Bayesian Generalized Nonlinear Models Offer Basis Free SINDy With Model Uncertainty

The paper specifies the BGNLM/SINDy setup with Yji ~ N(fj(xi), σ^2), uses Bernoulli priors on inclusion indicators, assigns Jeffreys priors to coefficients with σ^2 fixed, explores the model space via GMJMCMC, and selects the median probability model by thresholding p(γjk=1|D) at 0.5; however, it provides no derivations for the marginal likelihood, posterior inclusion probabilities, or the optimality of the 0.5 threshold. The candidate solution supplies these missing derivations and a coherent MCMC outline consistent with the paper’s stated approach. These points match the paper’s framework and claims (model and priors; GMJMCMC; and use of the median probability model) but go beyond it by filling in the mathematics the paper omits .