The lectures are at a beginning graduate level and assume only basic …
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
In order to promote students’ conceptual understanding and learning experience in introductory …
In order to promote students’ conceptual understanding and learning experience in introductory statistics, a technology task, which focuses on the probability distribution in which means are defined, was created using TinkerPlots, an exploratory data analysis and modeling software. The targeted audiences range from senior high school grade levels to college freshmen who are starting their introductory course in statistics. Students will be guided to explore and discover the movement behaviors of means of a set of numbers randomly generated from a fixed range of values characterized by a predetermined probability distribution. The cognitive, mathematical, technological and pedagogical natures of the task, as well as its association with the statistics education framework based on the Guidelines for Assessment and Instruction in Statistics Education (GAISE) by the American Statistical Association, will be elaborated. A brief discussion on what cognitive design principles this task satisfies will also be provided at the end.
This course covers topics such as sums of independent random variables, central …
This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.
Think Stats is an introduction to Probability and Statistics for Python programmers. …
Think Stats is an introduction to Probability and Statistics for Python programmers.
*Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. *If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
Think Stats is an introduction to Probability and Statistics for Python programmers. …
Think Stats is an introduction to Probability and Statistics for Python programmers.
*Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. *If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around …
This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions. For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order statistics and ranks in each coordinate. A more modern method, to be followed in this course, is to look for rotationally or affine invariant procedures. These can be based on empirical processes as in computer learning theory. Robustness, which developed mainly from around 1964, provides methods that are resistant to errors or outliers in the data, which can be arbitrarily large. Nonparametric methods tend to be robust.
The main goal of this course is to study the generalization ability …
The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
This course provides an introduction to probability and statistics, with emphasis on …
This course provides an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the Total Probability and Bayes' Theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.
These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform …
These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.
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