Statistique bayésienne

Résumé

La statistique bayésienne est une approche statistique fondée sur l'inférence bayésienne, où la probabilité exprime un degré de croyance en un événement. Le degré initial de croyance peut être basé sur des connaissances a priori, telles que les résultats d'expériences antérieures, ou sur des croyances personnelles concernant l'événement. La perspective bayésienne diffère d'un certain nombre d'autres interprétations de la probabilité, comme l'interprétation fréquentiste qui considère la probabilité comme la limite de la fréquence relative d'un événement après de nombreux essais. Les méthodes statistiques bayésiennes reposent sur le théorème de Bayes pour calculer et mettre à jour les probabilités après l'obtention de nouvelles données. Le théorème de Bayes décrit la probabilité conditionnelle d'un événement basée sur des informations ou des croyances antérieures sur l'événement ou les conditions liées à l'événement. Par exemple, dans l'inférence bayésienne, le théorème de Bayes peut

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https://fr.wikipedia.org/wiki/Statistique_bay%C3%A9sienne

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In this thesis, we assess a new framework called UMIN on a data-driven optimization problem. Such a problem happens recurrently in real life and can quickly become dicult to model when the input has a high dimensionality as images for instance. From the architecture of aircraft to the design of proteins, a great number of dierent techniques have already been explored. Based on former solutions, this work introduces a brand new Bayesian approach that updates previous frameworks. Former model architectures use generative adversarial networks on one side and a forward model on the other side to improve the accuracy of the results. However, employing a Bayesian network allows us to leverage its uncertainty estimates to enhance the accuracy of the results and also to reduce unrealistic samples output by the generator. By creating new experiments on a modern MNIST dataset and by reproducing former works taken as baseline, we show that the framework introduces in this work outperforms the previous method. The whole code is available at the following url: https://github.com/RomainGratier/Black-box_Optimization_via_Deep_ Generative-Exploratory_Networks.

2020

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Can we guess the destinations of attendees in a music festival from Bluetooth traces collected by 10 people with smartphones used as antennas? This project analyzes an existing dataset of Bluetooth traces from Paléo music festival in Nyon, Switzerland. The goal of the project is to follow Paléo festival attendees using collected Bluetooth traces and analyze specifications of the collected data in terms of precision and results, to predict attendees behaviour and crowd movement. The data was collected on July 24th, 2010 by ten agents scanning for visible Bluetooth devices. The methodology for tracing Paléo festival attendees is a Bayesian approach derived by Danalet et al. [2012].

2013

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Bayesian risk analysis of financial time series

Christophe Osinski

This thesis is a contribution to financial statistics. One of the principal concerns of investors is the evaluation of portfolio risk. The notion of risk is vague, but in finance it is always linked to possible losses. In this thesis, we present some measures allowing the valuation of risk with the help of Bayesian methods. An exploratory analysis of data is presented to describe the sampling properties of financial time series. This analysis allows us to understand the origins of the daily returns studied in this thesis. Moreover, a discussion of different models is presented. These models make strong assumptions on investor behaviour, which are not always satisfied. This exploratory analysis shows some differences between the behaviour anticipated under equilibrium models, and that of real data. The Bayesian approach has been chosen because it allows one to incorporate all the variability, in particular that associated with model choice. The models studied in this thesis allow one to take heteroskedasticity into account, as well as particular shapes of the tails of returns. ARCH type models and models based on extreme value theory are studied. One original aspect of this thesis is its use of Bayesian analysis to detect change points in financial time series. We suppose that a market has two phases, and that it switches from a state to the other at random. Another new contribution is a model integrating heteroskedasticity and time dependence of extreme values, by superposition of the model proposed by Bortot and Coles (2003) and a GARCH process. This thesis uses simulation intensively for the estimation of risk measures. The drawback of simulation is the amount of time needed to obtain accurate estimates. However, simulation allows one to produce results when direct calculation is not feasible. For example, simulation allows one to compute risk estimates for time horizons greater than one day. The methods presented in this thesis are illustrated on simulated data, and on real data from European and American markets. This thesis involved the construction of a library containing C and S code to perform risk analysis using GARCH and extreme value theory models. The results show that model uncertainty can be incorporated, and that risk measures for time horizons greater than one can be obtained by simulation. The methods presented in this thesis have a natural representation involving conditioning. Thus, they permit the computation of both conditional and unconditional risk estimates. Three methods are described: the GARCH method; the two-state GARCH method; and the HBC method. Unconditional risk estimation using the GARCH method is satisfactory on data which seem stationary, but not reliable on data which are non-stationary, such as data with change points. The two-state GARCH model does a little better, but gives very satisfactory results when the risk is estimated conditionally on time. The HBC method does not give satisfactory results.

EPFL2006

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Bayesian risk analysis of financial time series

Christophe Osinski

EPFL2006