Joonha Park

My recent work

Simulation-based inference for implicitly defined models

Simulation models defined implicitly via computer algorithms or specified rules for physical experiments are used increasingly often for various applications. I developed a theoretical foundation for statistical inference for implicilty defined models using a concept of simulation metamodel. Hypothesis tests can be carried out using this simulation metamodel. The inference procedure critically depends on a local asymptotic normality (LAN) result satisfied by the expectation function of a simulation-based log-likelihood estimator. This method can enable accurate parameter estimation and uncertainty quantification for partially observed, implicilty defined, stochastic models. For instance, it can be used for complex mechanistic models for partially observed Markov processes, where the bootstrap particle filter can give a simulation-based likelihood estimator, although the application area can be much broader than this class of models.

• Park, J. (2023) On simulation-based inference for implicitly defined models. ArXiv preprint: https://arxiv.org/abs/2311.09446.

An R package implementing the methods developed in this paper is available at https://github.com/joonhap/sbi.

Hamiltonian Monte Carlo methods for strongly multimodal distributions

Hamiltonian Monte Carlo (HMC) methods have favorable scaling properties with respect to the space dimensions, and thus have become popular tools for data analysis in many fields. However, one of the great weaknesses of HMC is that it does not perform well for multimodal target distributions. The Markov chains constructed by HMC methods typically have poor global mixing if the target distribution is multimodal. I have developed a method that combines HMC and the tempered transitions method, so that sampling from high-dimensional, strongly multimodal distributions can be carried out.

• Park, J. (2021) Sampling from multimodal target distributions using tempered Hamiltonian transitions. ArXiv preprint: https://arxiv.org/abs/2111.06871.

Source code for the tempered Hamiltonian transitions method is available at https://github.com/joonhap/tht_source.

An automated and adaptively tuned tempered Hamiltonian transitions method is currently under development.

Inference for spatio-temporal partially observed Markov processes

I have been developing a moderately scalable inference methodology for coupled stochastic dynamic models, such as those arising from spatio-temporal transmission dynamics of infectious diseases. Here is a recently published paper:

• Park, J. and Ionides, E. L. (2020) Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter. Statistics and Computing, doi: 10.1007/s11222-020-09957-3. view-only version available at https://rdcu.be/b5bMj

The implementation of related methods, including the codes and the data, can be found at the Github repository https://github.com/joonhap/GIRF.git.

• An R package SpatPomp is available (under continual developments) https://github.com/kidusasfaw/spatPomp. This package enables the users to define their models at an abstract level, and analyze data by using statistical methodologies. The SpatPomp package is an extension of the pomp package, and is developed for coupled, partially observed, Markov process models.

A more recent work on bagged filters can be found below. This paper utilizes the weak interaction assumption between different spatial units to construct accurate and low-variance log likelihood estimates.

• Ionides, E. L., Asfaw, K., Park, J., and King, A. A. (2021) Bagged filters for partially observed interacting systems, Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1974867

Markov chain Monte Carlo with sequential proposals (sp-MCMC):

A straightforward extension of the Metropolis-Hastings strategy in constructing Markov chains with a target invariant density can be made by allowing sequential proposals. The acceptance/rejection of the sequential proposals are coupled via a shared critical value which is drawn from the uniform(0,1) distribution.

This sequential-proposal framework is flexible, and enables developments of state-of-the-art algorithms. For example, we developed two variants of the NUTS algorithm, and a discrete-time bouncy particle sampler method. For more information, see the following paper.

• Park, J. and Atchadé, Y. (2020) Markov chain Monte Carlo algorithms with sequential proposals. Statistics and Computing, doi:10.1007/s11222-020-09948-4. view-only version available at (https://rdcu.be/b494g](https://rdcu.be/b494g)

• The implementation of the algorithms discussed in this paper can be found at https://github.com/joonhap/spMCMC.

Other published papers

• Ionides, E. L., Breto, C., Park, J., Smith, R. A. and King, A. A. (2017) Monte Carlo profile confidence intervals for dynamic systems. Journal of The Royal Society Interface, 14, 20170126. https://doi.org/10.1098/rsif.2017.0126

• Koopman, J. S., Henry, C. J., Park, J., Eisenberg, M. C., Ionides, E. L. and Eisenberg, J. N. (2017) Dynamics affecting the risk of silent circulation when oral polio vaccination is stopped. Epidemics. https://doi.org/10.1016/j.epidem.2017.02.013

• Kim, S.-H., Park, J. H., Yoon, W., Ra, W.-S. and Whang, I.-H. (2017) A note on sensor arrangement for long-distance target localization. Signal Processing, 133, 18–31. https://doi.org/10.1016/j.sigpro.2016.10.011

ArXiv preprints and manuscripts under preparation:

• Asfaw, L., Park, J., King, A. A., Ionides, E. L. (2023) Partially observed Markov processes with spatial structure via the R package spatPomp. Manuscript submitted for publication