Statistical Computing In R

The freely available R software environment is a user-friendly place to work on linear modeling tasks. Here, we demonstrate how basic parameters of multiple linear regression (MLR) models are obtained with R by only writing a few lines of code. An example dataset with calculated results is provided to get a hands-on start with MLR analysis.
We show that fitting a linear model (or rejecting it) for given
variables with sample data can be done in three basic steps: (1) importing the data via CSV file, (2) using function lm() to derive the model and (3) reporting results or extracting result values for further analysis.

The basic formulas required to perform a simple linear regression (SLR) analysis are reviewed. A sample data set with calculation results is provided for the purpose of testing and illustration. We demonstrate how an SLR model can be derived in different ways by Python and R programming. The provided code snippets are supposed to serve as hands-on starting points while evaluating relationships between two variables.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

This course introduces students to the scientific approach to social studies. Weekly classes and tutorials are geared toward helping the students gain a basic understanding of systematic social inquiry. In the lectures, students learn about the fundamentals of quantitative research, and accustom to strategies for data analysis, hypothesis testing, and statistical inference. Each lecture is followed by a computer lab session, where students put their knowledge to practice, and perform tasks that revolve around visualizing data, and conducting statistical analyses.

This article examines a sample of 1,584 glass beads from the Viking-Age settlement, harbor, and cemetery of Hedeby, Germany. By designating Munsell colors for each bead and performing cluster analysis on the mapped colors, it is possible to discern how the Viking-Age inhabitants of Hedeby perceived and used color. This analysis suggests that glass beads were used differently in different contexts, with color playing an apparently determinative role in bead selection. The colors derived from this analysis correspond to results obtained in other studies of Viking-Age material and linguistic evidence, affirming the validity of this approach and buttressing the importance of archaeological glass.

Matthew C. Delvaux, "Colors of the Viking Age: A Cluster Analysis of Glass Beads from Hedeby," Journal of Glass Studies 60 (2018): 41-67.

Resumen El método de Monte Carlo para la simulación estática es una herramienta que permite analizar situaciones que por su naturaleza probabilística y compleja no sería posible analizar utilizando métodos tradicionales de matemáticas y estadística. En este artículo se presenta un ejemplo ficticio que ilustra el uso de esta técnica aplicada a analizar y encontrar alternativas para un problema de calidad en manufactura. Se utilizó el método con una herramienta informática (R/RStudio) para la generación de las variables aleatorias y el posterior análisis de los resultados. Se logró establecer el impacto de distintas acciones orientadas a resolver un problema específico. Abstract Monte Carlo method for static simulation is a tool that allows the analysis of situations of a complex and probabilistic nature which would not be possible to analyze via traditional mathematical and/or statistical methods. This article presents a fictitious example that shows the use of this technique to find alternatives for the solution of a quality problem in a manufacturing environment. Monte Carlo Simulation was used with the aid of a software tool (R/RStudio) to generate random variables and the subsequent analysis of the results. It was possible to determine the impact of various solutions aimed towards solving a specific manufacturing problem. .

Provides readers with a comprehensive and thorough guide to the evidential approach in statistics. The approach uses likelihood ratios, rather than the probabilities used by other statistical inference approaches. The evidential approach is conceptually easier to grasp, and the calculations more straightforward to perform. This book explains how to express data in terms of the strength of statistical evidence for competing hypotheses. The evidential approach is currently underused, despite its mathematical precision and statistical validity. Evidence-Based Statistics is an accessible and practical text filled with examples, illustrations and exercises. Additionally, the companion website complements and expands on the information contained in the book. While the evidential approach is unlikely to replace probability-based methods of statistical inference, it provides a useful addition to any statistician’s “bag of tricks.” In this book: It explains how to calculate statistical evidence for commonly used analyses, in a step-by-step fashion. Analyses include: t tests, ANOVA (one-way, factorial, between- and within-participants, mixed), categorical analyses (binomial, Poisson, McNemar, rate ratio, odds ratio, data that’s ‘too good to be true’, multi-way tables), correlation, regression and nonparametric analyses (one sample, related samples, independent samples, multiple independent samples, permutation and bootstraps). Equations are given for all analyses, and R statistical code provided for many of the analyses. Sample size calculations for evidential probabilities of misleading and weak evidence are explained. Useful techniques, like Matthews’s critical prior interval, Goodman’s Bayes factor, and Armitage’s stopping rule are described. Recommended for undergraduate and graduate students in any field that relies heavily on statistical analysis, as well as active researchers and professionals in those fields, belongs on the bookshelf of anyone who wants to amplify and empower their approach to statistical analysis.

