Paleoclimatic reconstructions are generally based on the inversion of robust multivariate linear regression of indirect climate measures on contemporaneous direct climate observations.  However, realistic models of the response of proxy systems to environmental controls may be multivariate and/or nonlinear.  We will review recent work on what may be considered an intermediate class of such proxy system models.  The results complement and sharpen proxy data interpretations based solely on statistical analysis; they can be used to test validity of reconstruction assumptions, such as the stability of the statistical calibration process over time and the extent of bias arising from sparse heterogeneous data networks; and they can be developed as weak constraints in the next generation of proxy-based climate field reconstructions.