ONLINE COURSE – Introduction / Fundamentals of Bayesian Data Analysis statistics using R (FBDA01)

Wednesday 19th – Classes from 12:00 to 20:00

Topic 1: We will begin with a overview of what Bayesian data analysis is in essence and how it fits into statistics as it practiced generally. Our main point here will be that Bayesian data analysis is effectively an alternativeV school of statistics to the traditional approach, which is referred to variously as the classical, or sampling theory based, or frequentist based approach, rather than being a specialized or advanced statistics topic. However, there is no real necessity to see these two general approaches as being mutually exclusive and in direct competition, and a pragmatic blend of both approaches is entirely possible.

Topic 2: Introducing Bayes’ rule. Bayes’ rule can be described as a means to calculate the probability of causes
from some known effects. As such, it can be used as a means for performing statistical inference. In this section
of the course, we will work through some simple and intuitive calculations using Bayes’ rule. Ultimately, all of
Bayesian data analysis is based on an application of these methods to more complex statistical models, and so
understanding these simple cases of the application of Bayes’ rule can help provide a foundation for the more
complex cases.

Topic 3: Bayesian inference in a simple statistical model. In this section, we will work through a classic statistical inference problem, namely inferring the number of red marbles in an urn of red and black marbles, or equivalent problems. This problem is easy to analyse completely with just the use of R, but yet allows us to delve into all the key concepts of all Bayesian statistics including the likelihood function, prior distributions, posterior distributions, maximum a posteriori estimation, high posterior density intervals, posterior predictive intervals, marginal likelihoods, Bayes factors, model evaluation of out-of-sample generalization.

Thursday 20th – Classes from 12:00 to 20:00

Topic 1: We will begin with a overview of what Bayesian data analysis is in essence and how it fits into statistics as it practiced generally. Our main point here will be that Bayesian data analysis is effectively an alternative school of statistics to the traditional approach, which is referred to variously as the classical, or sampling theory based, or frequentist based approach, rather than being a specialized or advanced statistics topic. However, there is no real necessity to see these two general approaches as being mutually exclusive and in direct competition, and a pragmatic blend of both approaches is entirely possible.

Topic 2: Introducing Bayes’ rule. Bayes’ rule can be described as a means to calculate the probability of causes
from some known effects. As such, it can be used as a means for performing statistical inference. In this section
of the course, we will work through some simple and intuitive calculations using Bayes’ rule. Ultimately, all of
Bayesian data analysis is based on an application of these methods to more complex statistical models, and so
understanding these simple cases of the application of Bayes’ rule can help provide a foundation for the more
complex cases.

Topic 3: Bayesian inference in a simple statistical model. In this section, we will work through a classic statistical inference problem, namely inferring the number of red marbles in an urn of red and black marbles, or equivalent problems. This problem is easy to analyse completely with just the use of R, but yet allows us to delve into all the key concepts of all Bayesian statistics including the likelihood function, prior distributions, posterior Distributions, maximum a posteriori estimation, high posterior density intervals, posterior predictive intervals, marginal likelihoods, Bayes factors, model evaluation of out-of-sample generalization.