OpenIntro Statistics strives to be a complete introductory textbook of the highest caliber. Its core derives from the classic notions of statistics education and is extended by recent innovations. The textbook meets high quality standards and has been used at Princeton, Vanderbilt, UMass Amherst, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools.

LEARNING OBJECTIVE: Identify and distinguish between a parameter and a statistic.

LEARNING OBJECTIVE: Explain the concepts of sampling variability and sampling distribution.

Here is the link to the new Passion-Driven Statistics e-book!

http://bit.ly/Passion-DrivenStatistics

Passion-Driven Statistics is an NSF-funded, multidisciplinary, project-based curriculum that supports students in conducting data-driven research, asking original questions, and communicating methods and results using the language of statistics. The curriculum supports students to work with existing data covering psychology, health, earth science, government, business, education, biology, ecology and more. From existing data, students are able to pose questions of personal interest and then use statistical software (e.g. SAS, R, Python, Stata, SPSS) to answer them. The e-book is presented in pdf format for ease of use across platforms. It can also be customized by downloading and editing the .iba file (available through the link below) using the free “iBook Author” software.

http://bit.ly/EditPDSe-book

For more information, contact Lisa Dierker, ldierker@wesleyan.edu or check out the Passion-Driven Statistics website at https://passiondrivenstatistics.com/

Fundamentals of characterizing and recognizing patterns and features of interest in numerical data. Basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. Decision theory, statistical classification, maximum likelihood and Bayesian estimation, non-parametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research.

This course takes a broad-based look at poker theory and applications of poker analytics to investment management and trading.

The applets in this section of Statistical Java address Power. Users can perform one or two tailed tests for proportions or means for one or two samples. Set the parameters and drag the mouse across the graph to see how effect size affects power.

Prediction is at the heart of almost every scientific discipline, and the study of generalization (that is, prediction) from data is the central topic of machine learning and statistics, and more generally, data mining. Machine learning and statistical methods are used throughout the scientific world for their use in handling the "information overload" that characterizes our current digital age. Machine learning developed from the artificial intelligence community, mainly within the last 30 years, at the same time that statistics has made major advances due to the availability of modern computing. However, parts of these two fields aim at the same goal, that is, of prediction from data. This course provides a selection of the most important topics from both of these subjects.

Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Interpretations of the concept of probability. Basic probability rules; random variables and distribution functions; functions of random variables. Applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. Elements of statistics. Bayesian methods in engineering. Methods for reliability and risk assessment of complex systems, (event-tree and fault-tree analysis, common-cause failures, human reliability models). Uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling). Introduction to Markov models. Examples and applications from nuclear and chemical-process plants, waste repositories, and mechanical systems. Open to qualified undergraduates.

Explain how a density function is used to find probabilities involving continuous random variables.

This page of Statistical Java describes 11 different probability distributions including the Binomial, Poisson, Negative Binomial, Geometric, T, Chi-squared, Gamma, Weibull, Log-Normal, Beta, and F. Each distribution has its own applet.

Learning Objective: Apply probability rules in order to find the likelihood of an event.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis. Random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. Introduction to system reliability. Bayesian analysis and risk-based decision. Estimation of distribution parameters, hypothesis testing, and simple and multiple linear regressions. Poisson and Markov processes. Emphasis on application to engineering problems.

" This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice."

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

This applet from Statistical Java allows the user to generate bivariate data for analysis with simple linear regression. The page describes the equations used to generate the data and estimate the regression lines.

1). Identify the sampling method used in a study and discuss its implications and potential limitations.
2). Critically evaluate the reliability and validity of results published in mainstream media.
3). Summarize and describe the distribution of a categorical variable in context.

This material is a detailed exercise for students in introductory statistics. Students are asked to collect a random sample of data from a real estate website; conduct descriptive statistics (including confidence intervals); and write a report summarizing their findings.

This tutorial introduces the reader to some of the amazing capabilities of R to work with and map geographic data. Geographic data are data that contain spatial attributes (or spatial data) that define a geographic space (location, area, elevation, etc.) and non spatial attributes (f.e., population density, pollutant concentrations, temperature).

This tutorial was developed for one the units of the course “ENVS 420: Research Seminar in Environmental Sciences” offered at the University of Baltimore. However, it is hoped that readers outside of ENVS 420 who are interested in geospatial analysis and with a basic familiarity of R find this tutorial useful.

The use of an integrated developer environment (IDE) or an IDE like configuration such as the IDE RStudio (https://rstudio.com/) or the Nvim-R plug-in for the integration of vim/neovim and R (https://github.com/ jalvesaq/Nvim-R/tree/stable) is recommended but not necessary.

The tutorial was written with RMarkdown (v. 2.6) (Allaire et al., 2020; Xie et al., 2018, 2020) in R (v. 4.2.3) (R Core Team, 2020).