# 2023: Computational Statistics

The 23rd edition of the Geilo Winter School will take place in Geilo, Norway from Sunday January 22 to Friday January 27, 2023. The topic of the school will be computational statistics.

## Program

**Tor Erlend Fjelde and Jose Storopoli**

Turing is an ecosystem of Julia packages for Bayesian Inference using probabilistic programming. Models specified using Turing are easy to read and write — models work the way you write them. Like everything in Julia, Turing is fast. We are going to cover the basics of the Julia language and Turing. We proceed by learning how to define Bayesian models (or any sort of generative model) in Turing, the different MCMC samplers available, how to post-process your MCMC samples, how to perform diagnostics and predictive checks. We conclude with advanced Turing usage, such as performance, debugging and how to specify ODEs inside Turing models.

- Julia/Turing Basics
- Quick intro to Julia
- Basics of Turing

- Using Turing in practice
- How to define Bayesian/generative models
- Different MCMC samplers
- What to do after sampling (post-processing)
- Diagnostics
- Predictive Checks

- Advanced Turing usage
- Performance of Turing models
- Debugging Turing of models
- ODE in Turing models

- Cutting-edge MCMC algorithms research with Turing
- How to use the exposed interfaces in the Turing ecossystem
- Case example of Parallel MCMC Tempering

**Anne-Marie George**

1. Reinforcement Learning: Introduction and Problem Formulation

We start off by introducing the general framework and notation of reinforcement learning problems and their goals together with some examples. At the end of this session you should be able to detect whether a learning problem is a reinforcement learning problem, be able to formalise it and implement a framework in Python.

2. Reinforcement Learning: Algorithmic Solutions

We consider the underlying principles that lead to algorithmic solutions together with some basic algorithms to find optimal policies. At the end of this session you should be able to understand state- and action-values and use basic algorithms in Python to find optimal polices.

### Sara Martino

Latent Gaussian models (LGMs) are among the most commonly used classes of models in statistical applications and include generalised linear models, generalised additive models, smoothing spline models, linear state space models, log-¬Gaussian Cox processes, geostatistical models and much more.

In a Bayesian setting, inference on such models is hard as the posterior cannot be analytically derived. Markov Chain Monte Carlo (MCMC) is a powerful machine which allows to Bayesian inference in a very general context but that suffers of high computational costs. In the framework of LGM, deterministic inference offers a faster and often more precise alternative to MCMC. The Integrated Nested Laplace Approximation (INLA) algorithm makes use of the hierarchical structure of LGM and provides with fast and accurate posterior inference. Another advantage of INLA with respect to MCMC its generality. This makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. The INLA algorithm is readily available through the R-INLA package which make the method easily accessible to practitioners

During the week, we will cover the following topics:

1. Introduction to Latent Gaussian Models.

2. Deterministic inference for LGM.

3. Introduction to the R-INLA library.

### Geir Olve Storvik

Monte Carlo methods are today used on a wide range of problems, including Bayesian learning, solving differential equations, simulation experiments and just solving integrals. Through these lectures, we will discuss what Monte Carlo methods are, present several types of Monte Carlo methods as well as illustrating the methods on specific cases. Topics that will be covered are simple Monte Carlo, acceptance and importance sampling, variance reduction methods, Markov chain Monte Carlo (MCMC), sequential Monte Carlo (SMC), Reversible jump MCMC as well as Particle MCMC.

- What, how and why Monte Carlo
- The integration problem and integrations as expectations
- The Monte Carlo method and its properties
- Applications of Monte Carlo: Simulation experiments, Bayesian methods, differential equations
- Some variance reducing methods

- Markov chain Monte Carlo
- The General principle and requirements for convergence
- Gibbs sampler, Metropolis-Hastings, Hamiltonian Monte Carlo
- Convergence issues
- Examples

- Sequential Monte Carlo
- Sequential learning and state space models
- The sequential Monte Carlo method
- SMC for non-dynamic settings

- Advanced stuff
- Particle MCMC
- Reversible jump MCMC

## Schedule

All lectures will take place at Dr. Holms Hotel in Geilo, Norway. Participants will receive more information by email.

