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  1. No Access

    Book

    Uncertainty Quantification with R

    Bayesian Methods

    Eduardo Souza de Cursi in International Series in Operations Research & Management Science (2024)

  2. No Access

    Chapter

    Basic Bayesian Probabilities

    This chapter contains a historical introduction and presents the basic elements of the Bayesian approach in probabilities, namely, the notions of exchangeability and De Finetti’s theorem. The combination of un...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

  3. No Access

    Chapter

    Information and Entropy

    This chapter presents the notions connected to Shannon’s entropy and information, namely the joint, conditional, relative (Kullback–Leibler) entropies, and the mutual information, with their implementations in...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

  4. No Access

    Chapter

    Bayesian Inference

    This chapter presents the Bayesian approach for practical tasks, such as estimation, hypothesis testing, model or variable selection, and regression. The choice of priors is analyzed, by using Jeffreys approac...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

  5. No Access

    Chapter

    Beliefs

    This chapter presents the Dempster-Shafer theory of beliefs and plausibility, which can be seen as a formalism for the interpretation of probabilities in terms of degrees of belief. The basic notions are prese...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

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    Chapter

    Maximum Entropy

    This chapter presents the principle of maximum entropy, which furnishes a practical method for the generation of distributions. The representation of stochastic processes by Karhunen-Loève expansions is presen...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

  7. No Access

    Chapter

    Sequential Bayesian Estimation

    This chapter presents Monte-Carlo Markov Chain methods and connected topics, namely Importance Sampling, Metropolis-Hastings Algorithm, Kalman Filtering, Particle Filtering, and Bayesian Optimization. The use ...

    Eduardo Souza de Cursi in Uncertainty Quantification with R (2024)

  8. No Access

    Chapter

    Probabilities and Random Variables

    In this chapter, we present the fundamental elements of probability and statistics that are used in the book, namely the elements about random variables and random vectors, with particular attention to the use...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  9. No Access

    Chapter

    Stochastic Processes

    In this chapter, we consider stochastic processes, with a focus on MA, AR, ARMA, diffusion processes, Ito’s stochastic integrals, and Ito’s stochastic differential equations.

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  10. No Access

    Chapter

    Random Differential Equations

    In this chapter, we examine methods for the determination of the probability distributions of random differential equations. We present also methods for the analysis of orbits and trajectories under uncertainty.

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  11. No Access

    Chapter

    Optimization Under Uncertainty

    This chapter presents methods for the determination of the probability distribution of the solutions of continuous optimization problems: constrained or unconstrained, linear or nonlinear. We analyze also the ...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  12. No Access

    Book

    Uncertainty Quantification using R

    Eduardo Souza de Cursi in International Series in Operations Research & Management Science (2023)

  13. No Access

    Chapter

    Some Tips to Use R and RStudio

    This chapter presents the essentials of R, with a focus on the manipulation of variables, plotting, and the use of data frames and classes. We present also some useful packages for standard numerical methods, ...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  14. No Access

    Chapter

    Representation of Random Variables

    In this chapter, we present some methods to determine the distribution of a random variable from limited-sized samples. The methods are based on the representation of the random variable under consideration as...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

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    Chapter

    Uncertain Algebraic Equations

    In this chapter, we consider the situation where an unknown n-dimensional vector X has to be determined by solving a system of equations having the form F(X, U) = 0, where F is a map** from the n-dimensional...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  16. No Access

    Chapter

    UQ in Game Theory

    In this chapter, we examine mathematical games under uncertainty (for instance, in probabilities or payoffs). We examine also evolutionary dynamics associated with games and we present methods for the determin...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  17. No Access

    Chapter

    Reliability

    In this chapter, we present some tools for reliability analysis and reliability-based design optimization, such as the notions of reliability index and its determination by different methods, transformations o...

    Eduardo Souza de Cursi in Uncertainty Quantification using R (2023)

  18. No Access

    Chapter

    Random Differential Equations

    Differential equations are first of all equations, so that the methods used for equations may be used – at least in principle.

    Eduardo Souza de Cursi in Uncertainty Quantification and Stochastic Modelling with EXCEL (2022)

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    Chapter

    Some Tips to Use EXCEL®

    EXCEL® is a powerful software: a complete exploration of its possibilities cannot be made here. In this chapter, we present some tips that will be useful in the sequel.

    Eduardo Souza de Cursi in Uncertainty Quantification and Stochastic Modelling with EXCEL (2022)

  20. No Access

    Chapter

    Optimization Under Uncertainty

    In Sect. 2.2 (page 52), we introduced the classical mono-objective optimization problem.

    Eduardo Souza de Cursi in Uncertainty Quantification and Stochastic Modelling with EXCEL (2022)

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