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.
Bayesian Statistics: From Concept to Data Analysis
proposé par
University of California, Santa Cruz
À propos de ce cours
4.6
1,310 notes
Compétences que vous acquerrez
StatisticsBayesian StatisticsBayesian InferenceR Programming
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Probability 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 vidéos (Total 38 min), 4 lectures, 5 quiz
8 vidéos
Course introduction4 min
Lesson 1.1 Classical and frequentist probability6 min
Lesson 1.2 Bayesian probability and coherence3 min
Lesson 2.1 Conditional probability4 min
Lesson 2.2 Bayes' theorem6 min
Lesson 3.1 Bernoulli and binomial distributions5 min
Lesson 3.2 Uniform distribution5 min
Lesson 3.3 Exponential and normal distributions2 min
4 lectures
Module 1 objectives, assignments, and supplementary materials3 min
Background for Lesson 110 min
Supplementary material for Lesson 23 min
Supplementary material for Lesson 320 min
5 exercices pour s'entraîner
Lesson 116 min
Lesson 212 min
Lesson 3.120 min
Lesson 3.2-3.310 min
Module 1 Honors15 min
Semaine
2Statistical 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 vidéos (Total 59 min), 5 lectures, 4 quiz
11 vidéos
Lesson 4.2 Likelihood function and maximum likelihood7 min
Lesson 4.3 Computing the MLE3 min
Lesson 4.4 Computing the MLE: examples4 min
Introduction to R6 min
Plotting the likelihood in R4 min
Plotting the likelihood in Excel4 min
Lesson 5.1 Inference example: frequentist4 min
Lesson 5.2 Inference example: Bayesian6 min
Lesson 5.3 Continuous version of Bayes' theorem4 min
Lesson 5.4 Posterior intervals7 min
5 lectures
Module 2 objectives, assignments, and supplementary materials3 min
Background for Lesson 410 min
Supplementary material for Lesson 45 min
Background for Lesson 510 min
Supplementary material for Lesson 510 min
4 exercices pour s'entraîner
Lesson 48 min
Lesson 5.1-5.218 min
Lesson 5.3-5.416 min
Module 2 Honors6 min
Semaine
3Priors 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 vidéos (Total 66 min), 2 lectures, 4 quiz
9 vidéos
Lesson 6.2 Prior predictive: binomial example5 min
Lesson 6.3 Posterior predictive distribution4 min
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3 min
Lesson 7.2 Conjugate priors4 min
Lesson 7.3 Posterior mean and effective sample size7 min
Data analysis example in R12 min
Data analysis example in Excel16 min
Lesson 8.1 Poisson data8 min
2 lectures
Module 3 objectives, assignments, and supplementary materials3 min
R and Excel code from example analysis10 min
4 exercices pour s'entraîner
Lesson 612 min
Lesson 715 min
Lesson 815 min
Module 3 Honors8 min
Semaine
4Models 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 vidéos (Total 69 min), 5 lectures, 5 quiz
9 vidéos
Lesson 10.1 Normal likelihood with variance known3 min
Lesson 10.2 Normal likelihood with variance unknown3 min
Lesson 11.1 Non-informative priors8 min
Lesson 11.2 Jeffreys prior3 min
Linear regression in R17 min
Linear regression in Excel (Analysis ToolPak)13 min
Linear regression in Excel (StatPlus by AnalystSoft)14 min
Conclusion1 min
5 lectures
Module 4 objectives, assignments, and supplementary materials3 min
Supplementary material for Lesson 1010 min
Supplementary material for Lesson 115 min
Background for Lesson 1210 min
R and Excel code for regression5 min
5 exercices pour s'entraîner
Lesson 912 min
Lesson 1020 min
Lesson 1110 min
Regression15 min
Module 4 Honors6 min
4.6
350 avis38%
a commencé une nouvelle carrière après avoir terminé ces cours
21%
a bénéficié d'un avantage concret dans sa carrière grâce à ce cours
Meilleurs avis
par GS•Sep 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.
par JH•Jun 27th 2018
Great course. The content moves at a nice pace and the videos are really good to follow. The Quizzes are also set at a good level. You can't pass this course unless you have understood the material.
Enseignant
Herbert Lee
ProfessorApplied Mathematics and Statistics
À propos de 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.
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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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