Concept Of Probability Research Articles

The effect of COVID-19 on cancer incidences in the U.S

Fundamental data analysis assists in the evaluation of critical questions to discern essential facts and elicit formerly invisible evidence. In this article, we provide clarity into a subtle phenomenon observed in cancer incidences throughout the time of the COVID-19 pandemic. We analyzed the cancer incidence data from the American Cancer Society [1]. We partitioned the data into three groups: the pre-COVID-19 years (2017, 2018), during the COVID-19 years (2019, 2020, 2021), and the post-COVID-19 years (2022, 2023). In a novel manner, we applied principal components analysis (PCA), computed the angles between the cancer incidence vectors, and then added lognormal probability concepts in our analysis. Our analytic results revealed that the cancer incidences shifted within each era (pre, during, and post), with a meaningful change in the cancer incidences occurring in 2020, the peak of the COVID-19 era. We defined, computed, and interpreted the exceedance probability for a cancer type to have 1000 incidences in a future year among the breast, cervical, colorectal, uterine corpus, leukemia, lung & bronchus, melanoma, Hodgkin's lymphoma, prostate, and urinary cancers. We also defined, estimated, and illustrated indices for other cancer diagnoses from the vantage point of breast cancer in pre, during, and post-COVID-19 eras. The angle vectors post the COVID-19 were 72% less than pre-pandemic and 28% less than during the pandemic. The movement of cancer vectors was dynamic between these eras, and movement greatly differed by type of cancer. A trend chart of cervical cancer showed statistical anomalies in the years 2019 and 2021. Based on our findings, a few future research directions are pointed out.

IMPLEMENTASI METODE NAIVE BAYES CLASSIFIER UNTUK KLASIFIKASI SENTIMEN ULASAN PENGGUNA APLIKASI NETFLIX PADA GOOGLE PLAY

The COVID-19 pandemic has led to restrictions on activities in public places or facilities, such as cinemas. This has resulted in increased users of streaming service applications such as Netflix where users can access videos or movies online. Netflix users continue to increase from year to year, but its users began to decrease along with other streaming applications. Related to this, sentiment analysis was carried out on the classification of positive and negative reviews given by users on the Google Play website. The classification is expected to produce good accuracy and be analyzed so that it can be useful information for Netflix and potential users of streaming applications. The Naive Bayes Classifier method is a classification algorithm that is easy to apply and has high effectiveness for classifying text. This method utilizes the concept of conditional probability and has a strong assumption of independence. This study uses 2.850 Netflix application review data on Google Play which is then processed and divided into training data and test data with a ratio of 80:20. Classification with the Naive Bayes Classifier produces an accuracy value of 87,33%, a precision value of 87,6%, a recall value of 93,53%, and an F-measure value of 90,47% so it can be concluded that the performance of the Naive Bayes method is good for classifying user reviews of the Netflix.

Informed consent-patients' understanding of risk.

The central concept of informed consent is communication of the chance of a successful outcome. The risks and benefits are probabilistic concepts derived from populations; they do not map with any certainty to the individual. We tested patients' comprehension of basic probability concepts that are needed for informed consent. Patients (n=478) completed five questions designed to test risk estimates that are relevant to informed consent. The questions posed non-medical scenarios to avoid patients associating them with their clinical care. The questionnaire was in English and was only offered to patients whose nurse felt that they had sufficient English literacy to understand the questions. Out of a possible total of five correct answers, Asian patients scored lowest, and significantly less than Pākehā/Europeans (average total score 2.6±1.7 vs 3.6±1.4, p<0.001, 95% confidence interval 0.5 to 1.38). The total score for Māori/Pasifika was intermediate (3.2±1.4), yet they had the lowest deprivation index. This discordant finding may be due to poorer English literacy among Asian participants. On multiple linear regression, Asian ethnicity and advancing age were the independent predictors of a low score. Socio-economic deprivation decile and sex were not. When answering questions constructed according to best practice, many (but not all) patients have reasonable risk comprehension. Further improvement could target older patients, those of Asian ethnicity and probably all patients where English is a second language. Liberal use of interpreters is suggested.

