Bayesian Statistics

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.

This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, which introduces Bayesian methods through use of simple conjugate models. Real-world data often require more sophisticated models to reach realistic conclusions. This course aims to expand our “Bayesian toolbox” with more general models, and computational techniques to fit them. In particular, we will introduce Markov chain Monte Carlo (MCMC) methods, which allow sampling from posterior distributions that have no analytical solution. We will use the open-source, freely available software R (some experience is assumed, e.g., completing the previous course in R) and JAGS (no experience required). We will learn how to construct, fit, assess, and compare Bayesian statistical models to answer scientific questions involving continuous, binary, and count data. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. The lectures provide some of the basic mathematical development, explanations of the statistical modeling process, and a few basic modeling techniques commonly used by statisticians. Computer demonstrations provide concrete, practical walkthroughs. Completion of this course will give you access to a wide range of Bayesian analytical tools, customizable to your data.

Bayesian Statistics: Mixture Models introduces you to an important class of statistical models. The course is organized in five modules, each of which contains lecture videos, short quizzes, background reading, discussion prompts, and one or more peer-reviewed assignments. Statistics is best learned by doing it, not just watching a video, so the course is structured to help you learn through application. Some exercises require the use of R, a freely-available statistical software package. A brief tutorial is provided, but we encourage you to take advantage of the many other resources online for learning R if you are interested. This is an intermediate-level course, and it was designed to be the third in UC Santa Cruz's series on Bayesian statistics, after Herbie Lee's "Bayesian Statistics: From Concept to Data Analysis" and Matthew Heiner's "Bayesian Statistics: Techniques and Models." To succeed in the course, you should have some knowledge of and comfort with calculus-based probability, principles of maximum-likelihood estimation, and Bayesian estimation.

This course for practicing and aspiring data scientists and statisticians. It is the fourth of a four-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, Techniques and Models, and Mixture models. Time series analysis is concerned with modeling the dependency among elements of a sequence of temporally related variables. To succeed in this course, you should be familiar with calculus-based probability, the principles of maximum likelihood estimation, and Bayesian inference. You will learn how to build models that can describe temporal dependencies and how to perform Bayesian inference and forecasting for the models. You will apply what you've learned with the open-source, freely available software R with sample databases. Your instructor Raquel Prado will take you from basic concepts for modeling temporally dependent data to implementation of specific classes of models