Bayesian Statistics: Time Series Analysis

Go to Course: https://www.coursera.org/learn/bayesian-statistics-time-series-analysis

Introduction

**Course Review: Bayesian Statistics: Time Series Analysis on Coursera** **Overview:** The course "Bayesian Statistics: Time Series Analysis" is a meticulous deep dive into the realm of Bayesian statistics, specifically tailored for those involved in data science or statistics. As the final installment of a four-course sequence, it builds upon essential concepts accumulated in previous courses: Bayesian Statistics: From Concept to Data Analysis, Techniques and Models, and Mixture Models. The course focuses primarily on the intricacies of time series analysis, a crucial domain that deals with temporal data modeling and its dependencies. **Target Audience:** This course is designed for practicing and aspiring data scientists and statisticians. A solid understanding of calculus-based probability is a prerequisite, ensuring that participants have the foundational knowledge required to tackle complex statistical concepts and methodologies. **Syllabus Breakdown:** - **Week 1: Introduction to Time Series and the AR(1) Process** The course begins by laying down the groundwork for stationary time series processes. Learners examine the autocorrelation function and delve into the autoregressive process of order one (AR(1)). This week emphasizes parameter estimation through maximum likelihood and Bayesian inference, offering a robust start to the world of time series statistics. - **Week 2: The AR(p) Process** Building on the previous week’s content, this module expands the AR(1) concepts into a more generalized framework with the AR(p) process. Participants will explore maximum likelihood estimation and Bayesian posterior inference for AR(p), enriching their understanding of modeling complex time dependencies. - **Week 3: Normal Dynamic Linear Models, Part I** Here, learners are introduced to Normal Dynamic Linear Models (NDLMs), essential tools for time series analysis. With case studies and examples, the week focuses on model construction via the forecast function and discusses Bayesian techniques for filtering, smoothing, and forecasting, thus equipping students with practical skills for real-world applications. - **Week 4: Normal Dynamic Linear Models, Part II** This continuation of NDLMs digs deeper into advanced concepts and applications, solidifying the learner's command over these powerful models and their adaptability to various data scenarios. - **Week 5: Final Project** The culmination of the course is a hands-on final project that requires participants to apply their newly acquired skills on a time series dataset sourced from Google Trends. This practical task empowers students to put theory into practice and demonstrates their proficiency in Bayesian time series analysis. **Course Review:** The "Bayesian Statistics: Time Series Analysis" course is excellently structured, allowing learners to progressively build their knowledge. The clarity of presentation, combined with engaging instructional materials, enhances understanding and retention. In-depth discussions and practical examples ensure that abstract concepts are grounded in real-world contexts, making the course not just theoretical but highly applicable. Moreover, the final project is a highlight, as it compels participants to engage with authentic data and challenges them to think critically about their analysis. Learning outcomes are clearly defined, and feedback provided by instructors contributes to a supportive educational environment. **Recommendation:** I highly recommend the "Bayesian Statistics: Time Series Analysis" course to anyone eager to deepen their understanding of time series modeling through the lens of Bayesian statistics. Whether you are an aspiring data scientist looking to bolster your skill set or a seasoned statistician seeking to refine your knowledge of time-dependent variables, this course provides invaluable insights and practical experience. The structured syllabus, combined with expert instruction, ensures that participants leave with a comprehensive understanding and the confidence to apply Bayesian techniques to real-world data problems. In conclusion, if you're serious about advancing your data science journey, this course is undoubtedly a worthwhile investment.

Syllabus

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

This module defines stationary time series processes, the autocorrelation function and the autoregressive process of order one or AR(1). Parameter estimation via maximum likelihood and Bayesian inference in the AR(1) are also discussed.

This module extends the concepts learned in Week 1 about the AR(1) process to the general case of the AR(p). Maximum likelihood estimation and Bayesian posterior inference in the AR(p) are discussed.

Normal Dynamic Linear Models (NDLMs) are defined and illustrated in this module using several examples. Model building based on the forecast function via the superposition principle is explained. Methods for Bayesian filtering, smoothing and forecasting for NDLMs in the case of known observational variances and known system covariance matrices are discussed and illustrated.

In this final project you will use normal dynamic linear models to analyze a time series dataset downloaded from Google trend.