Using External Information for More Precise Inferences in General Regression Models

Empirical research usually takes place in a space of available external information, like results from single studies, meta-analyses, official statistics or subjective (expert) knowledge. The available information ranges from simple means and proportions to known relations between a multitude of variables or estimated distributions. In psychological research, external information derived from the named sources may be used to build a theory and derive hypotheses. In addition, techniques do exist that use external information in the estimation process, for example prior distributions in Bayesian statistics. In this paper, we discuss the benefits of adopting generalized method of moments with external moments, as another example for such a technique. Analytical formulas for estimators and their variances in the multiple linear regression case are derived. An R function that implements these formulas is provided in the supplementary material for general applied use. The effects of various practically relevant moments are analyzed and tested in a simulation study. A new approach to robustify the estimators against misspecification of the external moments based on the concept of imprecise probabilities is introduced. Finally, the resulting externally informed model is applied to a dataset to investigate the predictability of the premorbid intelligence quotient based on lexical tasks, leading to a reduction of variances and thus to narrower confidence intervals.

Neutrino oscillations as a single Feynman diagram

We propose an approach to neutrino oscillations in vacuum, based on quantum field theory (QFT). The neutrino emission and detection are identified with the charged-current vertices of a single second-order Feynman diagram for the underlying process, enclosing neutrino propagation between these two points. The key point of the presented approach is the definition of the space-time setup typical for neutrino oscillation experiments, implying macroscopically large but finite volumes of the source and detector separated by a sufficiently large distance L. We derive an L-dependent master formula for the charged lepton production rate, which provides the QFT basis for the analysis of neutrino oscillations. This formula depends on the underlying process and is not reducible to the conventional approach resorting to the concept of neutrino oscillation probability, which originates from non-relativistic quantum mechanics. We demonstrate that for some particular choice of the underlying process the derived master formula approximately coincides with the conventional one under some assumptions. In support to presented approach we show that it provides the QFT framework not only for neutrino–neutrino but also neutrino-antineutrino oscillations. It is also argued that the proposed formalism allows us to consistently incorporate medium effects, when neutrinos oscillate in dense matter.

The strategic prize game Le Her

AbstractLe Her is a strategic two-person prize game the classic version of which uses a deck of cards. Despite its simple rules, the analysis of the game is surprisingly complex. I describe a modern variant of Le Her that is amenable to elementary analysis, yet retains and highlights all central aspects of the classical game. This elementary analysis combines naturally central concepts of calculus (partial derivatives, multidimensional optimization, double integrals, fixed and saddle points) with major probabilistic concepts (random variable, event, independence) and basic notions in decision theory (Nash equilibrium). Due to its stimulating context as a strategic prize game Le Her offers an attractive illustration and an appealing application of learning goals and curricular contents which are otherwise often perceived as remote and abstract.

The Philosophy of Probability Values Behaviour, through Fractions and Composite Probability Function in the Continuous Case

This paper deals with probability theory, and it is an extension to a published paper that has the same title, but for the discrete case. This present paper is aiming to study probability values behavior, in the case of continuous sample space, through fractions intervals and composite function. This aim tends to study the value behavior rather than finding the value itself. Also, this aim requires usage of some concepts of continuity, geometric probability, and measure theory, which also need a brief treatment. This paper is mainly using an experiment with a design that helps to study the probability fractions values in the form of intervals in the case of one direction movement and in the case of different directions. As a result, every case reflects some aspects of probability values behavior and can clarify many important characteristics of the probability theory. In addition to applying the composite function by some important theorems of conditional probability. These are besides a proven proposition that helps to design experiment, upon the understanding of the case nature. In addition to a corollary that allows to visualize negative probability values, as a particular case (trial), that upon the validity of the explanation of negativity which should be consistent with the probability axioms.

Generalized Partitioned Local Depth

In this paper, we provide a generalization of the concept of cohesion as introduced recently by Berenhaut et al. (Proc Natl Acad Sci 119:2003634119, 2022). The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information.

