  Bayesian neural learning feature a rigorous approach to estimation and
uncertainty quantification via the posterior distribution of weights that
represent knowledge of the neural network. This not only provides point
estimates of optimal set of weights but also the ability to quantify
uncertainty in decision making using the posterior distribution. Markov chain
Monte Carlo (MCMC) techniques are typically used to obtain sample-based
estimates of the posterior distribution. However, these techniques face
challenges in convergence and scalability, particularly in settings with large
datasets and network architectures. This paper address these challenges in two
ways. First, parallel tempering is used used to explore multiple modes of the
posterior distribution and implemented in multi-core computing architecture.
Second, we make within-chain sampling schemes more efficient by using Langevin
gradient information in forming Metropolis-Hastings proposal distributions. We
demonstrate the techniques using time series prediction and pattern
classification applications. The results show that the method not only improves
the computational time, but provides better prediction or decision making
capabilities when compared to related methods.
