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A bayesian approach to markerless motion capture and activity recognition of multiple people
Techniques for Solving Sudoku Puzzles
Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three algorithms for solving Sudoku puzzles. Backtracking, simulated anne...
Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs
The purpose of this thesis is to study a numerical method for backward doubly stochastic differential equations (BDSDEs in short). In the last two decades, several methods were proposed to approximate solutions of standard backward stochastic differential equations. In this thesis, we propose an ext...
Numerical smoothing and hierarchical approximations for efficient option pricing and density estimation
When approximating the expectation of a functional of a certain stochastic process, the efficiency and performance of deterministic quadrature methods, and hierarchical variance reduction methods such as multilevel Monte Carlo (MLMC), is highly deteriorated in different ways by the low regularity of...
A comparative study on the performance of maximum likelihood, generalized least square, scale-free least square, partial least square and consistent partial least square estimators in structural equation modeling
Structural equation modeling offers various estimation methods for estimating parameters. The most used method in covariance-based structural equation modeling (CB-SEM) is the maximum likelihood (ML) estimator. The ML estimator is typically used when fitting models with normally distributed data. Th...
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Heterogeneity measures in hydrological frequency analysis: review and new developments
Some regional procedures to estimate hydrological quantiles at ungauged sites, such as the index-flood method, require the delineation of homogeneous regions as a basic step for their application. The homogeneity of these delineated regions is usually tested providing a yes/no decision. However, com...
Acceleration techniques of nested simulations in insurance
Stochastic approximations for financial risk computations
In this thesis, we investigate several stochastic approximation methods for both the computation of financial risk measures and the pricing of derivatives.As closed-form expressions are scarcely available for such quantities, %and because they have to be evaluated daily, the need for fast, efficient...
Training-Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network
Probabilistic inversion within a multiple‐point statistics framework is often computationally prohibitive for high‐dimensional problems. To partly address this, we introduce and evaluate a new training‐image based inversion approach for complex geologic media. Our approach relies on a deep neural ne...
Spectrum simulation of rough and nanostructured targets from their 2D and 3D image by Monte Carlo methods
Corteo is a program that implements Monte Carlo (MC) method to simulate ion beam analysis (IBA) spectra of several techniques by following the ions trajectory until a sufficiently large fraction of them reach the detector to generate a spectrum. Hence, it fully accounts for effects such as multiple...
Interactions between gaussian processes and bayesian estimation
Model learning and state estimation are crucial to interpret the underlying phenomena in many real-world applications. However, it is often challenging to learn the system model and capture the latent states accurately and efficiently due to the fact that the knowledge of the world is highly uncerta...
Sequential Monte Carlo pricing of American-style options under stochastic volatility models
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic program...
Hybrid PDE solver for data-driven problems and mother industry
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic prob...
Computational approach to the study of neurotransmitter release
Chemical synaptic transmission enables information flow in the brain between neurons. This process critically depends on neurotransmitter release, which is governed by calcium-regulated exocytosis. The speed, efficacy, and reliability of synaptic transmission are critically affected by the spatiotem...
Simulation methods for data transforming between administrative divisions in Poland
One of the most popular data sources used in economic and social studies are the results of households budgets survey (BGD). If the time horizon of study is long enough, the using of BGD results as a data source is connected with take account necessity of data prepared in different administration di...
Mixing LSMC and PDE Methods to Price Bermudan Options
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost...
Monte Carlo and quasi-Monte Carlo methods : application to calculations the Lasso estimator and the Bayesian Lasso estimator
The thesis contains 6 chapters. The first chapter contains an introduction to linear regression, the Lasso and the Bayesian Lasso problems. Chapter 2 recalls the convex optimization algorithms and presents the Fista algorithm for calculating the Lasso estimator. The properties of the convergence of...
GARCH Process Application in Risk Valuation for WIG20 Index
The recent economic crisis of 2008/2009 boosted a discussion about effectiveness of popular methods of controlling risk in financial markets, with value-at-risk approach being a topical issue. The paper contrasted a GARCH model for 1% VaR estimation for WIG20 with five basic approaches: variance-cov...
Bayesian prediction for non-full information on the example of electricity
The article was consecrated the bayesian modelling and forecasting on the ground the hierarchical models of time series in case missing data. The principles of bayesian modeling and forecasting were put-upon to analysis of production of electric power. In the article to building, estimation and pred...
Mean square solution of Bessel differential equation with uncertainties
A Research and Study Course for learning the concept of discrete randomvariable using Monte Carlo methods
Numerical analysis of partial differential equations with random coefficients, applications to hydrogeology
This work presents some results about probabilistic and deterministic numerical methods for partial differential equations with stochastic coefficients, with applications to hydrogeology. We first consider the steady flow equation in porous media with a homogeneous lognormal permeability coefficient...
Multilevel Monte Carlo methods and statistical inference for financial models
Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg
Uncertainty is often ignored in urban water systems modelling. Commercial software used in engineering practice often ignores the uncertainties of input variables and their propagation because of a lack of user-friendly implementations. This can have serious consequences, such as the wrong dimension...
Three Statistical Problems With Imprecisely or Incompletely Observed Data