We consider quantities that are uncertain because they depend on one
or many uncertain parameters. If the uncertain parameters are stochastic
the expected value of the quantity can be obtained by integrating the
quantity over all the possible values these parameters can take and dividing
the result by the volume of the parameter-space. Each additional
uncertain parameter has to be integrated over; if the parameters are many,
this give rise to high-dimensional integrals.
This report offers an overview of the theory underpinning four numerical
methods used to compute high-dimensional integrals: Newton-Cotes,
Monte Carlo, Quasi-Monte Carlo, and sparse grid. The theory is then applied
to the problem of computing the impact coordinates of a thrown ball
by introducing uncertain parameters such as wind velocities into Newton’s
equations of motion.
2016. , 29 p.