The next Bayes Days has not yet been scheduled, but will occur in late 2018 or early 2019. You can add yourself to the email list for announcements about it by sending a request by email to

### Tutorials

### Prior knowledge, proportions and probabilities of probabilities

#### Alejandro Diaz, Institute for Risk and Uncertainty, University of Liverpool, UK

Which proportion is higher: 5 out of a 10 or 400 out of 1000? The answer seems obvious. But if these proportions were number of successes divided by number of trials, would you still think the same? Is a baseball player who achieved 5 hits out of 10 chances throughout his career, better than one who achieved 400 hits out of 1000 chances? In this introductory tutorial, we will see how Bayesian inference helps us add context in order to make decisions. The key will reside on representing prior knowledge using a probability distribution for probabilities: the very famous and elegant beta distribution.### Bayesian linear regression and hierarchical models

#### Alfredo Garbuno, Institute for Risk and Uncertainty, University of Liverpool, UK

Bayesian data analysis allows researchers to conduct probabilistic inference about non-observable quantities in a statistical model. This introductory workshop is aimed at those interested in applying the Bayesian paradigm in their data analysis tasks.The tutorial will start with Bayesian linear regression models, and will provide guidelines for probabilistic enhancement to the model's complexity. This improvement will lead to the hierarchical regression model in which the Bayesian paradigm allows for a more flexible model, whilst providing a natural mechanism to prevent over-fitting. The session will present a classical Bayesian regression problem which can be followed through Python notebooks.

### Quantifying uncertainty using data and experts

#### Ullrika Sahlin,Centre for Environmental and Climate Research, Lund University, SE

This tutorial introduces some of the basic principles to quantify uncertainty by Bayesian probability. I will demonstrate a way to quantify uncertainty by integrating expert’s knowledge and data. Participants can follow practical examples in R, using existing R packages for expert’s elicitation (SHELF) and sampling from the posterior (rjags requiring JAGS). The first example is a simple risk classification problem under sparse information and several experts with differing judgements. The second example is the familiar task to quantify uncertainty in input parameters of an assessment model using different sources of information and where uncertainty in assessment output matters.

### Approximate Bayesian computation (ABC)

#### Brendan McCabe, Economics, Finance and Accounting, University of Liverpool, UK

This tutorial looks at how to do Bayesian Inference when it is too difficult to calculate the true likelihood and hence the exact posterior. (This is a Bayesian version of frequentist ‘indirect inference’ really.) We use model based summary statistics to match simulations form the assumed (difficult) model with the actual data at hand. Conventional approaches to ABC emphasize the role of parameter estimation but, in time series problems, forecasting is often the focus of attention and so it is to this dimension we direct our efforts. The role of Bayesian consistency is highlighted.

### Generating samples from strange probability distributions

#### Peter Green, Institute for Risk and Uncertainty, University of Liverpool, UK

When conducting a probabilistic analysis, we often end up having to generate samples from a probability distribution. This, for example, is a crucial part of Monte Carlo simulations. For better-known probability distributions (Gaussian, uniform etc.), some simple tricks allow us to generate samples without too much difficulty. For the more ‘strange-looking’ distributions – which commonly arise in a Bayesian analysis – the problem becomes more difficult. This tutorial describes methods which can be used to generate samples from generic probability distributions. They often form an essential part of a Bayesian analysis. The tutorial is aimed at beginners, and will cover basic sampling algorithms before describing Markov chain Monte Carlo (MCMC) and importance sampling algorithms. Sample Matlab code will also be provided.

### Location

Bayes Days is held in the Risk Institute Seminar Room in the Chadwick Building at the end of Peach Street in the heart of the University of Liverpool campus. Use the *south entrance* to the Chadwick Building; other entrances have no access to the Risk Institute. When you enter the building, you'll see the Muspratt Lecture Theatre. Turn left and enter the brown door, and follow signs to the Risk Institute Seminar Room.

**Chadwick Building**

University of Liverpool

Latitude: 53.404110 / 53°24'14.8"N,

Longitude: -2.964600 / 2°57'52.6"W

What3words: curiosity.memory.daring

**Postal Address:**

Institute for Risk and Uncertainty, University of Liverpool

Peach Street, Chadwick Building

L7 7BD Click here for directions