FKM-guideline “Analytical strength Assessment” – Background and current developments

The FKM-Guideline “Analytical Strength Assessment” contains an algorithm for both static and the fatigue strength assessment of components made of steel, cast iron, and aluminium alloys. Designed to be advantageous for industrial applications, this guideline expresses the design stress using a straightforward linear-elastic material behaviour.Starting with the material strength properties specified in technical standards, the relevant component properties for both static and fatigue strengths can be determined by considering all influencing factors. The safety level required for assessment can be adjusted using experience-based safety factors. The outcomes of the analytical strength assessment provide a measure of the degree of utilisation.While the FKM-Guideline has been successfully applied since 1994, continuous further development is necessary to ensure it remains at the forefront of industry standards. Key development areas include the improvement of the critical strain curve, introduction of a coordinate-invariant fatigue strength assessment procedure, conducting investigations on the accuracy of the calculation according to the FKM-Guideline as a precondition for the development of a probabilistic safety concept, and extension of the FKM-Guideline to additional material groups such as high-strength steel.

Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences

Possibility and probability are the two aspects of uncertainty, where uncertainty represents the ignorance of a given individual. The notion of alternative (or event) belongs to the domain of possibility. An event is intrinsically subdivisible and a quadratic metric, whose value is intrinsic or invariant, is used to study it. By subdividing the notion of alternative, a joint (bivariate) distribution of mass appears. The mathematical expectation of X is proved to be invariant using joint distributions of mass. The same is true for X12 and X12…m. This paper describes the notion of α-product, which refers to joint distributions of mass, as a way to connect the concept of probability with multilinear matters that can be treated through statistical inference. This multilinear approach is a meaningful innovation with regard to the current literature. Linear spaces over R with a different dimension can be used as elements of probability spaces. In this study, a more general expression for a measure of variability referred to a single random quantity is obtained. This multilinear measure is obtained using different joint distributions of mass, which are all considered together.

Meta-critical thinking, paradox, and probabilities

There is as much lack of clarity concerning what “critical thinking” involves, even among those charged with teaching it, as there is consensus that we need more emphasis on it in both academia and society. There is an apparent need to think critically about critical thinking, an exercise that might be called meta-critical thinking. It involves emphasizing a practice in terms of which “critical thinking” is helpfully carried out and clarifying one or more of the concepts in terms of which “critical thinking” is usually defined. The practice is distinction making and the concept that of evidence. Science advances by constructing models that explain real-world processes. Once multiple potential models have been distinguished, there remains the task of identifying which models match the real-world process better than others. Since statistical inference has in large part to do with showing how data provide support, i.e., furnish evidence, that the model/hypothesis is more or less likely while still uncertain, we turn to it to help make the concept more precise and thereby useful. In fact, two of the leading methodological paradigms—Bayesian and likelihood—can be taken to provide answers to the questions of the extent to which as well as how data provide evidence for conclusions. Examining these answers in some detail is a highly promising way to make progress. We do so by way of the analysis of three well-known statistical paradoxes—the Lottery, the Old Evidence, and Humphreys’—and the identification of distinctions on the basis of which their plausible resolutions depend. These distinctions, among others between belief and evidence and different concepts of probability, in turn have more general applications. They are applied here to two highly contested public policy issues—the efficacy of COVID vaccinations and the fossil fuel cause of climate change. Our aim is to provide some tools, they might be called “healthy habits of mind,” with which to assess statistical arguments, in particular with respect to the nature and extent of the evidence they furnish, and to illustrate their use in well-defined ways.

Analysis of Occupational Safety of Boat Lift Net’s Fishermen at the Bungus Ocean Fishing Port (PPS) Bungus West Sumatra

Boat lift nets are one of the fishing gears in PPS Bungus, data from December 2021; 142 Bagan boat boats departed to carry out fishing operations with the number of fishermen boats 6 - 21 people and the weight of the ship 8-30 GT. In recent years, there have been several work accidents experienced by Bagan boat fishermen, such as falling while walking on the boat deck, fatigue, stepping on rotten wood, and broken hands. This study aims to determine the cases of work accidents that occurred in boat-bagan fishermen in the period January 2022 - January 2023, describe the activities carried out by boat-bagan fishermen, and determine the level of risk experienced by boat-bagan fishermen. This study uses a descriptive observational method with data analysis of probability concepts, JSA, and HIRA using the 2004 Australia and New Zealand standard risk control matrix. The results showed that the activities carried out in the operation preparation stage at PPS Bungus were mainly carried out by laborers (non-fishermen), work accidents in 7 operation activities were classified into five low-risk accidents and two moderate-risk and work accidents in the post-operation stage occurred 4 out of 7 activities which were classified into three common risk accidents and one medium risk.

