques to address data imbalance. We also evaluated the performance in selecting the best combination in handling class imbalance learning in our dataset. The result shows that undersampling and ADSYN methods can improve the prediction of anticancer activity. Based on the two methods of balancing data, we have ten potential anticancer compounds from three medicinal plants in West Sulawesi.

Warren B. Kindzierski, S. Stanley Young, John D. Dunn

Odds ratios or p_values from individual observational studies can be combined to examine a common cause_effect research question in meta_analysis. However, reliability of individual studies used in meta_analysis should not be taken for granted as claimed cause_effect associations may not reproduce. An evaluation was undertaken on meta_analysis of base papers examining gas stove cooking, including nitrogen dioxide, NO2, and childhood asthma and wheeze associations. Numbers of hypotheses tested in 14 of 27 base papers, 52 percent, used in meta_analysis of asthma and wheeze were counted. Test statistics used in the meta_analysis, 40 odds ratios with 95 percent confidence limits, were converted to p_values and presented in p_value plots. The median and interquartile range of possible numbers of hypotheses tested in the 14 base papers was 15,360, 6,336_49,152. None of the 14 base papers made mention of correcting for multiple testing, nor was any explanation offered if no multiple testing procedure was used. Given large numbers of hypotheses available, statistics drawn from base papers and used for meta-analysis are likely biased. Even so, p-value plots for gas stove_current asthma and gas stove_current wheeze associations show randomness consistent with unproven gas stove harms. The meta-analysis fails to provide reliable evidence for public health policy making on gas stove harms to children in North America. NO2 is not established as a biologically plausible explanation of a causal link with childhood asthma. Biases_multiple testing and p-hacking_cannot be ruled out as explanations for a gas stove_current asthma association claim. Selective reporting is another bias in published literature of gas stove_childhood respiratory health studies. Keywords gas stove, asthma, meta-analysis, p-value plot, multiple testing, p_hacking

R.R. Ashurov, Yu.E. Fayziev

Initial boundary value problems with a time-nonlocal condition for a subdiffusion equation with the Riemann-Liouville time-fractional derivatives are considered. The elliptical part of the equation is the Laplace operator, defined in an arbitrary N−dimensional domain Ω with a sufficiently smooth boundary ∂Ω. The existence and uniqueness of the solution to the considered problems are proved. Inverse problems are studied for determining the right-hand side of the equation and a function in a time-nonlocal condition. The main research tool is the Fourier method, so the obtained results can be extended to subdiffusion equations with a more general elliptic operator.

Aleksandra Slavkovic, Jeremy Seeman

To quantify trade-offs between increasing demand for open data sharing and concerns about sensitive information disclosure, statistical data privacy (SDP) methodology analyzes data release mechanisms which sanitize outputs based on confidential data. Two dominant frameworks exist: statistical disclosure control (SDC), and more recent, differential privacy (DP). Despite framing differences, both SDC and DP share the same statistical problems at its core. For inference problems, we may either design optimal release mechanisms and associated estimators that satisfy bounds on disclosure risk, or we may adjust existing sanitized output to create new optimal estimators. Both problems rely on uncertainty quantification in evaluating risk and utility. In this review, we discuss the statistical foundations common to both SDC and DP, highlight major developments in SDP, and present exciting open research problems in private inference.

Christophe Chesneau, Farrukh Jamal

C. Adcock, A. Azzalini

Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

K. Modi, V. Gill

Abstract In this paper we introduce a new Unit Burr-III probability distribution with support interval (0,1). The proposed distribution possesses a flexible density function and bathtub shape hazard rate function. We derive the expressions for its mathematical and statistical properties. Probability distribution function of order statistics and expression for pth moment for derived distribution is also obtained. We calculate parameter estimates by using the technique of maximum likelihood estimation. We apply it on two real datasets and found that it provides better fit than other well known distributions.

Zachary Wojtowicz, S. Dedeo

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of these values that clarifies their function and shows how they fit together to guide explanation-making. The resulting taxonomy shows that core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework and provide insight into why people adopt the explanations they do. This framework not only operationalizes the explanatory virtues associated with, for example, scientific argument-making, but also enables us to reinterpret the explanatory vices that drive phenomena such as conspiracy theories, delusions, and extremist ideologies.