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.
教学大纲 - 您将从这门课程中学到什么
周
1完成时间为 3 小时
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 个视频 （总计 38 分钟）, 4 个阅读材料, 5 个测验
8 个视频
Lesson 1.1 Classical and frequentist probability6分钟
Lesson 1.2 Bayesian probability and coherence3分钟
Lesson 2.1 Conditional probability4分钟
Lesson 2.2 Bayes' theorem6分钟
Lesson 3.1 Bernoulli and binomial distributions5分钟
Lesson 3.2 Uniform distribution5分钟
Lesson 3.3 Exponential and normal distributions2分钟
4 个阅读材料
Module 1 objectives, assignments, and supplementary materials3分钟
Background for Lesson 110分钟
Supplementary material for Lesson 23分钟
Supplementary material for Lesson 320分钟
5 个练习
Lesson 116分钟
Lesson 212分钟
Lesson 3.120分钟
Lesson 3.2-3.310分钟
Module 1 Honors15分钟
周
2完成时间为 3 小时
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 个视频 （总计 59 分钟）, 5 个阅读材料, 4 个测验
11 个视频
Lesson 4.2 Likelihood function and maximum likelihood7分钟
Lesson 4.3 Computing the MLE3分钟
Lesson 4.4 Computing the MLE: examples4分钟
Introduction to R6分钟
Plotting the likelihood in R4分钟
Plotting the likelihood in Excel4分钟
Lesson 5.1 Inference example: frequentist4分钟
Lesson 5.2 Inference example: Bayesian6分钟
Lesson 5.3 Continuous version of Bayes' theorem4分钟
Lesson 5.4 Posterior intervals7分钟
5 个阅读材料
Module 2 objectives, assignments, and supplementary materials3分钟
Background for Lesson 410分钟
Supplementary material for Lesson 45分钟
Background for Lesson 510分钟
Supplementary material for Lesson 510分钟
4 个练习
Lesson 48分钟
Lesson 5.1-5.218分钟
Lesson 5.3-5.416分钟
Module 2 Honors6分钟
周
3完成时间为 2 小时
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 个视频 （总计 66 分钟）, 2 个阅读材料, 4 个测验
9 个视频
Lesson 6.2 Prior predictive: binomial example5分钟
Lesson 6.3 Posterior predictive distribution4分钟
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3分钟
Lesson 7.2 Conjugate priors4分钟
Lesson 7.3 Posterior mean and effective sample size7分钟
Data analysis example in R12分钟
Data analysis example in Excel16分钟
Lesson 8.1 Poisson data8分钟
2 个阅读材料
Module 3 objectives, assignments, and supplementary materials3分钟
R and Excel code from example analysis10分钟
4 个练习
Lesson 612分钟
Lesson 715分钟
Lesson 815分钟
Module 3 Honors8分钟
周
4完成时间为 3 小时
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 个视频 （总计 69 分钟）, 5 个阅读材料, 5 个测验
9 个视频
Lesson 10.1 Normal likelihood with variance known3分钟
Lesson 10.2 Normal likelihood with variance unknown3分钟
Lesson 11.1 Non-informative priors8分钟
Lesson 11.2 Jeffreys prior3分钟
Linear regression in R17分钟
Linear regression in Excel (Analysis ToolPak)13分钟
Linear regression in Excel (StatPlus by AnalystSoft)14分钟
Conclusion1分钟
5 个阅读材料
Module 4 objectives, assignments, and supplementary materials3分钟
Supplementary material for Lesson 1010分钟
Supplementary material for Lesson 115分钟
Background for Lesson 1210分钟
R and Excel code for regression5分钟
5 个练习
Lesson 912分钟
Lesson 1020分钟
Lesson 1110分钟
Regression15分钟
Module 4 Honors6分钟
4.6
388 个审阅27%
完成这些课程后已开始新的职业生涯
18%
通过此课程获得实实在在的工作福利
热门审阅
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.
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.
讲师
Herbert Lee
ProfessorApplied Mathematics and Statistics
关于 加州大学圣克鲁兹分校
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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