本课程是贝叶斯统计专项课程专项课程的一部分

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Herbert Lee

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贝叶斯统计专项课程加州大学圣克鲁兹分校

课程信息

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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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第 1 门课程（共 5 门）

贝叶斯统计专项课程

中级

完成时间大约为12 小时

英语（English）

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您将获得的技能

Statistics
Bayesian Statistics
Bayesian Inference
R Programming

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根据您的日程表重置截止日期。

可分享的证书

完成后获得证书

100% 在线

立即开始，按照自己的计划学习。

第 1 门课程（共 5 门）

贝叶斯统计专项课程

中级

完成时间大约为12 小时

英语（English）

对员工进行热门技能培训能否为您的公司带来益处？

体验 Coursera 企业版

授课教师

授课教师评分

4.59/5 （438 个评分）

Herbert Lee

提供方

加州大学圣克鲁兹分校

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内容评分91%（10,572 个评分）

周

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.

完成时间为 3 小时

8 个视频（总计 38 分钟）, 4 个阅读材料, 5 个测验

8 个视频

Course introduction4分钟

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 1: Demonstrate your knowledge30分钟

Lesson 2: Demonstrate your knowledge12分钟

Lesson 3.1: Demonstrate your knowledge30分钟

Lesson 3.2-3.3: Demonstrate your knowledge10分钟

Module 1 Honors15分钟

周

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.

完成时间为 3 小时

11 个视频（总计 59 分钟）, 5 个阅读材料, 4 个测验

11 个视频

Lesson 4.1 Confidence intervals4分钟

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 4: Demonstrate your knowledge8分钟

Lesson 5.1-5.2: Demonstrate your knowledge30分钟

Lesson 5.3-5.4: Demonstrate your knowledge30分钟

Module 2 Honors6分钟

周

周 3

完成时间为 3 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.

完成时间为 3 小时

9 个视频（总计 66 分钟）, 2 个阅读材料, 4 个测验

9 个视频

Lesson 6.1 Priors and prior predictive distributions3分钟

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 6: Demonstrate your knowledge30分钟

Lesson 7: Demonstrate your knowledge15分钟

Lesson 8: Demonstrate your knowledge15分钟

Module 3 Honors8分钟

周

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.

完成时间为 3 小时

9 个视频（总计 69 分钟）, 5 个阅读材料, 5 个测验

9 个视频

Lesson 9.1 Exponential data4分钟

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 9: Demonstrate your knowledge12分钟

Lesson 10: Demonstrate your knowledge20分钟

Lesson 11: Demonstrate your knowledge10分钟

Regression: Demonstrate your knowledge15分钟

Module 4 Honors6分钟

审阅

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来自BAYESIAN STATISTICS: FROM CONCEPT TO DATA ANALYSIS的热门评论

由 KB 提供Nov 13, 2020

A very good introduction to Bayesian Statistics.Couple of optional R modules of data analysis could have been introduced . However, prerequisites are essential in order to appreciate the course.

由 SP 提供Nov 21, 2020

Very insightful. I'd recommend this course to anyone who wants to learn how to adjust a model after observing data. Test questions were quite practical modeling real world scenarios.

由 MT 提供Jul 18, 2017

Exceptional course on probabilities and statistics from a Bayesian point of view. I would recommend this course to anyone wishing to learn more about probabilities and statistics.

由 MD 提供Feb 18, 2020

the notes for the lectures are missing.

In my opinion the notes, which includes the video materials could be very useful.

the course was good. I learnt some new concepts in bayesian thinking.

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关于贝叶斯统计专项课程

This Specialization is intended for all learners seeking to develop proficiency in statistics, Bayesian statistics, Bayesian inference, R programming, and much more. Through four complete courses (From Concept to Data Analysis; Techniques and Models; Mixture Models; Time Series Analysis) and a culminating project, you will cover Bayesian methods — such as conjugate models, MCMC, mixture models, and dynamic linear modeling — which will provide you with the skills necessary to perform analysis, engage in forecasting, and create statistical models using real-world data.

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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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Bayesian Statistics: From Concept to Data Analysis

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