Bias updating is a widespread adaptive procedure to allow inference models to pursue time variant features of a real world process. The aim of this work is to clarify the statistical consequences of bias updating to soft sensor estimates as well to point up the need of careful analysis of the effect of unmeasured disturbances on the true values of the variable of interest. It is shown that bias updated inferences are unbiased estimates of the true value but yields estimates whose variance are 100% larger than the ones obtained with no use of bias updating. It is suggested the use of a weighting factor to bias updating in order to balance statistical benefits and penalties. A case study of a soft sensor for weathering of LPG in oil refinery exemplifies the concepts discussed.