Process Noise and Optimum Observation in Conditional Stochastic Fields

Two issues are focused on: respectively, a problem of sequential updating with plural sets of data, and a problem of optimal allocation of observation points within the scope of conditional stochastic fields. Concerning the first issue, the mathematical and mechanical roles of process noises in the updating process of conditional stochastic fields are discussed. It is found that the greater the involvement of noises, the more reliably the latest datum is treated in the sequential updating process of plural observation data. The other issue is appraisal of observation allocation, in which two indices are proposed as rational indicators to examine where observation points are to be selected in order to have efficient updating. One index is defined as the geometric mean of the ratios of a posteriori standard deviation versus a priori standard deviation of each unknown parameter. The other one is similarly defined by using a priori and a posteriori standard deviations of responses. Both indices take values from zero to unity, and it is found that a smaller value close to zero means excellent allocation, since the deviation of a posteriori model parameters or responses becomes smaller.