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
oferecido por
Universidade da Califórnia, Santa Cruz
Informações sobre o curso
4.6
1,472 classificações
Habilidades que você terá
StatisticsBayesian StatisticsBayesian InferenceR Programming
Programa - O que você aprenderá com este curso
Semana
13 horas para concluir
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 vídeos (total de (Total 38 mín.) min), 4 leituras, 5 testes
8 videos
Lesson 1.1 Classical and frequentist probability6min
Lesson 1.2 Bayesian probability and coherence3min
Lesson 2.1 Conditional probability4min
Lesson 2.2 Bayes' theorem6min
Lesson 3.1 Bernoulli and binomial distributions5min
Lesson 3.2 Uniform distribution5min
Lesson 3.3 Exponential and normal distributions2min
4 leituras
Module 1 objectives, assignments, and supplementary materials3min
Background for Lesson 110min
Supplementary material for Lesson 23min
Supplementary material for Lesson 320min
5 exercícios práticos
Lesson 116min
Lesson 212min
Lesson 3.120min
Lesson 3.2-3.310min
Module 1 Honors15min
Semana
23 horas para concluir
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 vídeos (total de (Total 59 mín.) min), 5 leituras, 4 testes
11 videos
Lesson 4.2 Likelihood function and maximum likelihood7min
Lesson 4.3 Computing the MLE3min
Lesson 4.4 Computing the MLE: examples4min
Introduction to R6min
Plotting the likelihood in R4min
Plotting the likelihood in Excel4min
Lesson 5.1 Inference example: frequentist4min
Lesson 5.2 Inference example: Bayesian6min
Lesson 5.3 Continuous version of Bayes' theorem4min
Lesson 5.4 Posterior intervals7min
5 leituras
Module 2 objectives, assignments, and supplementary materials3min
Background for Lesson 410min
Supplementary material for Lesson 45min
Background for Lesson 510min
Supplementary material for Lesson 510min
4 exercícios práticos
Lesson 48min
Lesson 5.1-5.218min
Lesson 5.3-5.416min
Module 2 Honors6min
Semana
32 horas para concluir
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 vídeos (total de (Total 66 mín.) min), 2 leituras, 4 testes
9 videos
Lesson 6.2 Prior predictive: binomial example5min
Lesson 6.3 Posterior predictive distribution4min
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3min
Lesson 7.2 Conjugate priors4min
Lesson 7.3 Posterior mean and effective sample size7min
Data analysis example in R12min
Data analysis example in Excel16min
Lesson 8.1 Poisson data8min
2 leituras
Module 3 objectives, assignments, and supplementary materials3min
R and Excel code from example analysis10min
4 exercícios práticos
Lesson 612min
Lesson 715min
Lesson 815min
Module 3 Honors8min
Semana
43 horas para concluir
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 vídeos (total de (Total 69 mín.) min), 5 leituras, 5 testes
9 videos
Lesson 10.1 Normal likelihood with variance known3min
Lesson 10.2 Normal likelihood with variance unknown3min
Lesson 11.1 Non-informative priors8min
Lesson 11.2 Jeffreys prior3min
Linear regression in R17min
Linear regression in Excel (Analysis ToolPak)13min
Linear regression in Excel (StatPlus by AnalystSoft)14min
Conclusion1min
5 leituras
Module 4 objectives, assignments, and supplementary materials3min
Supplementary material for Lesson 1010min
Supplementary material for Lesson 115min
Background for Lesson 1210min
R and Excel code for regression5min
5 exercícios práticos
Lesson 912min
Lesson 1020min
Lesson 1110min
Regression15min
Module 4 Honors6min
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Melhores avaliações
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.
Instrutores
Herbert Lee
ProfessorApplied Mathematics and Statistics
Sobre Universidade da Califórnia, 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.
Perguntas Frequentes – FAQ
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Ao se inscrever para um Certificado, você terá acesso a todos os vídeos, testes e tarefas de programação (se aplicável). Tarefas avaliadas pelos colegas apenas podem ser enviadas e avaliadas após o início da sessão. Caso escolha explorar o curso sem adquiri-lo, talvez você não consiga acessar certas tarefas.
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Qual é a política de reembolso?
Existe algum auxílio financeiro disponível?
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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