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Bayesian Statistics: Time Series Analysis

Курс от University of California, Santa Cruz
Средний≈ 19.5 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course for practicing and aspiring data scientists and statisticians. It is the fourth of a four-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, Techniques and Models, and Mixture models. Time series analysis is concerned with modeling the dependency among elements of a sequence of temporally related variables. To succeed in this course, you should be familiar with calculus-based probability, the principles of maximum likelihood estimation, and Bayesian inference. You will learn how to build models that can describe temporal dependencies and how to perform Bayesian inference and forecasting for the models. You will apply what you've learned with the open-source, freely available software R with sample databases. Your instructor Raquel Prado will take you from basic concepts for modeling temporally dependent data to implementation of specific classes of models

Навыки, которые вы освоите

Time Series Analysis and ForecastingBayesian StatisticsForecastingModel EvaluationProbability DistributionR (Software)Statistical SoftwareR ProgrammingStatistical ProgrammingCorrelation AnalysisStatistical MethodsStatistical AnalysisStatistical Modeling

Программа курса

5 модулей · 81 учебных материалов

01Week 1: Introduction to time series and the AR(1) process 26 материалов

Introduction

🎥 Welcome to Bayesian Statistics: Time Series Видео📖 Introduction to RЧтение📖 List of References Чтение⭐️ Objectives of the Course Задание

Учитесь у экспертов

Raquel Prado

Professor

Bayesian Statistics: Time Series Analysis
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Обучение на Coursera

≈ 19.5 ч

5 модулей

Язык: Английский

Субтитры: Арабский, Французский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Нидерландский, Корейский, Немецкий, Русский, Тайский, Индонезийский, Шведский, Турецкий, Испанский, Хинди, Японский, Казахский, Польский

Часть программы вашего университета

Stationarity, the ACF and the PACF

🎥 Stationarity Видео🎥 The Autocorrelation Function (ACF) Видео📖 The Partial Autocorrelation Function (PACF)Чтение📖 Differencing and Smoothing Чтение🎥 ACF, PACF, Differencing and Smoothing: Examples Видео💻 R Code: Differencing and Filtering via Moving AveragesЧтение💻 R Code: Simulate Data from a White Noise ProcessЧтение✍️ Stationarity, the ACF, and the PACF Задание

The AR(1) process: Definition and properties

🎥 The AR(1) Видео📖 The PACF of the AR(1) Process Чтение🎥 Simulating from an AR(1) Process Видео💻 R Code: Sample Data from AR(1) ProcessesЧтение✍️ The AR(1) Definitions and Properties Задание

The AR(1): Maximum likelihood estimation and Bayesian inference

📖 Review of Maximum Likelihood and Bayesian Inference in Regression Чтение🎥 Maximum Likelihood Estimation in the AR(1)Видео💻 R code: MLE for the AR(1), ExamplesЧтение🎥 Bayesian Inference in the AR(1)Видео🎥 Bayesian Inference in the AR(1): Conditional Likelihood Example Видео💻 R Code: AR(1) Bayesian Inference, Conditional Likelihood Example Чтение ✍️ MLE and Bayesian Inference in the AR(1) Задание ✍️ Exercise: AR(1) Simulation, MLE, and Bayesian Inference in RЗадание📖 Bayesian Inference in the AR(1), Full Likelihood Example Чтение
02Week 2: The AR(p) process 20 материалов

The general AR(p) process

🎥 Definition and State-space RepresentationВидео🎥 Examples Видео🎥 ACF of the AR(p)Видео🎥 Simulating Data from an AR(p)Видео💻 R Code: Computing the Roots of the AR Polynomial Чтение💻 R Code: Simulating Data from an AR(p)Чтение📖 The AR(p): Review Чтение ✍️ Properties of AR Processes Задание

Bayesian inference in the AR(p)

🎥 Bayesian Inference in the AR(p): Reference Prior, Conditional Likelihood Видео💻 R Code: Maximum Likelihood Estimation, AR(p), Conditional Likelihood Чтение🎥 Model Order SelectionВидео🎥 Example: Bayesian Inference in the AR(p), Conditional Likelihood Видео💻 R Code: Bayesian Inference, AR(p), Conditional Likelihood Чтение💻 R Code: Model Order Selection Чтение
03Week 3: Normal dynamic linear models, Part I 20 материалов

The Normal Dynamic Linear Model: Definition, model classes, and the superposition principle

🎥 NDLM: Definition Видео🎥 Polynomial Trend ModelsВидео🎥 Regression Models Видео📖 Summary of Polynomial Trend and Regression Models Чтение🎥 The Superposition Principle Видео📖 Superposition Principle: General CaseЧтение✍️ The Normal Dynamic Linear ModelЗадание

Bayesian inference in the NDLM: Part I

🎥 Filtering Видео📖 Summary of the Filtering DistributionsЧтение🎥 Filtering in the NDLM: Example Видео💻 R Code: Filtering in the NDLM: Example Чтение🎥 Smoothing and Forecasting Видео📖 Summary of the Smoothing and Forecasting DistributionsЧтение

Testing branch

✍️ NDLM, Part I: Review Задание
04Week 4: Normal dynamic linear models, Part II14 материалов

Seasonal NDLMs

🎥 Fourier RepresentationВидео📖 Fourier Representation: Example 1Чтение🎥 Building NDLMs with Multiple Components: ExamplesВидео📖 Summary: DLM Fourier Representation Чтение✍️ Seasonal Models and SuperpositionЗадание

Bayesian inference in the NDLM: Part II

🎥 Filtering, Smoothing and Forecasting: Unknown Observational VarianceВидео📖 Summary of Filtering, Smoothing and Forecasting Distributions, NDLM Unknown Observational Variance Чтение🎥 Specifying the System Covariance Matrix via Discount FactorsВидео🎥 NDLM, Unknown Observational Variance: ExampleВидео💻 R Code: NDLM, Unknown Observational Variance Example Чтение✍️ NDLM Data AnalysisЗадание

Case studies

🎥 EEG Data Видео🎥 Google TrendsВидео

Testing branch

✍️ NDLM, Part IIЗадание
05Week 5: Final Project1 материалов

Data Analysis Project

✍️ Data Analysis ProjectЗадание
🎥 Spectral Representation of the AR(p)Видео
🎥 Spectral Representation of the AR(p): Example Видео
💻 R Code: Spectral Density of AR(p) Чтение
✍️ Spectral Representation of the AR(p)Задание
✍️ Exercise: Bayesian analysis of an EEG dataset using an AR(p) Задание
📖 ARIMA processesЧтение
🎥 Smoothing in the NDLM: ExampleВидео
💻 R Code: Smoothing in the NDLM, ExampleЧтение
🎥 Second Order Polynomial: Filtering and Smoothing ExampleВидео
🎥 Using the DLM Package in R Видео
💻 R Code: Using the DLM Package in RЧтение
✍️ NDLM: Sensitivity to the Model ParametersЗадание