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. Scalable simulation-baed inference for implicitly defined models using a metamodel for Monte Carlo log-likelihood estimator. ArXiv preprint: https://arxiv.org/abs/2311.09446.

An R package 'sbim' has been developed to facilitate the use of the methods developed in this paper, available at https://cran.r-project.org/web/packages/sbim/index.html. The most up-to-date developer version is available at my Github repository https://github.com/joonhap/sbi.

Automatically-tuned, Tempered Hamiltonian Monte Carlo methods for strongly multimodal, high-dimensional 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, HMC does not perform well for strongly 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 tempering technique in a way that enables highly efficient sampling from high-dimensional, strongly multimodal distributions. This method modulates the mass of the particle being simulated, such that the particle can escape a local mode during the first half of the simulated path and converge to a possibly different local mode during the second half. An automatic tuning strategy has been developed for ready implementation.

• Park, J. Sampling from high-dimensional, multimodal target distributions using automatically tuned, tempered Hamiltonian Monte Carlo. ArXiv preprint: https://arxiv.org/abs/2111.06871.

Source code for the automatically-tuned, tempered Hamiltonian Monte Carlo (ATHMC) is available at https://github.com/joonhap/athmc.

Inference for spatio-temporal partially observed Markov processes

I am interested in developing scalable inference methods for coupled, partially observed stochastic dynamic models. Such models are frequently used in spatio-temporal metapopulation dynamics, such as the transmission of infectious disease across connected geographic regions. Methods that my collaborators and I have developed are introduced in the following papers.

• 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
• 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 and the R package spatPomp https://cran.r-project.org/web/packages/spatPomp/index.html.

• Asfaw, K., Park, J., King, A. A., & Ionides, E. L. (2024). spatPomp: An R package for spatiotemporal partially observed Markov process models. Journal of Open Source Software, 9(104), 7008. https://joss.theoj.org/papers/10.21105/joss.07008

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