Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis-Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature [27] where the target distribution is explored using a continuous-time non-reversible piecewise-deterministic Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently of higher "energy", than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper "local" bounces which only involve the state variables associated to a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high dimensional models and large data sets.

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target distribution. This approach was recently combined with the theory of reproducing kernels to define a closed-form kernel Stein discrepancy (KSD) computable by summing kernel evaluations across pairs of sample points. We develop a theory of weak convergence for KSDs based on Stein's method, demonstrate that commonly used KSDs fail to detect non-convergence even for Gaussian targets, and show that kernels with slowly decaying tails provably determine convergence for a large class of target distributions. The resulting convergence-determining KSDs are suitable for comparing biased, exact, and deterministic sample sequences and simpler to compute and parallelize than alternative Stein discrepancies. We use our tools to compare biased samplers, select sampler hyperparameters, and improve upon existing KSD approaches to one-sample hypothesis testing and sample quality improvement.

Machine learning (ML), artificial intelligence (AI) and other modern statistical methods are providing new opportunities to operationalize previously untapped and rapidly growing sources of data for patient benefit. Whilst there is a lot of promising research currently being undertaken, the literature as a whole lacks: transparency; clear reporting to facilitate replicability; exploration for potential ethical concerns; and, clear demonstrations of effectiveness. There are many reasons for why these issues exist, but one of the most important that we provide a preliminary solution for here is the current lack of ML/AIspecific best practice guidance. Although there is no consensus on what best practice looks in this field, we believe that interdisciplinary groups pursuing research and impact projects in the ML/AI for health domain would benefit from answering a series of questions based on the important issues that exist when undertaking work of this nature. Here we present 20 questions that span the entire project life cycle, from inception, data analysis, and model evaluation, to implementation, as a means to facilitate project planning and post-hoc (structured) independent evaluation. By beginning to answer these questions in different settings, we can start to understand what constitutes a good answer, and we expect that the resulting discussion will be central to developing an international consensus framework for transparent, replicable, ethical and effective research in artificial intelligence (AI-TREE) for health.