Bayesian trans-dimensional soil behaviour type inference using conditional posterior proposals

Identification of subsurface geological profiles is indispensable to geotechnical design and construction. Subsurface stratification through Bayesian inversion of soil behaviour type index data, obtained from cone penetration tests, is achieved through the development of a novel three-block Markov chain Monte Carlo algorithm. Working in a trans-dimensional context, where the number of layers, layer depths and soil random field parameters are unknown, the algorithm is able to estimate the range of non-unique solutions or the uncertainty of these parameters. A blocking strategy has been applied that allows for the development of a formulation that primarily involves computationally inexpensive tasks such as sampling from truncated normal and Inv-Gamma distributions and evaluation of general normal densities. Part of this strategy involves the design of a novel proposal density for jumping between parameter spaces of different dimensions in the reversible jump Markov chain Monte Carlo applied in the first block. Optimal sampling in trans-dimensional problems with a single reversible jump Markov chain using random walk Metropolis–Hastings proposals is often difficult and requires ad hoc concatenation of multiple independent chains or sophisticated methods like parallel tempering or delayed rejection. The formulation presented in this study renders the conditional posterior density over the mean of the random field representing the soil parameters to be analytical, thereby allowing the corresponding proposals to be made directly from the conditional posterior. Hence, unlike most other existing algorithms, we avoid random walks altogether by sampling from the conditional posterior distribution directly. The algorithm is validated using synthetic and real soil behaviour type index data from benchmark problems. A standard normality check of the decorrelated residuals is used as a measure to test algorithm performance. Results show that the algorithm is able to identify the soil stratification parameters and random field properties correctly and also identify their uncertainties.