Application of {Approximate} {Bayesian} {Computation} algorithms for parameter estimation for {Gibbs} point processes based on partly missing data

@inproceedings{Gillot2025RM,
 abstract = {In galactic patterns, some of the data is often missing and methods to characterise such patterns need to be developed. Here, we concentrate on the special case where the point process describing the locations of galaxies is a Gibbs point process and takes place on the bounded region W = WX ∪ WY but it can be observed only in the region WY . In this situation, the likelihood of the underlying point process cannot be derived from the available observations, unless simulated data is produced via Markov Chain Monte Carlo (MCMC) procedures in the region WX , where direct observations are not available. This operation increases the general computational cost and the convexity of the likelihood can not be guaranteed. In order to overcome this drawback, we propose to use an Approximate Bayesian Computation (ABC) framework to estimate the model parameters based on partly missing data. This framework allows a theoretical construction of Metropolis-Hastings dynamics that samples from the joint distribution of the unobserved pattern and the parameter of interest, conditionally on the observed data. The theoretical properties of the proposed dynamics enable the construction of different approximate algorithms that exhibit good convergence properties. The proposed method is applied to simulated and real data.},
 author = {Gillot, N and Stoica, R S and Sarkka, A and Gemmerle, D},
 booktitle = {2025 {RING} meeting},
 language = {en},
 pages = {244--260},
 publisher = {ASGA},
 title = {Application of {Approximate} {Bayesian} {Computation} algorithms for parameter estimation for {Gibbs} point processes based on partly missing data},
 year = {2025}
}