arXiv subjects

Julie Lyng Forman

Publications and source records attributed to Julie Lyng Forman.

3 recordsLinked to original sources

arXiv2019

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.

stat.CO↗

arXiv2019

Bayesian inference for stochastic differential equation mixed effects models of a tumor xenography study

We consider Bayesian inference for stochastic differential equation mixed effects models (SDEMEMs) exemplifying tumor response to treatment and regrowth in mice. We produce an extensive study on how a SDEMEM can be fitted using both exact inference based on pseudo-marginal MCMC and approximate inference via Bayesian synthetic likelihoods (BSL). We investigate a two-compartments SDEMEM, these corresponding to the fractions of tumor cells killed by and survived to a treatment, respectively. Case study data considers a tumor xenography study with two treatment groups and one control, each containing 5-8 mice. Results from the case study and from simulations indicate that the SDEMEM is able to reproduce the observed growth patterns and that BSL is a robust tool for inference in SDEMEMs. Finally, we compare the fit of the SDEMEM to a similar ordinary differential equation model. Due to small sample sizes, strong prior information is needed to identify all model parameters in the SDEMEM and it cannot be determined which of the two models is the better in terms of predicting tumor growth curves. In a simulation study we find that with a sample of 17 mice per group BSL is able to identify all model parameters and distinguish treatment groups.

stat.AP↗

arXiv2014

Accelerating inference for diffusions observed with measurement error and large sample sizes using Approximate Bayesian Computation

In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large datasets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An Approximate Bayesian Computation (ABC) MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of "subsamples" from the assumed data generating model as well as a so-called "early rejection" strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered setup. Finally the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.

stat.CO↗