Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the mathematical foundations of proper scoring rules, including general characterization results and important families of scoring rules. We discuss their role in statistics and machine learning for estimation and forecast evaluation. Furthermore, we comment on interesting developments of their usage in applications.
Sediono Sediono, Toha Saifudin, Maria Setya Dewanti
et al.
Natural gas is a key energy commodity with significant global economic impact, and its pricing is influenced by factors like weather, energy policies, geopolitics, and supply-demand balance. The Russia-Ukraine conflict disrupted Russia’s gas exports, causing price volatility and affecting global markets, including Indonesia. This has heightened the need for accurate price prediction to support policy and investment decisions. Previous studies show ARIMA-GARCH models predict well but need pulse function intervention for sudden shocks. This study aims to apply pulse function intervention analysis, which captures the immediate effects of external events on time-series data, to improve the precision of natural gas price forecasts, aiding government and industry decision-makers. The optimal intervention model for predicting natural gas prices on the New York Mercantile Exchange is the Probabilistic ARIMA (0,2,1) with a pulse function intervention order of b=0, r=2, and s=0. Using this model with the pulse function intervention approach yields consistent fluctuation patterns over time and achieves a MAPE value of 12.2586%, indicating that the model provides good predictive accuracy.
The estimation of finite population mean is always of interest for different sampling techniques and it is the basic measure to find for sample to estimate one of the most applicable central tendency. In literature, under simple random sampling without replacement people used rank or empirical distribution function as dual use of an auxiliary variable in estimation method to improve the efficiency of the estimator. In this paper, we proposed a class of regression-cum-exponential estimator using two auxiliary variables and also the dual use of one of the auxiliary variables in the form of its empirical distribution function. The mean square error of the proposed estimator in derived and compared with existing estimators using empirical study based on real life populations. The simulation study is also conducted to assess the sampling stability using empirical mean square error. The results show that the proposed estimator is performing much better than its competitors not due the dual use of auxiliary variables rather using additional suitable auxiliary variable. The study concludes that dual use of auxiliary variable is not the right choice to improve the efficiency of an estimator rather using additional auxiliary variable(s).
I Nyoman Widana, Ni Luh Putu Suciptawati, Sulma Sulma
Program Education plays a vital role in improving human resources. But on the other hand, education costs are not cheap. For this reason, people need to prepare education funds from an early age. One way is to take part in an education insurance program. This is a business opportunity that a village-owned enterprise (BUMDes) can run by offering education insurance services to the public. This research aims to develop and use programming software to calculate education insurance premiums offered by BUMDes. The method used is The Equivalence Principle method. Based on the case study, the premium price calculated using software that has been developed is very competitive – below market price, depending on the interest rate and fees charged.
Arefeh Dehghani tafti, Yunes Jahani, Sara Jambarsang
et al.
In the last few decades, in many research fields, different methods were introduced to discover groups with the same trends in longitudinal data. The clustering process is an unsupervised learning method, which classifies longitudinal data based on different criteria by performing algorithms. The current study was performed with the aim of reviewing various methods of longitudinal data clustering, including two general categories of non-parametric methods and model-based methods. PubMed, SCOPUS, ISI, Ovid, and Google Scholar were searched between 2000 and 2021. According to our systematic review, the non-parametric k-means Clustering Method utilizing Euclidean distance emerges as a leading approach for clustering longitudinal data This research, with an overview of the studies done in the field of clustering, can help researchers as a toolbox to choose various methods of longitudinal data clustering in idea generation and choosing the appropriate method in the classification and analysis of longitudinal data.
Yunda Sasha Paradilla, Memi Nor Hayati, Sifriyani Sifriyani
Cluster analysis is an analysis that is useful in summarizing data by grouping objects based on certain similarity characteristics. One of the group analysis is Fuzzy Gustafson-Kessel (FGK) which is the development of the Fuzzy C-Means (FCM) method. The FGK method has a good way in adjusting the form of cluster membership function correctly for a data. This study aims to determine the results of the optimal number of groups based on the Partition Coefficient (PC) and Classification Entropy (CE) validity indexes and to find out the results of grouping 56 districts/cities on the island of Kalimantan based on poverty issue factors in 2021. The optimal number of groups using the FGK method based on the validity indexes of PC and CE are two groups. The first group and the second group each consist of 28 districts/cities in Kalimantan Island.
AbstractThis paper uses actual data on horse racing to illustrate probabilities, odds, and expected values, and offers cautionary remarks about applying textbook formulas to gambling on real‐world sporting events.
Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional consideration. In this
article the inverse problem of determination is considered, which depends on time, lowest term coefficient in differential equation in partial derivatives of fourth order in time with initial and boundary conditions from an additional integral observation. Under some conditions of regularity, consistency and orthogonality of data by using of the contraction principle the unique solvability of the solution of the coefficient identification problem on a sufficiently small time interval has been proved.
