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Statistical Estimation for Data Science and AI · LearnSpace
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Statistical Estimation for Data Science and AI

Курс от University of Colorado Boulder
Средний≈ 29.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course introduces statistical inference, sampling distributions, and confidence intervals. Students will learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) and the Master of Science in Artificial Intelligence (MS-AI) degrees offered on the Coursera platform. These interdisciplinary degrees bring together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the CU degrees on Coursera are ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Learn more about the MS-AI program at https://www.coursera.org/degrees/ms-artificial-intelligence-boulder Logo adapted from photo by Christopher Burns on Unsplash.

Навыки, которые вы освоите

Statistical InferenceProbability & StatisticsProbability DistributionStatistical MethodsStatistical AnalysisProbabilitySampling (Statistics)Applied MathematicsStatistics

Программа курса

6 модулей · 94 учебных материалов

01Start Here! 9 материалов

Welcome to the Course!

Course Updates and Accessibility SupportЧтениеWelcome to Statistical InferenceВидеоWelcome to Statistical InferenceЧтениеEarn Academic Credit for your Work!Чтение

Учитесь у экспертов

Jem Corcoran

Associate Professor

Statistical Estimation for Data Science and AI
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Обучение на Coursera

≈ 29.4 ч

6 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Course SupportЧтение
Assessment ExpectationsЧтение
AI Citation and AcknowledgementЧтение
Course Resources and ReadingЧтение
An Introduction to Jupyter Notebooks and RЛабораторная
02Point Estimation28 материалов

Lesson 1: Review of Discrete and Continuous Random Variables

Discrete Random Variables and Probability Mass FunctionsВидеоImportant Discrete DistributionsЧтениеAI Policy QuizЗаданиеRecognizing Discrete DistributionsЗаданиеContinuous Random Variables and Probability Density FunctionsВидеоImportant Continuous DistributionsЧтениеCalculations with Continuous DistributionsЗаданиеTable Summarizing Important Distributions Чтение

Lesson 2: Joint Distributions

Joint Distributions and IndependenceВидеоJoint DistributionsЧтение

Lesson 3: The Gamma Distribution

The Gamma DistributionВидеоVideo Slides: The Gamma DistributionЧтение

Lesson 4: Transformations of Distributions

Transformations of DistributionsВидеоVideo Slides for Transformations of DistributionsЧтение

Lesson 5: Expectation and Properties of Expectation

Expectation and Properties of ExpectationВидеоVideo Slides for Expectation and Properties of ExpectationЧтениеProbability, Expectation, and VarianceЗадание

Lesson 6: Variance and Covariance

Variance and CovarianceВидеоVideo Slides for Variance and CovarianceЧтение

Lesson 7: Estimators and Sampling Distributions

Estimators and Sampling DistributionsВидеоVideo Slides for Estimators and Sampling DistributionsЧтениеThe Shape of DataЛабораторная

Lesson 8: Distributions of Sums

Distributions of SumsВидеоVideo Slides for Distributions of SumsЧтение

Lesson 9: Method of Moments Estimators

Method of Moments EstimatorsВидеоVideo Slides for Method of Moments EstimatorsЧтениеMethod of Moments EstimationЗадание

Module One Summary Assignment

Point EstimationПрограммирование
03Maximum Likelihood Estimation14 материалов

Lesson 1: A Motivating Example

A Motivating ExampleВидеоVideo Slides for A Motivating ExampleЧтение

Lesson 2: Notation, Terminology, and First Complete Examples

Notation, Terminology, and First Complete ExamplesВидеоVideo Slides for Notation, Terminology, and First Complete ExamplesЧтение

Lesson 3: Multiple Parameters and Parameters in the Support of a Distribution

MLEs for Multiple and Support ParametersВидеоVideo Slides for MLEs for Multiple and Support ParametersЧтениеFinding MLEsЗадание

Lesson 4: The Invariance Property of Maximum Likelihood Estimators

The Invariance PropertyВидеоVideo Slides for The Invariance PropertyЧтениеSampling Distributions of MLEsЛабораторная

