<p>A critical question in climate science is whether climate model simulations are statistically consistent with observations. If simulations and observations are treated as realizations of Vector Autoregressive (VAR) models, then deciding that simulations and observations came from the same process is equivalent to deciding that the parameters of the respective VAR models are equal. This framework has been developed in parts 1–5 of this series of papers, including extensions to account for annual cycles and radiative forcing. However, the associated tests have been derived under the restriction of equal noise covariances. Previous studies have only allowed unequal noise variances in univariate settings. This paper presents a general test of parameter equality that applies to multivariate models, incorporates external forcing, and does not assume equal noise covariances. Monte Carlo experiments indicate that the test statistic is well approximated by a chi-squared distribution for large degrees of freedom, but that this distribution underestimates upper quantiles when the degrees of freedom are small. This bias can be partially compensated by adopting a more stringent significance level (e.g., using a 1 % level to achieve a nominal 5 % Type I error rate). Applying the method to monthly 2 m-temperature from an observational data set and climate model simulations aggregated over five regional domains reveals that most climate models tested differ significantly from the observational data set, both in their transfer coefficients for radiative forcing and in their AR coefficients, indicating differences in the representation of both internal and forced variability.</p>
This study explores the role of cognitive performance in the general health of older Europeans aged 50 and over, focusing on gender differences, using data from 336,500 respondents in the sixth wave of the Survey of Health, Aging, and Retirement in Europe (SHARE). Cognitive functioning was assessed through self-rated reading and writing skills, orientation in time, numeracy, memory, verbal fluency, and word-list learning. General health status was estimated by constructing a composite index of physical and mental health-related measures, including chronic diseases, mobility limitations, depressive symptoms, self-perceived health, and the Global Activity Limitation Indicator. Participants were classified into good or poor health status, and logistic regression models assessed the predictive significance of cognitive variables on general health, supplemented by a relative importance analysis to estimate relative effect sizes. The results indicated that males had a 51.1% lower risk of reporting poor health than females, and older age was associated with a 4.0% increase in the odds of reporting worse health for both genders. Memory was the strongest predictor of health status (26% of the model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula>), with a greater relative contribution than the other cognitive variables. No significant gender differences were found. While this study estimates the odds of reporting poorer health in relation to gender and various cognitive characteristics, adopting a lifespan approach could provide valuable insights into the longitudinal associations between cognitive functioning and health outcomes.
<p>Comparisons of observed and modeled climate behavior often focus on central tendencies, which overlook other important distributional characteristics related to quantiles and variability. We propose two permutation procedures, standard and stratified, for assessing the accuracy of climate models. Both procedures eliminate the need to model cross-correlations in the data, encouraging their application in a variety of contexts. By making only slightly stronger assumptions, the stratified procedure dramatically strengthens the ability to detect a difference in the distribution of observed and climate model data. The proposed procedures allow researchers to identify potential model deficiencies over space and time for a variety of distributional characteristics, providing a more comprehensive assessment of climate model accuracy, which will hopefully lead to further model refinements. The proposed statistical methodology is applied to temperature data generated by the state-of-the-art North American Coordinated Regional Climate Downscaling Experiment (NA-CORDEX).</p>
In the present paper sets related to invariant Riemannian metrics of positive sectional and (or) Ricci curvature on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the influence of the normalized Ricci flow. For invariant Riemannian metrics of the Wallach spaces which admit positive sectional curvature and belong to a given invariant surface of the normalized Ricci flow equation we establish that they form a set bounded by three connected and pairwise disjoint regular space curves such that each of them approaches two others asymptotically at infinity. Analogously, for all generalized Wallach spaces with coincided parameters the set of Riemannian metrics which belong to the invariant surface of the normalized Ricci flow and admit positive Ricci curvature is bounded by three space curves each consisting of exactly two connected components as regular curves. Mutual intersections and asymptotical behaviors of these components are studied as well. We also establish that curves corresponding to Ka¨hler metrics of spaces under consideration form separatrices of saddles of a three-dimensional system of nonlinear autonomous ordinary differential equations obtained from the normalized Ricci flow equation.
