My book Uncertainty Quantification and Predictive Computational Science presents the reader with a variety of techniques to compute, understand, and defend the uncertainties in predictions made by computational models.  The book covers the

• modeling of input uncertainties
• sensitivity analysis
• Monte Carlo methods (and related techniques)
• polynomial chaos expansions
• reliability methods
• surrogates to replace simulation codes
• predictive models
• treating epistemic uncertainties

Knowledge of statistics and advanced mathematics is not a prerequisite for the reader. All concepts are introduced in a way that is graspable by readers with an understanding of calculus, differential equations, and basic numerical methods.

The publisher’s website for the book can be found here.

  Smolyak quadrature is covered in the discussion of polynomial chaos.

Pseudo Monte Carlo methods can be used to sample inputs with better convergence than simple random sampling.