Lesson 5: Mean Squared Error, Bias and Relative Efficiency

Mean Squared Error, Bias, and Relative EfficiencyВидеоVideo Slides for Mean Squared Error, Bias and Relative EfficiencyЧтениеInvariance, Mean-Squared Error, and EfficiencyЗадание

Module Two Summary Assignment

Maximum Likelihood EstimationПрограммирование
04Large Sample Properties of Maximum Likelihood Estimators14 материалов

Lesson 1: Fisher Information and the Cramér-Rao Lower Bound

Fisher Information and the Cramer-Rao Lower BoundВидеоVideo Slides for Fisher Information and the Cramér-Rao Lower BoundЧтение

Lesson 2: Computational Simplifications for the Cramér-Rao Lower Bound

Computational Simplifications for the CRLBВидеоVideo Slides for Computational Simplifications for the CRLBЧтениеThe Cramer-Rao Lower BoundЗадание

Lesson 3: Convergence for Sequences of Random Variables

The Weak Law of Large NumbersВидеоVideo Slides for The Weak Law of Large NumbersЧтение

Lesson 4: The Central Limit Theorem

The Central Limit TheoremВидеоVideo Slides for The Central Limit TheoremЧтениеCentral Limit Theorem Lab WalkthroughЛабораторная

Lesson 5: Properties of Maximum Likelihood Estimators

Large Sample Properties of MLEsВидеоVideo Slides for Large Sample Properties of MLEsЧтениеFurther Computations with MLEsЗадание

Module Three Summary Assignment

Large Sample Properties of MLEsПрограммирование
05Confidence Intervals Involving the Normal Distribution15 материалов

Lesson 1: A Normal Introduction to Confidence Intervals

Let's Build a Confidence Interval!ВидеоVideo Slides for Let's Build a Confidence Interval!Чтение

Lesson 2: The t and Chi-Squared Distributions and the Sample Variance

The Chi-Squared and t- DistributionsВидеоVideo Slides for the Chi-Squared and t-DistributionsЧтениеExploring the Normal, t, and Chi-Squared RelationshipsЛабораторная

Lesson 3: One Sample Confidence Intervals Based on the t-Distribution

t-Distribution Confidence IntervalsВидеоVideo Slides for t-Distribution Confidence IntervalsЧтениеConfidence Intervals Involving the Normal DistributionЗадание

Lesson 4: Two Sample Confidence Intervals for Means

Confidence Intervals for the Difference Between Population MeansВидеоVideo Slides for Confidence Intervals for the Difference Between Population MeansЧтение

Lesson 5: Small Population Confidence Intervals for Differences in Means

Small Sample Confidence Intervals for the Difference Between Population MeansВидеоVideo Slides for Small Sample Confidence Intervals for the Difference Between Population MeansЧтениеConfidence Intervals for Differences Between MeansЗаданиеConfidence Intervals in RЛабораторная

Module Four Summary Assignment

Normal Distribution Confidence IntervalsПрограммирование
06Beyond Normality: Confidence Intervals Unleashed!14 материалов

Lesson 1: A Confidence Interval for Proportions

A Confidence Interval for ProportionsВидеоVideo Slides for A Confidence Interval for ProportionsЧтение

Lesson 2: Confidence Intervals for Variances and a Difference of Propoertions

Confidence Intervals for VariancesВидеоVideo Slides for Confidence Intervals for VariancesЧтениеConfidence Intervals for Proportions and VariancesЗадание

Lesson 3: A Confidence Interval for a Ratio of Variances

A Confidence Interval for a Ratio of VariancesВидеоVideo Slides for A Confidence Interval for a Ratio of VariancesЧтение

Lesson 4: General Confidence Intervals

Who Needs Normality?ВидеоVideo Slides for Who Needs Normality?Чтение

Lesson 5: General Confidence Intervals 2

General Confidence Intervals 2ВидеоVideo Slides for General Confidence Intervals 2ЧтениеNon-Normal Confidence Intervals in RЛабораторнаяBuild Your Own Confidence IntervalsЗадание

Assignments

Confidence Intervals Unleashed!Программирование