The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution

The focus of operations research is the existence of a problem that requires making an appropriate decision that helps reduce risk and achieves a good level of performance. Operations research methods depend on formulating realistic issues through mathematical models consisting of a goal function and constraints, and the optimal solution is the ideal decision, despite the multiplicity of these methods. However, we encounter many complex issues that cannot be represented mathematically, or many issues that cannot be studied directly. Here comes the importance of the simulation process in all branches of science, as it depends on applying the study to systems similar to real systems and then projecting this. The results if they fit on the real system. So simulation is the process of building, testing, and running models that simulate complex phenomena or systems using specific mathematical models. The simulation process depends on generating a series of random numbers subject to a regular probability distribution in the field [0, 1], and then converting these random numbers into random variables subject to the distribution law. Probability, according to which the system to be simulated operates, using appropriate techniques for both the probability density function and the cumulative distribution function. Classical studies have provided many techniques that are used during the simulation process, and to keep pace with the great scientific development witnessed by our contemporary world, we found that a new vision must be presented for this. Techniques A vision based on the concepts of neutrosophics, the science founded by the American mathematical philosopher Florentin Smarandache. The year 1995, in which new concepts of probabilities and probability distributions are used, as we presented in previous research some techniques from a neutrosophic perspective, and as an extension of what we presented previously, we present in this research a neutrosophic vision of the Box and Muller technique used to generate random variables that follow a normal distribution.

Application of mathematical modeling in probability theory and mathematical statistics

In this academic paper, the application of mathematical modeling in the fields of probability theory and mathematical statistics is rigorously explored. This study advocates for the integration of mathematical modeling into the pedagogical framework of these disciplines, proposing it as a strategic enhancement to traditional teaching methodologies. The incorporation of such models is posited to catalyze the cultivation of creative thinking capabilities within students. The discourse following this proposal delves into the intricate details, highlighting both theoretical underpinnings and practical applications of this integration. By infusing mathematical modeling into the curriculum, the initiative aims to enrich students’ comprehension and application of complex statistical and probabilistic concepts, thereby equipping them with the tools to innovatively tackle real- world problems.

Information processes in stochastic models for strategic thinking operations

It constitutes a particularly valuable adoption that the family of infinitely divisible distributions is frequently employed as a very suitable choice for investigating theoretical and practical properties of structural probabilistic concepts. In particular, this family is valuable in construction and study of mathematical expressions, or equivalently stochastic models, with extensive practical applicability. The present paper focuses on the development and investigation of a stochastic model by making use of the extremely useful concept of infinitely divisibility. In addition, the paper offers an application of the introduced mathematical expressions in making realistic decisions in the extremely important area of various information processes.

Toward a Better Understanding of Statistical Significance and p Values in Nursing

Background: Nursing aims to rely on the best evidence, yet nurses frequently struggle with statistics, impeding the integration of research into practice. The misuse of statistical significance and p values is a pervasive issue, widely debated across disciplines but often overlooked in nursing.Objective: This study seeks to elucidate key arguments surrounding the misuse of p values, assess their relevance to nursing, and propose recommendations for improvement.Approach: Conducting a critical literature review on the interpretation and reporting of statistical significance and its practical implications among nurses, nursing students, and scholars.Results: The literature reveals widespread misunderstandings of probability concepts in classical statistics, leading to the misuse of p values. Some scholars propose abandoning p values altogether due to these challenges. Rather than dismissing p values, this article provides insights into their historical context and proper application. Recommendations are offered for accurately interpreting results and integrating supplementary metrics. Fostering statistical competencies already at the undergraduate level can enhance statistical literacy and alleviate statistics anxiety among nursing students, a prevalent issue. Early exposure to statistical methods in nursing education empowers nurses to actively engage in research. Additional recommendations include preregistering analysis plans to mitigate publication bias and exploring alternative approaches such as Bayesian methods.Conclusions: While p values serve as a valuable tool for preliminary assessment against randomness in nursing research, their widespread misunderstanding necessitates multiple measures for accurate interpretation and understanding of statistical significance. It is imperative for nurse educators and researchers to incorporate these recommendations into their practices.

