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Given measurements m/sub 1/,m/sub 2/,...,m/sub J/ representing radar cross-sections of a given resolution element at different polarizations and/or different frequency bands, the authors consider the problem of making an "optimal" estimate of the actual dielectric constant /spl epsiv/ and the rms surface height h that gave rise to the particular {m/sub j/} observed. To obtain such an algorithm, the authors start with a data catalog consisting of careful measurements of the soil parameters /spl epsiv/ and h, and the corresponding remote sensing data {m/sub j/}. They also assume that they have used these data to write down, for each j, an average formula which associates an approximate value of m/sub j/ to a given pair (/spl epsiv/;h). Instead of deterministically inverting these average formulas, they propose to use the data catalog more fully and quantify the spread of the measurements about the average formula, then incorporate this information into the inversion algorithm. This paper describes how they accomplish this using a Bayesian approach. In fact, their method allows them to (1) make an estimate of /spl epsiv/ and h that is optimal according to the authors' criteria; (2) place a quantitatively honest error bar on each estimate, as a function of the actual values of the remote sensing measurements; (3) fine-tune the initial formulas expressing the dependence of the remote sensing data on the soil parameters; (4) take into account as many (or as few) remote sensing measurements as they like in making their estimates of /spl epsiv/ and h, in each case producing error bars to quantify the benefits of using a particular combination of measurements.