Bayesian Statistics: From Concept to Data Analysis

University of California, Santa Cruz

À propos de ce cours

This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Niveau intermédiaire

Approx. 20 hours to complete

Recommandé : Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics.

English

Sous-titres : English

Compétences que vous acquerrez

Bayesian InferenceR ProgrammingStatisticsBayesian

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Niveau intermédiaire

Approx. 20 hours to complete

Recommandé : Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics.

English

Sous-titres : English

Syllabus - What you will learn from this course

1

Section

3 hours to complete

Probability and Bayes' Theorem

In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables....

8 videos (Total 38 min), 4 readings, 5 quizzes

8 videos

Course introduction4m

Lesson 1.1 Classical and frequentist probability6m

Lesson 1.2 Bayesian probability and coherence3m

Lesson 2.1 Conditional probability4m

Lesson 2.2 Bayes' theorem6m

Lesson 3.1 Bernoulli and binomial distributions5m

Lesson 3.2 Uniform distribution5m

Lesson 3.3 Exponential and normal distributions2m

4 readings

Module 1 objectives, assignments, and supplementary materials3m

Background for Lesson 110m

Supplementary material for Lesson 23m

Supplementary material for Lesson 320m

5 practice exercises

Lesson 116m

Lesson 212m

Lesson 3.120m

Lesson 3.2-3.310m

Module 1 Honors15m

2

Section

3 hours to complete

Statistical Inference

This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals....

11 videos (Total 59 min), 5 readings, 4 quizzes

11 videos

Lesson 4.1 Confidence intervals4m

Lesson 4.2 Likelihood function and maximum likelihood7m

Lesson 4.3 Computing the MLE3m

Lesson 4.4 Computing the MLE: examples4m

Introduction to R6m

Plotting the likelihood in R4m

Plotting the likelihood in Excel4m

Lesson 5.1 Inference example: frequentist4m

Lesson 5.2 Inference example: Bayesian6m

Lesson 5.3 Continuous version of Bayes' theorem4m

Lesson 5.4 Posterior intervals7m

5 readings

Module 2 objectives, assignments, and supplementary materials3m

Background for Lesson 410m

Supplementary material for Lesson 45m

Background for Lesson 510m

Supplementary material for Lesson 510m

4 practice exercises

Lesson 48m

Lesson 5.1-5.218m

Lesson 5.3-5.416m

Module 2 Honors6m

3

Section

2 hours to complete

Priors and Models for Discrete Data

In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters....

9 videos (Total 66 min), 2 readings, 4 quizzes

9 videos

Lesson 6.1 Priors and prior predictive distributions3m

Lesson 6.2 Prior predictive: binomial example5m

Lesson 6.3 Posterior predictive distribution4m

Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3m

Lesson 7.2 Conjugate priors4m

Lesson 7.3 Posterior mean and effective sample size7m

Data analysis example in R12m

Data analysis example in Excel16m

Lesson 8.1 Poisson data8m

2 readings

Module 3 objectives, assignments, and supplementary materials3m

R and Excel code from example analysis10m

4 practice exercises

Lesson 612m

Lesson 715m

Lesson 815m

Module 3 Honors8m

4

Section

3 hours to complete

Models for Continuous Data

This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression. ...

9 videos (Total 69 min), 5 readings, 5 quizzes

9 videos

Lesson 9.1 Exponential data4m

Lesson 10.1 Normal likelihood with variance known3m

Lesson 10.2 Normal likelihood with variance unknown3m

Lesson 11.1 Non-informative priors8m

Lesson 11.2 Jeffreys prior3m

Linear regression in R17m

Linear regression in Excel (Analysis ToolPak)13m

Linear regression in Excel (StatPlus by AnalystSoft)14m

Conclusion1m

5 readings

Module 4 objectives, assignments, and supplementary materials3m

Supplementary material for Lesson 1010m

Supplementary material for Lesson 115m

Background for Lesson 1210m

R and Excel code for regression5m

5 practice exercises

Lesson 912m

Lesson 1020m

Lesson 1110m

Regression15m

Module 4 Honors6m

Instructor

Herbert Lee

Professor

About University of California, Santa Cruz

UC Santa Cruz is an outstanding public research university with a deep commitment to undergraduate education. It’s a place that connects people and programs in unexpected ways while providing unparalleled opportunities for students to learn through hands-on experience....

Frequently Asked Questions

When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
What will I get if I pay for this course?
If you pay for this course, you will have access to all of the features and content you need to earn a Course Certificate. If you complete the course successfully, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. Note that the Course Certificate does not represent official academic credit from the partner institution offering the course.
What is the refund policy?
Is financial aid available?
Yes! Coursera provides financial aid to learners who would like to complete a course but cannot afford the course fee. To apply for aid, select "Learn more and apply" in the Financial Aid section below the "Enroll" button. You'll be prompted to complete a simple application; no other paperwork is required.
What are the pre-requisites for this course?
You should have exposure to the concepts from a basic statistics class (for example, probability, the Central Limit Theorem, confidence intervals, linear regression) and calculus (integration and differentiation), but it is not expected that you remember how to do all of these items. The course will provide some overview of the statistical concepts, which should be enough to remind you of the necessary details if you've at least seen the concepts previously. On the calculus side, the lectures will include some use of calculus, so it is important that you understand the concept of an integral as finding the area under a curve, or differentiating to find a maximum, but you will not be required to do any integration or differentiation yourself.
What computing resources are expected for this course?
Data analysis is done using computer software. This course provides the option of Excel or R. Equivalent content is provided for both options. A very brief introduction to R is provided for people who have never used it before, but this is not meant to be a course on R. Learners using Excel are expected to already have basic familiarity of Excel.

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Bayesian Statistics: From Concept to Data Analysis