GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms

Noise enhanced spontaneous chaos in semiconductor superlattices at room temperature

Physical systems exhibiting fast spontaneous chaotic oscillations are used to generate high-quality true random sequences in random number generators. The concept of using fast practical entropy sources to produce true random sequences is crucial to make storage and transfer of data more secure at very high speeds. While the first high-speed devices were chaotic semiconductor lasers, the discovery of spontaneous chaos in semiconductor superlattices at room temperature provides a valuable nanotechnology alternative. Spontaneous chaos was observed in 1996 experiments at temperatures below liquid nitrogen. Here we show spontaneous chaos at room temperature appears in idealized superlattices for voltage ranges where sharp transitions between different oscillation modes occur. Internal and external noises broaden these voltage ranges and enhance the sensitivity to initial conditions in the superlattice snail-shaped chaotic attractor thereby rendering spontaneous chaos more robust.Comment: 6 pages, 4 figures, revte

Accelerating delayed-acceptance Markov chain Monte Carlo algorithms

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster, albeit approximate, DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. When the evaluation of the likelihood function is computationally intensive, our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC. However, the acceleration is highly problem dependent. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our algorithm can return reliable Bayesian inference. As a computationally intensive case study, we introduce a novel stochastic differential equation model for protein folding data.Comment: 40 pages, 21 figures, 10 table