Approximate Bayesian computing (ABC) and Bayesian Synthetic likelihood (BSL) are two popular families of methods to evaluate the posterior distribution when the likelihood function is not available or tractable. For existing variants of ABC and BSL, the focus is usually first put on the simulation algorithm, and after that the form of the resulting approximate posterior distribution comes as a consequence of the algorithm. In this paper we turn this around and firstly define a reasonable approximate posterior distribution by studying the distributional properties of the expected discrepancy, or more generally an expected evaluation, with respect to generated samples from the model. The resulting approximate posterior distribution will be on a simple and interpretable form compared to ABC and BSL.

Secondly a Markov chain Monte Carlo (MCMC) algorithm is developed to simulate from the resulting approximate posterior distribution. The algorithm was evaluated on a synthetic data example and on the Stepping Stone population genetics model, demonstrating that the proposed scheme has real world applicability. The algorithm demonstrates competitive results with the BSL and sequential Monte Carlo ABC algorithms, but is outperformed by the ABC MCMC.

Millimeter-wave (mmWave) radio is a key building block in 5G and beyond cellular networks. However, mmWave channels are very sensitive to environmental conditions and depend on Line-of-Sight  connections to provide very high data rates. Achieving reliable, consistent communication — i.e., a steady link rate together with low delay — over mmWave links is therefore a challenging problem. The goal of this work is to explore the use of predictive control to manage and simultaneously use multiple available mmWave paths to achieve reliable consistent communication by means of a multipath proxy. We investigate transient solutions of Markov Modulated Fluid Queues (MMFQ) to model the short-term evolution of the proxy’s packet queue, consistent with the use of Markovian models to capture the behavior of mmWave channel blocking. We propose a combination of models that can be solved using newly proposed matrix-analytic techniques in a timely enough manner for use in real-time control. This gives us a prediction, over a short time horizon, of either proxy queue distributions or probabilities of reaching particular proxy buffer levels. Thus, it enables the proxy to make preemptive path decisions in order to maintain a desired Quality of Service. A proof-of-concept simulation study demonstrates the efficacy of our proposed MMFQ-based predictive approach over both static and purely reactive control approaches. Further, we explore the potential benefits of a hybrid approach to path management, combining both predictive and reactive control. This can allow the controller to cater for unforeseen events that cannot be forecast by the predictive controller, mitigating the resulting extra queuing and corresponding delay spikes.