In the paper, the boundary value problem for the loaded heat equation is solved, and the loaded term is represented as the Riemann-Liouville derivative with respect to the time variable. The domain of the unknown function is the cone. The order of the derivative in the loaded term is less than 1, and the load moves along the lateral surface of the cone, that is in the domain of the desired function. The boundary value problem is studied in the case of the isotropy property in an angular coordinate (case of axial symmetry). The problem is reduced to the Volterra integral equation, which is solved by the method of the Laplace integral transformation. It is also shown by direct verification that the resulting function satisfies the boundary value problem.
Food is the main need for every individual that must always be fulfilled. For Indonesia, food is identified with rice because this type of food is a commodity consumed by the Indonesian population. Therefore, the rice crisis can be interrupt economic resilience and national stability. National rice consumption from year to year will continue to increase in line with the increase in Indonesia's population. Although, Indonesia is the third-largest country in the world in producing the most, Indonesia still depends on rice imports. This was done by the government to maintain the national rice supply.The rice supply chain in Indonesia has not been optimum, as indicated by the relatively small profits of producer. In this research, we construct the maximum profit model of direct and indirect media sales of rice for producer, distributor, and retailer. And then, we determine the optimum solution of the model and analysis of the factors in the rice supply chain that affect it. The results showed that changes in the proportion of demand greatly affects the resulting optimal profit.
Vilijandas Bagdonavičius, Vydas Čekanavičius, Rūta Levulienė
et al.
Julius Kruopis was born on 21.02.1941 in Utena district. In 1963 he graduated from Vilnius University, Faculty of Physics and Mathematics. In 1964–1966 he worked as a trainee lecturer at the Department of Probability Theory and Number Theory of the Faculty of Mathematics of Vilnius University. In 1966–1969 he studied at the post-graduate course of the Steklov Institute of Mathematics of the USSR (supervisor was the famous Russian mathematician Professor Login Bolshev) and defended the thesis of a candidate of mathematical sciences (the current equivalent is PhD thesis).
Returning to Lithuania after postgraduate studies, J. Kruopis worked as a senior lecturer at the Department of Probability Theory and Number Theory of the Faculty of Mathematics of Vilnius University, and in 1971 transferred to the newly established Department of Applied Mathematics (he worked as an associate professor since 1972). In 1991 this department was renamed the Department of Mathematical Statistics. Since 2013, J. Kruopis has been an affiliated professor of the Department of Mathematical Statistics.
In 1980–1986 J. Kruopis headed the Department of Applied Mathematics. He established and fostered new traditions, and aimed for the majority of students' theses to have a clear applied nature. He led such works himself and encouraged other teachers to do the same. From the very first days of scientific work, the talent of J. Kruopis became evident through mathematical and statistical modeling of real processes.
PhD thesis ``Estimation of Markov processes parameters'' by J. Kruopis, defended in 1969 in Moscow (supervised by prof. L. Bolshev), has a clear applied character. Statistical modeling of tick-borne encephalitis virus infection and immunity formation processes was performed. Methods of queueing theory and mathematical statistics were used for modeling and statistical estimation of model parameters. A detailed analysis of the obtained results was carried out using real data. In addition, the thesis presents the assessment of the transition probabilities of Markov processes with migration. The findings are used for demographic and reliability data analysis.
Having returned to Lithuania, Julius developed a very wide range of activities in the application of statistical methods in many companies and factories. He consulted engineers of Kaunas radio factory, Panevėžys factory of kinescopes ``Ekranas'' and joint stock company ``AB Lietkabelis'', Vilnius drill, ``Venta'', ``Vilma'', radio components factories, Šiauliai TV factory, Dniepropetrovsk tire factory ``Dnieproshina'', Moscow Aviation Institute, and others. Julius Kruopis grasped the essence of technological processes very quickly. A particularly long and fruitful cooperation was established with the Kaunas radio plant. Under the leadership of Julius, a number of factories managers and engineers defended PhD theses.
