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1,439 個評分
388 個審閱

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中級

完成時間大約為21 小時

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

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StatisticsBayesian StatisticsBayesian InferenceR Programming

100% 在線

立即開始,按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

中級

完成時間大約為21 小時

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

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
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....
8 個視頻 (總計 38 分鐘), 4 個閱讀材料, 5 個測驗
8 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
4 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
5 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
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....
11 個視頻 (總計 59 分鐘), 5 個閱讀材料, 4 個測驗
11 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
5 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
4 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
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....
9 個視頻 (總計 66 分鐘), 2 個閱讀材料, 4 個測驗
9 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
2 個閱讀材料
Module 3 objectives, assignments, and supplementary materials3分鐘
R and Excel code from example analysis10分鐘
4 個練習
Lesson 612分鐘
Lesson 715分鐘
Lesson 815分鐘
Module 3 Honors8分鐘
4
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. ...
9 個視頻 (總計 69 分鐘), 5 個閱讀材料, 5 個測驗
9 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
5 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
5 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
388 個審閱Chevron Right

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完成這些課程後已開始新的職業生涯

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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

Avatar

Herbert Lee

Professor
Applied Mathematics and Statistics

關於 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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  • 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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