This paper discusses the methodologies and datasets used in the cartographic study of morphological change in a 19th century residential scheme in Mulhouse, France. It examines (1) the availability and comparability of existing datasets (spatial, historical and archival), (2) the collection of new data from field surveys to historical maps, building permits, photographs, and planning documents by means of visual mapping, drawing, text review, and recording, and (3) their pre-processing including their transformation, cleansing, and integration using specialised tools, such as GIS, Rhino, Grasshopper, and RStudio.
The final outcome is a detailed and georeferenced three-dimensional model for the entire housing scheme of Cité Ouvrière that includes all 1,253 buildings (in volumes) and plots (in polygons) in their original (circa 1897) and current state. The produced model combines the accuracy of smaller-size data with the extent of bigger-size data. Its extent, level of aggregation and detail make it possible to use for cartographic research and spatial analysis at different scales and link it to available geographic information employed for municipal and national planning. Specifically, the model has already been proven valuable in revealing patterns of change and measuring the impact of the building densification process at the microlevel (Kostourou, 2021). This is because it can support a granular, longitudinal historical study that spans over 150 years and cover different spatial scales (from the neighbourhood to the building) while serving as a tool to systematically document transformations in the built form across scales and illustrating how local individual processes contribute to the formation and transformation of the larger whole.
The paper introduces an integrated framework for mapping physical changes of buildings and plots, by joining historical research, spatial analytics, and architectural modelling. Proposed as a solution to the inadequacy of current frameworks and datasets, the new methodology is able to collect and combine available information from online sources, archival documents, and field work; create and process high resolution and aggregate data; overcome limitations of current cartographic studies and open up possibilities for researchers to exploit two-dimensional and three-dimensional, categorical and numerical data for the analysis of spatial structures.

Correspondence Analysis (CA) is a statistical exploratory technique frequently used in many research fields to graphically visualize the structure of contingency tables. Many programs, both commercial and free, perform CA but none of them as yet provides a visual aid to the interpretation of the results. The 'CAinterprTools' package, designed to be used in the free R statistical environment, aims at filling that gap. A novel-to-medium R user has been considered as target. 15 commands enable to easily obtain charts that help (and are relevant to) the interpretation of the CA's results, freeing the user from the need to inspect and scrutinize tabular CA outputs, and to look up values and statistics on which further calculations are necessary. The package also implements tests to assess the significance of the input table's total inertia and individual dimensions.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

Deterioration of freeway traffic flow condition due to bottlenecks can be ameliorated with ramp metering.  A challenge in ramp metering is that it is not possible to process data in real-time and use the output in a control algorithm.  This is due to the fact that by the time processing is completed and a control measure applied, the traffic state will have changed. A solution to this problem is to forecast the traffic state and implement a control measure based on the forecast.  A dual-state Kalman filter was used to forecast traffic data at two locations on a freeway (I-84).  A Kalman filter is an optimal recursive data processing algorithm; predictions are based on only the previous time-step’s prediction and all previous data do not need to be stored and reprocessed with new measurements.  A coordinated feedback ramp metering control logic was implemented. The closed-loop system seeks to control the traffic density on the mainline while minimizing on-ramp queues through weighting functions.  The integration of the Kalman filter with the ramp meter control logic accomplishes the ramp meter algorithmic scheme in which is proactive to changes in freeway conditions by controlling a forecasted state.  In this closed-loop framework, real-time forecasts are produced with a continuously updated prediction that minimizes errors and recursively improves with each successive measurement. MATLAB was used to model the closed-loop control system as well as modify the input output constraints to evaluate and tune controller performance.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

This article provides a summary of a selection of some of the high-performance parallel packages (libraries) available from the Comprehensive R Archive Network (CRAN) using the statistical software R. These packages can utilize multicore systems often found in modern personal computers as well as computer cluster or grid computing in order to provide linear speed up the computations in many of advanced statistical modern applications. Some illustrative R parallel codes are given in order to introduce the reader to some basic ideas about parallel programming in R packages.