Booking a train/checking the train schedule is done through Vy. The hotel is a walkable distance from the train station in Geilo.

You can subscribe to the calendar by using this link.

## Lecturers

### Tor Erlend Fjelde

Tor Erlend Fjelde is a PhD student in the Computational and Biological Learning (CBL) lab at University of Cambridge. Prior to this he completed a Honours BSc in Mathematics at the University of Edinburgh. His main research interests generally fall within the realms of Bayesian inference, be that the theory of Markov Chain Monte Carlo (MCMC), or practical applications. In addition, he is one of the core maintainers of the probabilistic programming language (PPL) in Julia called Turing.jl.

### Anne-Marie George

Anne-Marie George is a Postdoc in the computer science department at the University of Oslo, Norway, since 2021. She obtained her PhD from the University College Cork, Ireland in 2019. Through her prior postdoc position in TU Berlin and her current position, she has experience in Computational Social Choice, as well Reinforcement Learning. Her current research focuses on preference elicitation problems for multi-agent settings. She is also interested in the axiomatic and experimental analysis of fairness in decision making. Anne-Marie teaches graduate courses on Reinforcement Learning and Adaptive Decision Making at UiO.

### Sara Martino

Sara Martino is Associate Professor at the Department of Mathematical Science at the Norwegian University of Science and Technology, Norway which she joined in 2018 after working for 8 years as researcher at SINTEF Energy Research. She holds a PhD in Statistics from NTNU from 2007. Her research focuses on spatial and computational Bayesian statistics with a particular focus on approximate Bayesian inference methods. She is interested in applications in a wide range of scientific fields from ecology and air quality to multistate survival models.

### Jose Storopoli

Jose Storopoli is Associate Professor and Researcher of the Department of Computer Science at Universidade Nove de Julho - UNINOVE located in São Paulo, Brazil. He's Director of Education and Training at PUMAS-AI. He teaches undergraduate and graduate courses in Data Science, Statistics, Bayesian Statistics, Machine Learning and Deep Learning using Julia, R, Python, and Stan, and researches, publishes and advises PhD candidates on topics about Bayesian Statistical Modeling and Machine Learning applied to Decision Making. He's a member of the Turing.jl Developer Team.

### Geir Olve Storvik

Geir Storvik is Professor in statistics at University of Oslo. His research interest includes Monte Carlo methods (sequential Monte Carlo and Markov chain Monte Carlo), state space and Bayesian hierarchical modelling and Bayesian machine learning. Through his involvement in BigInsight (a center for research based innovation) and the Norwegian Computing Center he has a long experience in applying statistical modelling and computational statistics to real applications, including COVID-19 pandemics, catch-at-age estimation in fisheries, and fault detection based on industrial sensor data.

## Important Information

See the About page for general information about the winter school.

## Costs and registration

There is no registration fee for the winter school, but participants must cover their own travel costs and hotel costs at Dr. Holms. To register, please fill out this form.

## Room allocation

The winter school has a limited number of rooms at Dr. Holms which will be reserved on a first come first serve basis. **We have in previous years exceeded our room allocation, so please register as early as possible!**

## Posters

We welcome all posters to be presented, and will make space in the program for a poster session in which participants can present their work to colleagues and others. The aim of the session is to make new contacts and share your research, and it is an informal event. You need to indicate in your registration if you want to present a poster during the poster session. Please limit your poster to A0 in portrait orientation.

## Organizing Committee

The organizing committee for the Geilo Winter School consists of

- Torkel Andreas Haufmann, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).
- Øystein Klemetsdal, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).
- Signe Riemer-Sørensen, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).

To get in touch with the committee, send an email __.__