Bayesian updating normal distribution

With the advent of kernel machines in the machine learning community, models based on Gaussian processes have become commonplace for problems of regression (kriging) and classification as well as a host of more specialized applications.

Gaussian Processes for Machine Learning, Carl Edward Rasmussen and Chris Williams, the MIT Press, 2006, online version.

Life is full of all sorts of risks, chances, and gambles. How can we accurately model the unpredictable world around us? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.

Via probability and advanced strategy, you'll learn how to optimize your chances to win probabilistic games.

- Finite sample properties of an estimator - Large sample properties of an estimator - Almost sure convergence - Convergence in probability and law of large numbers - Convergence in mean square - Convergence in distribution and Central Limit Theorem - Asymptotic distribution - Continous mapping theorem and delat method (slides) and (Matlab Codes) - Introduction - Likelihood function - Maximum Likelihood Estimator - Score, Gradient, Hessian and Fisher information matrix - Asymptotic properties of the maximum likelihood estimator - Application to the multiple linear regression model - Application to the probit and logit model (slides) and (Matlab Codes) - Introduction - The multiple linear regression model - Parametric and semi-parametric specifications - The Ordinary Least Squares (OLS) estimator - Statistical properties of the OLS - Finite sample properties of the OLS - Asymptotic properties of the OLS (slides) (videos) and (Matlab Codes) - Introduction - Statistical hypothesis testing and inference - Tests in the multiple linear regression model - The Student t-test - The Fisher test - Maximum Likelihood Estimation (MLE) and Inference - The Likelihood Ratio (LR) test - The Wald test - The Lagrange Multiplier (LM) or score test (slides) and (Matlab Codes) - The generalized linear regression model - Inefficiency of the Ordinary Least Squares - Generalized Least Squares (GLS) - Feasible Generalized Least Squares (FGLS) - Heteroscedasticity - White correction for heteroscedasticity - OLS and robust inference - Testing for heteroscedasticity: Breusch-Pagan and White tests (statement) and (Correction)- MLE and Weibull distribution- Wald test, LM test, LR test- OLS and multiple linear regression model __________________________ Site Value-at-Risk : Prvisions de Value-at-Risk et Backtesting Consultez le site Value-at-Risk ddi aux prvisions de Value-at-Risk (modles GARCH univaris et mthodes non paramtriques) et aux procdures de Backtesting : Estimation (Maximum de Vraisemblance et Pseudo Maximum de Vraisemblance) - Distributions Conditionnelles des modles GARCH (Student, Skewed Student et GED) - Tests d'effets ARCH - Modles GARCH asymtriques (EGARCH, QGARCH, LSTGARCH, ANSTGARCH, TGARCH, GJR-GARCH..) - Applications sous SAS : model GARCH et Value-at-Risk- Introduction : qu'est ce que le backtesting ?

- Dfinitions : violation de la Va R, couverture non conditionnelle et conditionnelle.

The best way to evaluate the uncertainty depends on the definitions of the source models and the amount and quality of information available to the modeller.Exercices Excel Feuille de calcul excel: Va R paramtrique / Va R non-paramtrique, Va R HS, WHS, Risk Metrics, Va R de portefeuille, Va R marginale, Va R incrmentale, CVa R..Programmes SAS, Exercices et Examens ) d'estimation de modles ARCH-GARCH avec distributions de Student, GED, Skewed Student.By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science.This course will make you a better mathematical problem-solver across several exciting topics, including algebra, geometry, number theory, and discrete math.

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We'll connect the dots between various strategies, so that you can tackle math competition problems (even the ones that don't look like problems you've seen before)!

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