École d’hiver 2019

3-6 février 2019

M. Yves Tillé, UNINE (Président); Mme Caroline Gillardin, UNINE (coordinatrice)

Prof. Mustafa Khammash, ETH Zürich

Prof. Jonas Peters, Université de Copenhagen

Prof. Alastair Young, Imperial College London

Prof. Mustafa Khammash (ETH Zürich)

Title : Probabilistic Methods for Biochemical Reaction Networks

I will present some of the main methodologies for modeling and analysis of stochastic dynamics in living cells. I will start by describing the origin of randomness in living cells, which will motivate the need for adopting probabilistic models cellular behavior. I will present a class of Markov process models for chemical kinetics that will allow us to describe a large class of problems in cell biology. I will then develop methods for density function and statistical moments computation and show their use in model parameters inference.

Part 1: I will start with a simple introduction to basic concepts in molecular biology, using use gene expression as a simple example for motivating a probabilistic approach to modeling cellular dynamics. I will describe how cell population measurements are obtained in experimental labs and then discuss the quality and nature of the resulting biological data samples.

Part 2: I will present the main approach for describing stochastic chemical kinetics and show how it serves as a general framework for modeling biochemical reactions in living cells. I will then discuss Monte Carlo methods for obtaining statistical samples of the cellular variables of interest. Finally, I will motivate and derive Kolmogorov's forward equation as well as equations describing the evolution of the statistical moments of the modeled cellular random variables, and will discuss their solutions for a class of biological problems of interest.

Part 3: Here I will discuss state-of-the art methods for computing/estimating probability density functions and statistical moments of cellular species and highlight the main challenges and open problems related to their solution. I will end by discussing the problem of statistical inference of model parameters in the context of available computational methods and the type of data that can be measured experimentally

PDF Lecture 1

PDF Lecture 2

PDF Lecture 3

Prof. Jonas Peters (Copenhagen University)

Title : Causality in Statistics

In the field of causality we want to understand how a system reacts under interventions (e.g. in gene knock-out experiments). These questions go beyond statistical dependences and can therefore not be answered by standard regression or classification techniques. In this part of the program you will learn about the interesting problem of causal inference and recent developments in the field. No prior knowledge about causality is required.

Part 1: We introduce structural causal models and formalize interventional distributions. We define causal effects and show how to compute them if the causal structure is known.

Part 2: We present three ideas that can be used to infer causal structure from data: (1) finding (conditional) independences in the data, (2) restricting structural equation models and (3) exploiting the fact that causal models remain invariant in different environments.

Part 3: We show how causal concepts could be used in more classical statistical and machine learning problems.

Instruction for downloading lectures and others

Prof. Alastair Young (Imperial College London)

Title : Principled statistics for data science

We will consider the key principles and desiderata that should guide statistical inference in contemporary data science settings. The course will review key ideas of statistical inference, and highlight important developments for both classical inference, where the statistical objective is formulated before data collection, and for the selective setting where objectives are only set after examination of data.

Part 1. The statistical inference problem will be formulated and guiding principles described and justified, from both frequentist and Bayesian perspectives. Focus will be on general, likelihood-based approaches, and distinctions between the requirements of classical and selective inference will be drawn.

Part 2. Higher-order likelihood-based methods based on both analytic and bootstrap distributional approximations will be discussed for the classical setting, and evaluated in terms of the need for principled and inferentially valid approaches to statistical analysis.

Part 3. Contemporary developments in Bayesian and frequentist statistical methodology will be described and evaluated in terms of the identified principles and requirements, with focus on the selective inference context.

PDF Lectures 1-2-3

Programme

Les Diablerets (VD)

Eurotel Victoria

1865 Les Diablerets (VD)

www.eurotel-victoria.ch/diablerets/

Accès aux Diablerets :

EN VOITURE Autoroute A9, direction Grand St-Bernard, sortie Aigle. Puis la route Aigle - Les Diablerets - Col du Pillon (20km). 

EN AVION Aéroports internationaux de: - Genève (120 km) - Zürich (250 km) - Bâle (200 km)

EN TRAIN  (HORAIRE DES TRAINS - RAILWAY TIMETABLE)  International TGV Paris - Lausanne. En hiver, TGV des Neiges Paris - Lausanne - Aigle.

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