Bayesian Modelling, Inference, Prediction and Decision-Making

Overview
Bayesian methods offer an approach to inference, prediction and decision-making that allow you to synthesize all relevant sources of information in drawing conclusions and making decisions in the presence of uncertainty: you can bring together information both internal to, and external to, your data set to create a logically consistent summary of all that's known about the problem you're studying.
This course will:

• Compare and contrast the frequentist and Bayesian conceptions of probability, highlighting the strengths and weaknesses of both;
• Review maximum-likelihood fitting of statistical models;
• Show you how to obtain Bayesian solutions to inferential and predictive problems analytically and in closed form (when such solutions are available); and
• Introduce you to simulation-based Bayesian model-fitting using Markov-chain Monte Carlo (MCMC) methods, in the freeware packages WinBUGS and R, when closed-form solutions are not possible.

The course will be based on a series of practical real-world studies.

Who Should Attend?
Statisticians, biostatisticians, epidemiologists, data analysts, data-miners, machine-learning specialists and data scientists who wish to broaden and deepen:

• Their understanding of Bayesian methods and
• Their toolkits for using Bayesian models to find meaningful patterns, arrive at statistically sound inferences and predictions, and make better decisions.

Some graduate coursework in statistics (or an allied field such as biostatistics, epidemiology or machine learning) will provide sufficient mathematical background for participants. To get the most out of the course, participants should be comfortable with hearing the course presenter discuss:
However, all necessary concepts will be approached in a sufficiently intuitive manner that rustiness on these topics will not prevent understanding of the key ideas.

• Differentiation and integration of functions of several variables and
  
• Discrete and continuous probability distributions (joint, marginal, and conditional) for several variables at a time.
  

This course assumes no previous exposure to Bayesian ideas or methods.

How You Will Benefit
You will:

• Gain a deeper understanding of maximum-likelihood-based methods and when they can be expected to behave in a sub-optimal manner;
  
• Broaden and deepen your facility in the fitting and interpretation of Bayesian models to solve important problems in science, public policy and business; and
  
• Learn how to write your own programs in WinBUGS and R to fit Bayesian models in your own work.
  

What Do We Cover?

• Background and basics: strengths and weaknessed of the classical, frequentist and Bayesian probability paradigms
  
• Sequential learning via Bayes' Theorem
  
• Coherence as a form of internal calibration
  
• Bayesian decision theory via maximization of expected utility
  
• Review of frequentist modelling and maximum-likelihood inference
  
• Exchangeability as a Bayesian concept parallel to frequentist independence
  
• Prior, posterior, and predictive distributions
  
• Bayesian conjugate analysis of binary outcomes, and comparison with frequentist modelling
  
• Conjugate analysis of integer-valued outcomes (Poisson modelling)
  
• Conjugate analysis of continuous outcomes (Gaussian modelling)
  
• Multivariate unknowns and marginal posterior distributions
  
• Introduction to simulation-based computation, including rejection sampling and Markov chain Monte Carlo (MCMC) methods
  
• MCMC implementation strategies.
  

Software
Practical work will be done in: A mixture of R and WinBUGS
Note: For practical work, participants must bring their own laptop with fully licensed versions of the chosen software.

Extra Information
Related Courses: This is part of a series of Bayesian Modelling courses, presented by Professor David Draper:

• Bayesian Modelling, Inference, Prediction and Decision-Making (2 days)
  
• Bayesian Hierarchical Modelling (1 day)
  
• Bayesian Model Specification (1 day)
  
• Bayesian Non-Parametric Modelling and Case Studies in Bayesian Data Science (1 day)
  

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Course Dates
Next run to be announced

Duration: 2 days
Price: £TBC
An academic discount is available for this course

Apply Now
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Please note that there will not be any printed notes for this course. Materials for 2017 can be seen on the following links:

• Bayesian Modeling, Inference, Prediction and Decision-Making (external link)
• Bayesian Hierarchical Modeling (external link)
• Bayesian Model Specification (external link)
• Bayesian Non-Parametric Modelling and Case Studies in Bayesian Data Science (external link)

Other Related Courses:

• Practical Bayesian Data Analysis
• Bayesian Analysis Made Easy

Guest Presenter (last updated September 2017): David Draper
David Draper is a Professor of Statistics in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (USA); he has also been a Senior Principal Research Scientist at both eBay Research Labs and at Amazon Research, where he developed new methods for Bayesian analysis of very large data sets in the discipline of data science, and he is currently in a consultative role as Senior Analyst at the social finance company SoFi.
He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), and the Royal Statistical Society (RSS); from 2001 to 2003 he served as the President-Elect, President, and Past President of the International Society for Bayesian Analysis (ISBA).
He is the author or co-author of about 150 contributions to the methodological and applied statistical literature, including articles in the Journal of the Royal Statistical Society (Series A, B and C), the Journal of the American Statistical Association, the Annals of Applied Statistics, Bayesian Analysis, Statistical Science, the New England Journal of Medicine, and the Journal of the American Medical Association; his 1995 JRSS-B article on assessment and propagation of model uncertainty has been cited more than 1,600 times, and taken together his publications have been cited about 14,000 times.
His research is in the areas of Bayesian inference and prediction, model uncertainty and empirical model-building, hierarchical Modelling, Markov Chain Monte Carlo methods, Bayesian nonparametric methods and data science, with applications mainly in medicine, health policy, education, environmental risk assessment and eCommerce.
His short courses have received Excellence in Continuing Education Awards from the American Statistical Association on two occasions, corresponding to days 1 and 2 of this week of courses (20-24 November 2017). He has won or been nominated for major teaching awards everywhere he has taught (the University of Chicago; the RAND Graduate School of Public Policy Studies; the University of California, Los Angeles; the University of Bath (UK); and the University of California, Santa Cruz).
He has a particular interest in the exposition of complex statistical methods and ideas in the context of real-world applications.

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