Uncertainty-aware traction force microscopy
Fig 3
Hierarchical Bayesian TFM formulation for adaptive and self-consistent regularization.
The problem of choosing a regularization parameter is treated in a Bayesian formulation. Substrate deformation () is the observed quantity, and it is modeled as the additive contribution of traction stresses (
), locally resolved PIV measurement uncertainty
and a global model error
that is unknown. The hierarchical formulation allows to express unknown hyper-parameters (
for the prior on traction stress field and the model error term as random variables to be inferred. Therefore, a non-informative hyper-prior (
) is specified to the hyper-parameters. The priors can encode reasonable assumptions such as smoothness and global force balance. Markov Chain Monte Carlo (MCMC), specifically an hybrid Gibbs sampling, is used for inference from the marginal posterior distribution,
.