ABSTRACT
This chapter takes a general and agnostic approach to the basic building blocks of uncertainty quantification but the authors will make connections to function approximation and Autonomous Experimentation regularly. Uncertainty quantification as a term has propagated from a set of well-defined mathematical and statistical tools to somewhat of a buzzword in recent decades. Probability density functions are the equivalent of probability mass functions for continuous random variables. A probability density function is an integrable function such that Following the logic for probability mass functions, probability density functions have to be greater than 0 everywhere and satisfy There is some ambiguity when it comes to the term probability distribution. Within probability theory, uncertainty quantification, and statistics, MCMC is used to approximate posteriors. Combined with the idea of kernels to calculate covariances between unobserved point-pairs, this allows us to predict posterior distributions for function values in unobserved regions, which makes the stochastic process a powerful tool for uncertainty quantification and Autonomous Experimentation.