Especially valuable are his works in the application of statistical methods. These applications are mainly related to optimization of control systems, regulation and management of technological processes (acceptance control of materials and details, intermediate control of manufactured details and nodes, outgoing production control, metrological control of measuring devices, product reliability control, etc.).
Although J. Kruopis work is dominated by works on statistical applications, there are also theoretical works on mathematical statistics. For example, the problem of making an optimal decision when choosing a distribution from several possible alternative distributions was examined. There are several works by J. Kruopis related to the application of statistical methods in reliability theory and survival analysis. Although J. Kruopis always considered himself primarily a statistician, he also achieved important results in probability theory.
In 1986 J. Kruopis introduced shifted Poisson approximation, which unlike the usual Poisson approximation has two parameters and, therefore, is comparable to normal approximation. Moreover, for integer-valued random variables, the accuracy of shifted Poisson approximation can be measured in total variation metric. In contrast, the accuracy of normal approximation to discrete random variables is measured in weaker uniform metric only.
A large part of J. Kruopis research in Probability Theory is related to so-called Signed Compound Poisson approximations – a topic very new in the early eighties. J. Kruopis introduced so-called left-hand-side and right-hand-side factorial cumulants and practically solved the problem of the choice of parameters for such approximations.
J. Kruopis is the co-author of several monographs: ``Quality of mechatronic products. Selective control'', ``Nonparametric tests for complete data'', ``Nonparametric tests for censored data''. While working at the university, J. Kruopis supervised a large number of undergraduate, bachelor, and master theses. Under his supervision Vanda Bikelienė (Asymptotic distribution of sums of samples from finite populations, 1981) and Natalja Kosareva (Asymptotic analysis of statistics distributions in the scheme of sets of particles arrangement with equal probabilities, 1986) defended their doctoral theses in mathematics.
J. Kruopis wrote the first textbook on mathematical statistics in Lithuania.
In the last years of his work at the university, he wrote a comprehensive four-part textbook ``Mathematical Statistics'' with V. Bagdonavičius and e-book ``Mathematical statistics Problems with Solutions'' together with V. Bagdonavičius and R. Levuliene.
One of the main features of J. Kruopis as the head of the department was his great trust in the young lecturers of the department. He did not support the usual practice of other departments where lectures were given by senior and more experienced lecturers, while novice assistants only conducted exercises. J. Kruopis always sought that from the first days of work at the department, all teachers had at least one full course of lectures-exercises-exams.
J. Kruopis instilled his passion for mathematics and its applications not only in students but also in his children, who both graduated from the Faculty of Mathematics and Informatics. Julius was a person of quick, constructive thinking, always restrained, tactful and modest. Both students and colleagues liked him very much.
1 Novartis, Basel, Switzerland, 2 Department of Clinical Epidemiology and Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, Netherlands, 3 Institute for Community Medicine, SHIPKEF University Medicine of Greifswald, Greifswald, Germany, 4 Department of Mathematics, Faculty of Mathematics, Natural Sciences and Information Technology, University of Primorska, Koper, Slovenia, 5 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, United States of America
Most studies of Augmented Reality (AR) in education have considered students' learning outcomes and motivation. Previous studies have revealed that AR has the potential to help students learn abstract conceptions in mathematics. In this paper, a series of statistics and probability lessons using AR installed on tablets was designed and developed to examine the effect of the AR technology by comparing the conceptions and learning approaches of junior high school students with different levels of self‐efficacy. A total of 101 students were divided into two groups based on their mathematics learning self‐efficacy. The analysis of the results shows that AR applications in mathematics courses can help students with higher self‐efficacy to pay closer attention to higher level conceptions. It can also help higher self‐efficacy students to apply more advanced strategies when learning mathematics. [ABSTRACT FROM AUTHOR]