Background: Globally, millions of children aged below 5 years die every year and some of these deaths could have been prevented. Though a global problem, under-five mortality is also a major public health problem in Ghana with a rate of 60 deaths per 1000 live births. Identification of drivers of mortality among children aged below 5 years is an important problem that needs to be addressed because it could help inform health policy and intervention strategies aimed at achieving the United Nations SDG Goal 3 target 2. The aim of this study is to develop a predictive model and to identify determinants of under-five mortality.

This package implements statistical methods for estimating and inferring the mean of functional data. The methods are based on simultaneous confidence bands and local polynomial fitting. They feature: bandwidth selection by plug-in and cross-validation, goodness-of-fit tests for parametric models, equality tests for two-sample problems, and plotting functions.

In this study, the effect of dust accumulation on the performance of photovoltaic (PV) module has been shown. A statistical analysis has been conducted on a medium sized sample data collected from 30 hours of experimental work to obtain an empirical coefficient like temperature coefficients of short circuit current and open circuit voltage usually provided by manufacturers. This coefficient will be named dust coefficient of short circuit current and it will represent a predefined range of environmental conditions and soiling amounts; as the available testing conditions, and the statistical model prediction limits bound the coefficient extent of applicability.

Almost all available statistical packages are capable of performing Multivariate Analysis of Variance (MANOVA) from raw data. Some of statistical packages have capability to perform independent sample t-test, ANOVA and some other tests of significance on summary data, but you come across not single software that has the capability to perform MANOVA directly on summary data. A STATA programme has been written to perform Multivariate ANOVA on summary data.

The purpose of this book is to teach students of social science statistics courses how to program in R for data analysis. Primarily focusing on Base R, this book will teach R “from the ground up,” teaching the fundamentals without using external packages unless necessary or for quick demonstrations on the programming language’s extensions. Overall, I hope that students will learn enough from this book to conduct data analysis in R independently.

In my recent works, I propose a new theory of experience and chance, or the theory of certainties, which is a synthesis of two dual theories: Kolmogorov's theory of probabilities and a new theory of believabilities. The theory of experience and chance is based on axiomatics, adding to the Kolmogorov axiomatics of probability theory an axiom of co~event, a new concept defined as a pair of dual objects, one of which serves as a Kolmogorov event in probability space and the other - as an event in the dualistic believability space. One of my papers gives a theory of dual co~event-based means and examples of its use for processing
statistics of ``approving voting'' in elections and in forestry. In this paper, I will go into more detail in examples of processing the statistics
of ``approving voting'' in forestry, where a group of forestry experts is actually engaged in ``approving voting'' when they label the trees of the
forest, labelling those that according to their opinions must be felling. My goal is to show in these examples that the theory of experience and
chance is an effective tool for constructing co~evnts models of experts' behavior in different fields.

Imagine that you are conducting an experiment, as a result of which the event occurs or does not occur. You must determine whether this event occurred or not. Your experience tells you that many times in the past you, being exactly in the same circumstances, only in half of the cases came to the conclusion this event happened. In this situation I would say your believability of this event happened is equaled to the half. But you can't answer in this way. You are required to answer only either ``Yes'' or ``No''. What would you do in this situation? You must not think such situations are big rare. Refresh your memory what are you doing every day under uncertainty? Every day you are doing only it and no more. The question arises how you do this action?
If I say you ``toss a coin in your mind, or in your thoughts'' I'll do the mistake. The point is every one of us has an ability to make the believabilistic choice. You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.
Therefore, to denote this action, I will choose the new expression ``tossing an experienced coin'' in an experienced experiment that becomes dual to the usual expression ``tossing a coin'' in a random experiment.

'chi.perm' is an R function which allows to perform the chi-square test of independence on the basis of  permuted tables, whose number is selected by user. For the rationale of this approach, see for instance the nice description provided by Beh E.J., Lombardo R. 2014, Correspondence Analysis: Theory, Practice and New Strategies, Chichester, Wiley, at pages 62-64.

I have prepared this material for a 2-days "intensive" course directed to scientists at the Diamond Light Source Ltd, in Oxfordshire, in 2013. You are welcome to use the material for your own purpose (and, please, acknowledge my contribution in case it's useful to you).