Unlocking datasets by calibrating populations of models to data density: a study in atrial electrophysiology

The understanding of complex physical or biological systems nearly always requires a characterization of the variability that underpins these processes. In addition, the data used to calibrate these models may also often exhibit considerable variability. A recent approach to deal with these issues has been to calibrate populations of models (POMs), multiple copies of a singlemathematicalmodel butwith different parameter values, in response to experimental data. To date, this calibration has been largely limited to selectingmodels that produce outputs that fallwithin the ranges of the data set, ignoring any trends that might be present in the data. We present here a novel and general methodology for calibrating POMs to the distributions of a set of measured values in a data set.We demonstrate our technique using a data set from a cardiac electrophysiology study based on the differences in atrial action potential readings between patients exhibiting sinus rhythm (SR) or chronic atrial fibrillation (cAF) and the Courtemanche-Ramirez-Nattel model for human atrial action potentials. Not only does our approach accurately capture the variability inherent in the experimental population, but we also demonstrate how the POMs that it produces may be used to extract additional information from the data used for calibration, including improved identification of the differences underlying stratified data.We also show how our approach allows different hypotheses regarding the variability in complex systems to be quantitatively compared

A Laplace-based algorithm for Bayesian adaptive design

This article presents a novel Laplace-based algorithm that can be used to find Bayesian adaptive designs under model and parameter uncertainty. Our algorithm uses Laplace importance sampling to provide a computationally efficient approach to undertake adaptive design and inference when compared to standard approaches such as those based on the sequential Monte Carlo (SMC) algorithm. Like the SMC approach, our new algorithm requires very little problem-specific tuning and provides an efficient estimate of utility functions for parameter estimation and/or model choice. Further, within our algorithm, we adopt methods from Pareto smoothing to improve the robustness of the algorithm in forming particle approximations to posterior distributions. To evaluate our new adaptive design algorithm, three motivating examples from the literature are considered including examples where binary, multiple response and count data are observed under considerable model and parameter uncertainty. We benchmark the performance of our new algorithm against: (1) the standard SMC algorithm and (2) a standard implementation of the Laplace approximation in adaptive design. We assess the performance of each algorithm through comparing computational efficiency and design selection. The results show that our new algorithm is computationally efficient and selects designs that can perform as well as or better than the other two approaches. As such, we propose our Laplace-based algorithm as an efficient approach for designing adaptive experiments.</p

An Adaptative sequential Monte Carlo method for approximate bayesian computation

10.1007/s11222-011-9271-yStatistics and Computing2251009-102

On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

We present a variant of the sequential Monte Carlo sampler by incorporating the partial rejection control mechanism of Liu (2001). We show that the resulting algorithm can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers, and provide a central limit theorem. Finally, the sampler is adapted for application under the challenging approximate Bayesian computation modelling framework