Yongsheng Rao, Saeed Kosari, Seyed Mahmoud Sheikholeslami
et al.
An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex v with f(v)=1 is adjacent to at least one vertex with label greater than 1, and iii) all vertices labeled by 0 are an independent set. The weight of an OIDRDF is the sum of its function values over all vertices. The outer-independent double Roman domination number γoidR (G) is the minimum weight of an OIDRDF on G. It has been shown that for any tree T of order n ≥ 3, γoidR (T) ≤ 5n/4 and the problem of characterizing those trees attaining equality was raised. In this article, we solve this problem and we give additional bounds on the outer-independent double Roman domination number. In particular, we show that, for any connected graph G of order n with minimum degree at least two in which the set of vertices with degree at least three is independent, γoidR (T) ≤ 4n/3.
In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question.
Millions of measuring instruments are verified each year before being placed on the markets worldwide. In the EU, such initial conformity assessments are regulated by the Measuring Instruments Directive (MID). The MID modules F and F1 on product verification allow for statistical acceptance sampling, whereby only random subsets of instruments need to be inspected. This article re-interprets the acceptance sampling conditions formulated by the MID. The new interpretation is contrasted with the one advanced in WELMEC guide 8.10, and three advantages have become apparent. First, an economic advantage of the new interpretation is a producers’ risk bounded from above, such that measuring instruments with sufficient quality are accepted with a guaranteed probability of no less than 95%. Second, a conceptual advantage is that the new MID interpretation fits into the well known, formal framework of statistical hypothesis testing. Thirdly, the new interpretation applies unambiguously to finite-sized lots, even very small ones. We conclude that the new interpretation is to be preferred and suggest re-formulating the statistical sampling conditions in the MID. Re-interpreting the MID conditions implies that currently available sampling plans are either not admissible or not optimal. We derive a new acceptance sampling scheme and recommend its application. Supplementary materials for this article are available online.
Political institutions and public administration (General), Probabilities. Mathematical statistics
Single-molecule fluorescence microscopy probes nanoscale, subcellular biology in real time. Existing methods for analyzing single-particle tracking data provide dynamical information, but can suffer from supervisory biases and high uncertainties. Here, we introduce a new approach to analyzing single-molecule trajectories: the Single-Molecule Analysis by Unsupervised Gibbs sampling (SMAUG) algorithm, which uses nonparametric Bayesian statistics to uncover the whole range of information contained within a single-particle trajectory (SPT) dataset. Even in complex systems where multiple biological states lead to a number of observed mobility states, SMAUG provides the number of mobility states, the average diffusion coefficient of single molecules in that state, the fraction of single molecules in that state, the localization noise, and the probability of transitioning between two different states. In this paper, we provide the theoretical background for the SMAUG analysis and then we validate the method using realistic simulations of SPT datasets as well as experiments on a controlled in vitro system. Finally, we demonstrate SMAUG on real experimental systems in both prokaryotes and eukaryotes to measure the motions of the regulatory protein TcpP in Vibrio cholerae and the dynamics of the B-cell receptor antigen response pathway in lymphocytes. Overall, SMAUG provides a mathematically rigorous approach to measuring the real-time dynamics of molecular interactions in living cells. Statement of Significance Super-resolution microscopy allows researchers access to the motions of individual molecules inside living cells. However, due to experimental constraints and unknown interactions between molecules, rigorous conclusions cannot always be made from the resulting datasets when model fitting is used. SMAUG (Single-Molecule Analysis by Unsupervised Gibbs sampling) is an algorithm that uses Bayesian statistical methods to uncover the underlying behavior masked by noisy datasets. This paper outlines the theory behind the SMAUG approach, discusses its implementation, and then uses simulated data and simple experimental systems to show the efficacy of the SMAUG algorithm. Finally, this paper applies the SMAUG method to two model living cellular systems—one bacterial and one mammalian—and reports the dynamics of important membrane proteins to demonstrate the usefulness of SMAUG to a variety of systems.
Though statistics is covered in secondary-school curricula, it is usually limited to few lessons and mainly taught in a procedural approach. There seems to be a gap between the education of mathematics teachers and the demands on their practice. Learning statistics from a mathematical perspective does not qualify to teach the subject properly. Therefore, we developed a pedagogical intervention that consists in a training program for teaching aimed at mathematics pre-service teachers and focused on activity-based learning. Two workshops and a web-site were designed: first, to improve competencies in teaching statistics at secondary level, and second, to positively influence attitudes towards statistics. Workshops about descriptive statistics and probability were focused on real-data analysis from media, games, and simulations. Over several years, more than 500 teachers attended these workshops, which were positively evaluated in terms of content, relevance, and applicability. A follow-up survey 2–5 years later showed that most teachers are teaching statistics in their classes, which can be seen as great step forward to bring statistics into the classroom. First published February 2020 at Statistics Education Research Journal Archives
Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.