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.
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Intermediate Level

Niveau intermédiaire

Clock

Approx. 20 hours to complete

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

English

Sous-titres : English

Compétences que vous acquerrez

Bayesian InferenceR ProgrammingStatisticsBayesian
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Intermediate Level

Niveau intermédiaire

Clock

Approx. 20 hours to complete

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

English

Sous-titres : English

Syllabus - What you will learn from this course

1

Section
Clock
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....
Reading
8 videos (Total 38 min), 4 readings, 5 quizzes
Video8 videos
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
Reading4 readings
Module 1 objectives, assignments, and supplementary materials3m
Background for Lesson 110m
Supplementary material for Lesson 23m
Supplementary material for Lesson 320m
Quiz5 practice exercises
Lesson 116m
Lesson 212m
Lesson 3.120m
Lesson 3.2-3.310m
Module 1 Honors15m

2

Section
Clock
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....
Reading
11 videos (Total 59 min), 5 readings, 4 quizzes
Video11 videos
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
Reading5 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
Quiz4 practice exercises
Lesson 48m
Lesson 5.1-5.218m
Lesson 5.3-5.416m
Module 2 Honors6m

3

Section
Clock
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....
Reading
9 videos (Total 66 min), 2 readings, 4 quizzes
Video9 videos
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
Reading2 readings
Module 3 objectives, assignments, and supplementary materials3m
R and Excel code from example analysis10m
Quiz4 practice exercises
Lesson 612m
Lesson 715m
Lesson 815m
Module 3 Honors8m

4

Section
Clock
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. ...
Reading
9 videos (Total 69 min), 5 readings, 5 quizzes
Video9 videos
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
Reading5 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
Quiz5 practice exercises
Lesson 912m
Lesson 1020m
Lesson 1110m
Regression15m
Module 4 Honors6m
4.6
Direction Signs

38%

started a new career after completing these courses
Briefcase

83%

got a tangible career benefit from this course

Top Reviews

By GSSep 1st 2017

Good intro to Bayesian Statistics. Covers the basic concepts. Workload is reasonable and quizzes/exercises are helpful. Could include more exercises and additional backgroung/future reading materials.

By JCNov 7th 2017

I've learned how to process data and analyze data from studies, that's a wonderful ability I think everybody should try to learn in order to not get manipulated by the media. Thanks for this course!

Instructor

Avatar

Herbert Lee

Professor

About University of California, Santa Cruz

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Frequently Asked Questions

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  • 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.

  • 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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