A classroom experience about the application of research-based learning for the teaching of probability in engineering

&lt;abstract&gt; &lt;p&gt;We explored the implementation of a Research-Based Learning (RBL) for the teaching and learning of probability in engineering education. The approach provided a student-centered learning environment, integrating practical activities within an active learning conception. A detailed RBL task in connection with weather forecasting was described, highlighting a methodical 10-day learning process that considers research, practical application, and reflection. The effectiveness of this RBL task was evaluated through thematic analysis of student reflective essays, focusing on their learning experiences and challenges. The analysis revealed enhanced understanding of probability, varied student engagement, and the value of practical learning. It also identified challenges in conceptualizing abstract probability concepts. The findings highlighted the RBL's potential in improving students' conceptual grasp and application of probability in real-world scenarios, providing key insights for future educational strategies in engineering. This study contributes to the broader discourse on innovative teaching methodologies in engineering education, demonstrating the impact of active, inquiry-based learning approaches.&lt;/p&gt; &lt;/abstract&gt;

Deduction and construction of a discrete probability function (Binomial and Geometric) with analytical development of expected value and variance

The present work deals with the construction and deduction of a discrete probability function, where the objective is the understanding of the mathematical foundations of probability for its correct application, interpretation and verification in solving probability problems. For this purpose we rely on the theory of didactic situations of Brousseau (1997) and Sadovsky (2005). Teaching strategies are proposed with didactic model materials that improve student learning by promoting the analysis and understanding of various foundations of probability (Panizza, 2003). The importance of close communication between teachers and students in the teaching-learning process for the resolution, interpretation and verification of probability problems is highlighted. The software used in this research was Wolfram Mathematica, which facilitates mathematical writing, calculations, and the construction of graphs using a simple interface. This software makes work easier by fostering student autonomy in the development of skills for analysis and problem solving. We believe that these materials will contribute to the improvement of teaching-learning processes on the fundamentals and concepts of probability.

MODERN NUMERICAL METHODS OF ANALYSIS OF STATISTICAL DATA IN THE SCHOOL COURSE

Mathematical modelling of practical statistical problems is a current topic in the school course, related to the development of various approaches and methods of modern solutions to many practical problems. The purpose of mathematical statistics is the development of methods of statistical observation and the collection and analysis of statistical data. The given article shows several numerical methods for studying mathematical statistics in the school course: measurements of central tendency, measurements of position, measurements of dispersion. Measures of central tendency indicate the “center” of the data along a number line and are usually reported as values representing the data. There are three common measures of central tendency: the arithmetic mean, the median, and the mode. Position metrics represent the three most basic positions in a list of numeric data, ordered from smallest to largest: start, end, and middle. In addition to these, the most common measures of position, quartiles and percentages, are also presented. Measures of dispersion show the degree to which the data are spread out. Among the measures of dispersion of the statistic, the rank, interquartile range, and standard deviation are presented. The practice of solving statistical problems serves to develop the skills of using probabilistic statistical concepts and methods at school, so the work presents the brief content of each method, calculation formulas, and examples.

Interpreting Warn-on-Forecast System Guidance, Part I: Review of Probabilistic Guidance Concepts, Product Design, and Best Practices

The Warn-on-Forecast System (WoFS) is a convection-allowing ensemble prediction system designed to primarily provide guidance on thunderstorm hazards from the meso-beta to storm-scale in space and from several hours to less than one hour in time. This article describes unique aspects of WoFS guidance product design and application to short-term severe weather forecasting. General probabilistic forecasting concepts for convection allowing ensembles, including the use of neighborhood, probability of exceedance, percentile, and paintball products, are reviewed, and the design of real-time WoFS guidance products is described. Recommendations for effectively using WoFS guidance for severe weather prediction include evaluation of the quality of WoFS storm-scale analyses, interrogating multiple probabilistic guidance products to efficiently span the envelope of guidance provided by ensemble members, and application of conceptual models of convective storm dynamics and interaction with the broader mesoscale environment. Part II of this study provides specific examples where WoFS guidance can provide useful or potentially misleading guidance on convective storm likelihood and evolution.