  The goal of this paper is to demonstrate the general modeling and practical
simulation of random equations with mixture model parameter random variables.
Random equations, understood as stationary (non-dynamical) equations with
parameters as random variables, have a long history and a broad range of
applications. The specific novelty of this explorative study lies on the
demonstration of the combinatorial complexity of these equations with mixture
model parameters. In a Bayesian argumentation framework we derive a general
likelihood function and posterior density of approximate best fit solutions
while avoiding significant restrictions about the type of nonlinearity of the
equation or mixture models, and demonstrate their numerically efficient
implementation for the applied researcher. In the results section, we are
specifically focusing on expressive example simulations of approximate
likelihood/posterior solutions for random linear equation systems, nonlinear
systems of random conic section equations, as well as applications to portfolio
optimization, stochastic control and random matrix theory in order to show the
wide applicability of the presented methodology.
