CHAPTER 10
GAUSSIAN INFORMATION
In this chapter we look at linear systems with stochastic disturbances. Imagine, for example, that we want to determine a physical state of a certain object by repeated measurement. Then, the observed measurement results are always composed of the real state and some unknown measurement errors. In many important applications, however, these stochastic disturbances may be assumed to have a normal or Gaussian distribution. Together with accompanying observations, such a system forms what we call a Gaussian information. We are going to discuss in this chapter how inference from Gaussian information can be carried out. This leads to a compact representation of Gaussian information in the form of Gaussian potentials, and it will be shown that these potentials form a valuation algebra. We may therefore apply local computation for the inference process which exploits the structure of the Gaussian information. This chapter is largely based on (Eichenberger, 2009).
Section 10.1 defines an important form of Gaussian information that is used for assumption-based reasoning. This results in a particular stochastic structure, called precise Gaussian hint, which is closely related to the Gaussian potentials of Instance 1.6. In fact it provides meaning to these potentials and shows that combination and projection of Gaussian potentials reflect natural operations on the original Gaussian information. This gives sense to the valuation algebra of Gaussian potentials ...
