Mapping the probability of ripened subsoils using Bayesian logistic regression with informative priors

Abstract

One of the first soil forming processes in marine and fluviatile clay soils is ripening, the irreversible change of physical and chemical soil properties, especially consistency, under influence of air. We used Bayesian binomial logistic regression (BBLR) to update the map showing unripened subsoils for a reclamation area in the west of The Netherlands. Similar to conventional binomial logistic regression (BLR), in BBLR the binary target variable (the subsoil is ripened or unripened) is modelled by a Bernoulli distribution. The logit transform of the `probability of success' parameter of the Bernoulli distribution was modelled as a linear combination of the covariates soil type, freeboard (the desired water level in the ditches, compared to surface level) and mean lowest groundwater table. To capture all available information, Bayesian statistics combines legacy data summarized in a ‘prior’ probability distribution for the regression coefficients with actual observations. Our research focused on quantifying the influence of priors with different information levels, in combination with different sample sizes, on the resulting parameters and maps. We combined subsamples of different size (ranging from 5% to 50% of the original dataset of 676 observations) with priors representing different levels of trust in legacy data and investigated the effect of sample size and prior distribution on map accuracy. The resulting posterior parameter distributions, calculated by Markov chain Monte Carlo simulation, vary in centrality as well as in dispersion, especially for the smaller datasets. More informative priors decreased dispersion and pushed posterior central values towards prior central values. Interestingly, the resulting probability maps were almost similar. However, the associated uncertainty maps were different: a more informative prior decreased prediction uncertainty. When using the ‘overall accuracy’ validation metric, we found an optimal value for the prior information level, indicating that the standard deviation of the legacy data regression parameters should be multiplied by 10. This effect is only detectable for smaller datasets. The Area Under Curve validation statistic did not provide a meaningful optimal multiplier for the standard deviation. Bayesian binomial logistic regression proved to be a flexible mapping tool but the accuracy gain compared to conventional logistic regression was marginal and may not outweigh the extra modelling and computing effort.