UCSC - Bayesian Statistics: Time Series Analysis
- Offered byCoursera
Bayesian Statistics: Time Series Analysis at Coursera Overview
Duration | 22 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
Bayesian Statistics: Time Series Analysis at Coursera Highlights
- Flexible deadlines in accordance to your schedule.
- Earn a Certificate upon completion
Bayesian Statistics: Time Series Analysis at Coursera Course details
- 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
Bayesian Statistics: Time Series Analysis at Coursera Curriculum
Week 1: Introduction to time series and the AR(1) process
Welcome to Bayesian Statistics: Time Series
Stationarity
The autocorrelation function (ACF)
ACF, PACF, Differencing and Smoothing: Examples
The AR(1)
Simulating from an AR(1) process
Maximum likelihood estimation in the AR(1)
Bayesian inference in the AR(1)
Bayesian inference in the AR(1): Conditional likelihood example
Introduction to R
List of References
The partial autocorrelation function (PACF)
Differencing and Smoothing
R Code: Differencing and filtering via moving averages
R Code: Simulate data from a white noise process
The PACF of the AR(1) process
R Code: Sample data from AR(1) processes
Review of maximum likelihood and Bayesian inference in regression
R code: MLE for the AR(1), examples
R Code: AR(1) Bayesian inference, conditional likelihood example
Bayesian inference in the AR(1), full likelihood example
Objectives of the course
Stationarity, the ACF and the PACF
The AR(1) definitions and properties
MLE and Bayesian inference in the AR(1)
Week 2: The AR(p) process
Definition and state-space representation
Examples
ACF of the AR(p)
Simulating data from an AR(p)
Bayesian inference in the AR(p): Reference prior, conditional likelihood
Model order selection
Example: Bayesian inference in the AR(p), conditional likelihood
Spectral representation of the AR(p)
Spectral representation of the AR(p): Example
Rcode: Computing the roots of the AR polynomial
Rcode: Simulating data from an AR(p)
The AR(p): Review
Rcode: Maximum likelihood estimation, AR(p), conditional likelihood
Rcode: Bayesian inference, AR(p), conditional likelihood
Rcode: Model order selection
Rcode: Spectral density of AR(p)
ARIMA processes
Properties of AR processes
Spectral representation of the AR(p)
Week 3: Normal dynamic linear models, Part I
NDLM: Definition
Polynomial trend models
Regression models
The superposition principle
Filtering
Filtering in the NDLM: Example
Smoothing and forecasting
Smoothing in the NDLM: Example
Second order polynomial: Filtering and smoothing example
Using the dlm package in R
Summary of polynomial trend and regression models
Superposition principle: General case
Summary of the filtering distributions
Rcode. Filtering in the NDLM: Example
Summary of the smoothing and forecasting distributions
Rcode: Smoothing in the NDLM, Example
Rcode: Using the dlm package in R
The Normal Dynamic Linear Model
NDLM, Part I: Review
Week 4: Normal dynamic linear models, Part II
Fourier representation
Building NDLMs with multiple components: Examples
Filtering, Smoothing and Forecasting: Unknown observational variance
Specifying the system covariance matrix via discount factors
NDLM, Unknown Observational Variance: Example
EEG data
Google trends
Fourier Representation: Example 1
Summary: DLM Fourier representation
Summary of Filtering, Smoothing and Forecasting Distributions, NDLM unknown observational variance
Rcode: NDLM, Unknown Observational Variance Example
Seasonal Models and Superposition
NDLM, Part II
Week 5: Final Project
Bayesian Statistics: Time Series Analysis at Coursera Admission Process
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