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
ofrecido por
Universidad de California en Santa Cruz
Acerca de este Curso
4.6
1,479 calificaciones
Habilidades que obtendrás
StatisticsBayesian StatisticsBayesian InferenceR Programming
Programa - Qué aprenderás en este curso
Semana
13 horas para completar
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 videos (Total 38 minutos), 4 readings, 5 quizzes
8 videos
Lesson 1.1 Classical and frequentist probability6m
Lesson 1.2 Bayesian probability and coherence3m
Lesson 2.1 Conditional probability4m
Lesson 2.2 Bayes' theorem6m
Lesson 3.1 Bernoulli and binomial distributions5m
Lesson 3.2 Uniform distribution5m
Lesson 3.3 Exponential and normal distributions2m
4 lecturas
Module 1 objectives, assignments, and supplementary materials3m
Background for Lesson 110m
Supplementary material for Lesson 23m
Supplementary material for Lesson 320m
5 ejercicios de práctica
Lesson 116m
Lesson 212m
Lesson 3.120m
Lesson 3.2-3.310m
Module 1 Honors15m
Semana
23 horas para completar
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 videos (Total 59 minutos), 5 readings, 4 quizzes
11 videos
Lesson 4.2 Likelihood function and maximum likelihood7m
Lesson 4.3 Computing the MLE3m
Lesson 4.4 Computing the MLE: examples4m
Introduction to R6m
Plotting the likelihood in R4m
Plotting the likelihood in Excel4m
Lesson 5.1 Inference example: frequentist4m
Lesson 5.2 Inference example: Bayesian6m
Lesson 5.3 Continuous version of Bayes' theorem4m
Lesson 5.4 Posterior intervals7m
5 lecturas
Module 2 objectives, assignments, and supplementary materials3m
Background for Lesson 410m
Supplementary material for Lesson 45m
Background for Lesson 510m
Supplementary material for Lesson 510m
4 ejercicios de práctica
Lesson 48m
Lesson 5.1-5.218m
Lesson 5.3-5.416m
Module 2 Honors6m
Semana
32 horas para completar
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 videos (Total 66 minutos), 2 readings, 4 quizzes
9 videos
Lesson 6.2 Prior predictive: binomial example5m
Lesson 6.3 Posterior predictive distribution4m
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3m
Lesson 7.2 Conjugate priors4m
Lesson 7.3 Posterior mean and effective sample size7m
Data analysis example in R12m
Data analysis example in Excel16m
Lesson 8.1 Poisson data8m
2 lecturas
Module 3 objectives, assignments, and supplementary materials3m
R and Excel code from example analysis10m
4 ejercicios de práctica
Lesson 612m
Lesson 715m
Lesson 815m
Module 3 Honors8m
Semana
43 horas para completar
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 videos (Total 69 minutos), 5 readings, 5 quizzes
9 videos
Lesson 10.1 Normal likelihood with variance known3m
Lesson 10.2 Normal likelihood with variance unknown3m
Lesson 11.1 Non-informative priors8m
Lesson 11.2 Jeffreys prior3m
Linear regression in R17m
Linear regression in Excel (Analysis ToolPak)13m
Linear regression in Excel (StatPlus by AnalystSoft)14m
Conclusion1m
5 lecturas
Module 4 objectives, assignments, and supplementary materials3m
Supplementary material for Lesson 1010m
Supplementary material for Lesson 115m
Background for Lesson 1210m
R and Excel code for regression5m
5 ejercicios de práctica
Lesson 912m
Lesson 1020m
Lesson 1110m
Regression15m
Module 4 Honors6m
25%
comenzó una nueva carrera después de completar estos cursos
17%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Principales revisiones
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.
Instructores
Herbert Lee
ProfessorApplied Mathematics and Statistics
Acerca de Universidad de California en 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.
Preguntas Frecuentes
¿Cuándo podré acceder a las lecciones y tareas?
Una vez que te inscribes para obtener un Certificado, tendrás acceso a todos los videos, cuestionarios y tareas de programación (si corresponde). Las tareas calificadas por compañeros solo pueden enviarse y revisarse una vez que haya comenzado tu sesión. Si eliges explorar el curso sin comprarlo, es posible que no puedas acceder a determinadas tareas.
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Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.
¿Cuál es la política de reembolsos?
¿Hay ayuda económica disponible?
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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