課程信息
4.6
1,241 ratings
330 reviews
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....
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Intermediate Level

中級

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

完成時間大約為20 小時
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您將獲得的技能

StatisticsBayesian StatisticsBayesian InferenceR Programming
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Intermediate Level

中級

Clock

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

完成時間大約為20 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
完成時間為 3 小時

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 個視頻(共 38 分鐘), 4 個閱讀材料, 5 個測驗
Video8 個視頻
Lesson 1.1 Classical and frequentist probability6分鐘
Lesson 1.2 Bayesian probability and coherence3分鐘
Lesson 2.1 Conditional probability4分鐘
Lesson 2.2 Bayes' theorem6分鐘
Lesson 3.1 Bernoulli and binomial distributions5分鐘
Lesson 3.2 Uniform distribution5分鐘
Lesson 3.3 Exponential and normal distributions2分鐘
Reading4 個閱讀材料
Module 1 objectives, assignments, and supplementary materials3分鐘
Background for Lesson 110分鐘
Supplementary material for Lesson 23分鐘
Supplementary material for Lesson 320分鐘
Quiz5 個練習
Lesson 116分鐘
Lesson 212分鐘
Lesson 3.120分鐘
Lesson 3.2-3.310分鐘
Module 1 Honors15分鐘

2

章節
Clock
完成時間為 3 小時

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 個視頻(共 59 分鐘), 5 個閱讀材料, 4 個測驗
Video11 個視頻
Lesson 4.2 Likelihood function and maximum likelihood7分鐘
Lesson 4.3 Computing the MLE3分鐘
Lesson 4.4 Computing the MLE: examples4分鐘
Introduction to R6分鐘
Plotting the likelihood in R4分鐘
Plotting the likelihood in Excel4分鐘
Lesson 5.1 Inference example: frequentist4分鐘
Lesson 5.2 Inference example: Bayesian6分鐘
Lesson 5.3 Continuous version of Bayes' theorem4分鐘
Lesson 5.4 Posterior intervals7分鐘
Reading5 個閱讀材料
Module 2 objectives, assignments, and supplementary materials3分鐘
Background for Lesson 410分鐘
Supplementary material for Lesson 45分鐘
Background for Lesson 510分鐘
Supplementary material for Lesson 510分鐘
Quiz4 個練習
Lesson 48分鐘
Lesson 5.1-5.218分鐘
Lesson 5.3-5.416分鐘
Module 2 Honors6分鐘

3

章節
Clock
完成時間為 2 小時

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 個視頻(共 66 分鐘), 2 個閱讀材料, 4 個測驗
Video9 個視頻
Lesson 6.2 Prior predictive: binomial example5分鐘
Lesson 6.3 Posterior predictive distribution4分鐘
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3分鐘
Lesson 7.2 Conjugate priors4分鐘
Lesson 7.3 Posterior mean and effective sample size7分鐘
Data analysis example in R12分鐘
Data analysis example in Excel16分鐘
Lesson 8.1 Poisson data8分鐘
Reading2 個閱讀材料
Module 3 objectives, assignments, and supplementary materials3分鐘
R and Excel code from example analysis10分鐘
Quiz4 個練習
Lesson 612分鐘
Lesson 715分鐘
Lesson 815分鐘
Module 3 Honors8分鐘

4

章節
Clock
完成時間為 3 小時

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 個視頻(共 69 分鐘), 5 個閱讀材料, 5 個測驗
Video9 個視頻
Lesson 10.1 Normal likelihood with variance known3分鐘
Lesson 10.2 Normal likelihood with variance unknown3分鐘
Lesson 11.1 Non-informative priors8分鐘
Lesson 11.2 Jeffreys prior3分鐘
Linear regression in R17分鐘
Linear regression in Excel (Analysis ToolPak)13分鐘
Linear regression in Excel (StatPlus by AnalystSoft)14分鐘
Conclusion1分鐘
Reading5 個閱讀材料
Module 4 objectives, assignments, and supplementary materials3分鐘
Supplementary material for Lesson 1010分鐘
Supplementary material for Lesson 115分鐘
Background for Lesson 1210分鐘
R and Excel code for regression5分鐘
Quiz5 個練習
Lesson 912分鐘
Lesson 1020分鐘
Lesson 1110分鐘
Regression15分鐘
Module 4 Honors6分鐘
4.6
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38%

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Briefcase

83%

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創建者 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.

創建者 JHJun 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.

講師

Herbert Lee

Professor
Applied Mathematics and Statistics

關於 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....

常見問題

  • 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.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

  • 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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