Pain and pain chronification are incompletely understood and unresolved medical problems that continue to have a high prevalence. It has been accepted that pain is a complex phenomenon. Contemporary methods of computational science can use complex clinical and experimental data to better understand the complexity of pain. Among data science techniques, machine learning is referred to as a set of methods (Fig. 1) that can automatically detect patterns in data and then use the uncovered patterns to predict or classify future data, to observe structures such as subgroups in the data, or to extract information from the data suitable to derive new knowledge. Together with (bio)statistics, artificial intelligence and machine learning aim at learning from data. Although statistics can be regarded as a branch of mathematics, artificial intelligence and machine learning have developed from computer science (Ref. 58; see also https://en.wikipedia. org/wiki/Artificial_intelligence). The initial definition of artificial intelligence originates from Alan Turing who proposed an experiment where 2 players, who can either be human or artificial, try to convince a human third player, that they are also humans. The test of artificial intelligence is passed if the third player cannot tell who is the machine. Important steps in the development of machine learning were the first creation of the computer learning program, which was a checker game, and the first neural network called the perceptron. Statistics uses mathematical equations to model probability relationships between data variables, whereas machine learning learns from data without the necessity of previous knowledge. It aims at optimization and performance of an algorithm rather than on the analysis of the probabilities of observations, given a known underlying data distribution. Nevertheless, both machine learning and statistics techniques are working in concert for pattern recognition, knowledge discovery, and data mining and share partly the same methods such as regression, which is used widely in statistics but is also considered as a classification method in machine learning (Fig. 1). In the present research context, when provided with painrelated data, machine-learned methods are able to learn a mapping of complex features to a known class, that is, to predict a pain phenotype class from a complex pattern of acquired parameters. After the machine has learned the prediction of a pain-related phenotype, the algorithm can subsequently be used on new data from which the class membership of a novel yet unclassified subject can be identified. However, machine learning methods can also be used for pattern recognition in complex pain-related data to reveal traces of an underlying molecular background or for knowledge discovery in big data in a drug discovery or repurposing context. The increasing use of contemporary methods of computational science is reflected in the rising number of reports using machine learning for pain research (Table 1). This review is focused on machine-learned technologies applied to general pain research that allow one to analyze and predict pain phenotypes and to obtain knowledge from experimental and clinical pain-related data.
Soraya Moradi, Elham Maraghi, Azar Babaahmadi
et al.
Introduction: Anxiety in students is a challenge of educational systems. The present study was conducted to investigate the efficiency of Pop Quiz (unannounced formative tests) in teaching biostatistics to postgraduate midwifery students and its effects on their statistics anxiety, test anxiety and statistical analysis skills.
Methods: This quasi-experimental study conducted during the first semester of the academic year of 2019-2020 in the Faculty of Nursing and Midwifery, Ahvaz Jundishapur University of Medical Sciences. The MSc midwifery students were divided into two separate classes. One of the classes was randomly selected for educational intervention (Pop Quiz). Teaching via the lecture method considered as control method. Test anxiety and statistical anxiety questionnaires were completed by the students in both groups before the educational intervention, during and at the end of semester. The final exam score considered as the statistical skills score.Data were analyzed in SPSS 22 using Fisher's exact test and GEE model.
Results: Thirty eight MSC midwifery students (12 in intervention group and 26 in comparison group)were recruited in this study. The mean and standard deviation of the exam score of students in lecture and Pop Quiz groups were respectively 14.43 ± 3.80 and 15.95 ± 2.79 (P=0.182). The patterns of change in test anxiety score differed significantly over time between the two teaching methods (P = 0.003). Although, there was a decreasing trend in mean score of statistics anxiety scores in Pop Quiz group in comparison with lecture based group, but there were not statistically significant differences.
Conclusion: Applying Pop Quiz to teaching biostatistics reduces test anxiety and statistics anxiety and increases statistical analysis skills in postgraduate midwifery students
We consider sparse count data models with the sparsity rate ? = N/n = O(1) where N = N (n) is the number of observations and n ? ? is the number of cells. In this case the plug-in estimator of the structural distribution of expected frequencies is inconsistent. If ? = O(n ?? ) for some ? > 0, the nonparametric maximum likelihood estimator, in general, is also inconsistent. Assuming that some auxiliary information on the expected frequencies is available, we construct a consistent estimator of the structural distribution.
