  Parameter estimation is a growing area of interest in statistical signal
processing. Some parameters in real-life applications vary in space as opposed
to those that are static. Most common methods in estimating parameters involve
solving an optimization problem where the cost function is assembled variously;
for example, maximum likelihood and maximum a posteriori methods. However,
these methods do not have exact solutions to most real-life problems. It is for
this reason that Monte Carlo methods are preferred. In this paper, we treat the
estimation of parameters which vary with space. We use Metropolis-Hastings
algorithm as a selection criteria for the maximum filter likelihood.
Comparisons are made with the use of joint estimation of both the spatially
varying parameters and the state. We illustrate the procedures employed in this
paper by means of two hyperbolic SPDEs: the advection and the wave equation.
The Metropolis-Hastings procedure registers better estimates.
