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
от партнера
University of California, Santa Cruz
Об этом курсе
4.6
Оценки: 1,305
Приобретаемые навыки
StatisticsBayesian StatisticsBayesian InferenceR Programming
Программа курса: что вы изучите
Неделя
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 videos (Total 38 min), 4 материалов для самостоятельного изучения, 5 тестов
8 видео
Lesson 1.1 Classical and frequentist probability6мин
Lesson 1.2 Bayesian probability and coherence3мин
Lesson 2.1 Conditional probability4мин
Lesson 2.2 Bayes' theorem6мин
Lesson 3.1 Bernoulli and binomial distributions5мин
Lesson 3.2 Uniform distribution5мин
Lesson 3.3 Exponential and normal distributions2мин
4 материала для самостоятельного изучения
Module 1 objectives, assignments, and supplementary materials3мин
Background for Lesson 110мин
Supplementary material for Lesson 23мин
Supplementary material for Lesson 320мин
5 практического упражнения
Lesson 116мин
Lesson 212мин
Lesson 3.120мин
Lesson 3.2-3.310мин
Module 1 Honors15мин
Неделя
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 videos (Total 59 min), 5 материалов для самостоятельного изучения, 4 тестов
11 видео
Lesson 4.2 Likelihood function and maximum likelihood7мин
Lesson 4.3 Computing the MLE3мин
Lesson 4.4 Computing the MLE: examples4мин
Introduction to R6мин
Plotting the likelihood in R4мин
Plotting the likelihood in Excel4мин
Lesson 5.1 Inference example: frequentist4мин
Lesson 5.2 Inference example: Bayesian6мин
Lesson 5.3 Continuous version of Bayes' theorem4мин
Lesson 5.4 Posterior intervals7мин
5 материала для самостоятельного изучения
Module 2 objectives, assignments, and supplementary materials3мин
Background for Lesson 410мин
Supplementary material for Lesson 45мин
Background for Lesson 510мин
Supplementary material for Lesson 510мин
4 практического упражнения
Lesson 48мин
Lesson 5.1-5.218мин
Lesson 5.3-5.416мин
Module 2 Honors6мин
Неделя
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 videos (Total 66 min), 2 материалов для самостоятельного изучения, 4 тестов
9 видео
Lesson 6.2 Prior predictive: binomial example5мин
Lesson 6.3 Posterior predictive distribution4мин
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3мин
Lesson 7.2 Conjugate priors4мин
Lesson 7.3 Posterior mean and effective sample size7мин
Data analysis example in R12мин
Data analysis example in Excel16мин
Lesson 8.1 Poisson data8мин
2 материала для самостоятельного изучения
Module 3 objectives, assignments, and supplementary materials3мин
R and Excel code from example analysis10мин
4 практического упражнения
Lesson 612мин
Lesson 715мин
Lesson 815мин
Module 3 Honors8мин
Неделя
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 videos (Total 69 min), 5 материалов для самостоятельного изучения, 5 тестов
9 видео
Lesson 10.1 Normal likelihood with variance known3мин
Lesson 10.2 Normal likelihood with variance unknown3мин
Lesson 11.1 Non-informative priors8мин
Lesson 11.2 Jeffreys prior3мин
Linear regression in R17мин
Linear regression in Excel (Analysis ToolPak)13мин
Linear regression in Excel (StatPlus by AnalystSoft)14мин
Conclusion1мин
5 материала для самостоятельного изучения
Module 4 objectives, assignments, and supplementary materials3мин
Supplementary material for Lesson 1010мин
Supplementary material for Lesson 115мин
Background for Lesson 1210мин
R and Excel code for regression5мин
5 практического упражнения
Lesson 912мин
Lesson 1020мин
Lesson 1110мин
Regression15мин
Module 4 Honors6мин
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Лучшие рецензии
автор: 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.
автор: 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.
Преподавателя
Herbert Lee
ProfessorApplied Mathematics and Statistics
О 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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