Salmon Noce Aulele, Helda Y. Taihuttu, Mozart W. Talakua
Analisis konjoin adalah salah satu analisis statistik multivariat yang dapat digunakan untuk mengetahui keadaan suatu produk atau jasa. Pada penelitian ini analisis konjoin diterapkan untuk mengetahui penilaian dosen terhadap pembukaan program studi statistika di universitas pattimura. Atribut yang perlu diperhatikan yaitu jumlah dosen, banyaknya ruangan kuliah, peminat program studi, kondisi laboratorim, kondisi perpustakan, dan pengguna lulusan. Data diperoleh dari 50 dosen FMIPA. Hasil penelitian ini diketahui bahwa keadaan Program Studi Statistika nantinya memiliki karakteristik dosen statistika cukup, ruangan kuliah kurang, peminat program studi banyak, kondisi laboratorium baik, kondisi perpustakaan dan pengguna lulusan banyak dan menurut pendapat dosen FMIPA atribu yang sangat perlu diperhatikan adalah atribut jumlah dosen.
Kata kunci: Analisis Konjoin, Penilaian Dosen, Program Studi Statistika
The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only little is known about the conditions on the underlying network structure which ensure network Lasso to be accurate. By leveraging concepts of compressed sensing, we address this gap and derive precise conditions on the underlying network topology and sampling set which guarantee the network Lasso for a particular loss function to deliver an accurate estimate of the entire underlying graph signal. We also quantify the error incurred by network Lasso in terms of two constants which reflect the connectivity of the sampled nodes.
Die Welt, in der die amtliche Statistik ihre Aufgaben wahrzunehmen hat, hat sich dramatisch verändert. Die strategische Position der amtlichen Statistik ist schwierig geworden: Die Umorientierung der Wirtschaftspolitik seit den sechziger Jahren hat die
Bedeutung zentraler Ergebnisse der amtlichen Statistik (wie etwa der Volkswirtschaftlichen
Gesamtrechnung) für die heimischen Entscheidungsträger reduziert. Gleichzeitig erfordern die durch den Beitritt Österreichs zur Europäischen Union eingegangenen Verpflichtungen aber eine signifikante Leistungsausweitung der amtlichen Statistik. Der Widerstand der Respondenten wächst. Deregulierung und Liberalisierung erschweren in vielen Fällen die
Arbeit der Statistik. Kennzeichen der neuen Wirtschaft wie neue Arten wirtschaftlicher
Aktivitäten, neue Formen von Beschäftigungsverhältnissen und Arbeitszeitregelungen sind mit traditionellen Instrumenten schwierig in den Griff zu bekommen.
Ein erfolgreiches Bestehen der amtlichen Statistik in Österreich setzt voraus, daß die neue Führung bürokratische Hindernisse überwinden und eine Aufwertung der Tätigkeit der Anstalt – auch im Urteil der Öffentlichkeit – erreichen kann.
Based on a stationary Poisson point process, a wireless network model with random propagation effects (shadowing and/or fading) is considered in order to examine the process formed by the signal-to-interference-plus-noise ratio (SINR) values experienced by a typical user with respect to all the base stations in the down-link channel. This SINR process is completely characterized by deriving its factorial moment measures, which involve numerically tractable, explicit integral expressions. This novel framework naturally leads to expressions for the k-coverage probability, including the case of random SINR threshold values considered in multi-tier network models. While the k-coverage probabilities correspond to the marginal distributions of the order statistics of the SINR process, a more general relation is presented, connecting the factorial moment measures of the SINR process to the joint densities of these order statistics. This gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations. The presented framework consisting of the mathematical representations of SINR characteristics with respect to the factorial moment measures holds for the whole domain of SINR, and is amenable to considerable model extension.