Cox processes provide a principled Bayesian nonparametric framework for modeling event-based data through an underlying intensity function. However, existing inference methods for estimating the intensity typically rely on computationally expensive Markov chain Monte Carlo sampling or approximate inference techniques. In addition, to ensure tractability, these methods often define priors over indirect latent structures, making them challenging to interpret. In this paper, we introduce the Martingale Posterior Cox Process (MPCP), which recasts Bayesian intensity estimation as inference over unobserved events given the observed event history. This perspective avoids the need to define complex priors while retaining the flexibility of nonparametric modeling. We propose a scalable, GPU-friendly copula-based predictive update, and provide strong theoretical guarantees for the convergence of the predictive resampling algorithm. Empirically, we show that MPCP provides excellent performance in both simulations and real data at a fraction of the computational cost of competing Bayesian approaches.
Martingale posteriors and related predictive resampling methods replace the likelihood--prior pair used within Bayesian inference with a predictive model for future observations. These methods are simple to implement and increasingly popular due to their computational efficiency, but little is known about their ability...
Hui Wang, Edwin Fong, David T. Frazier· 0 citations
The Bayesian approach to inverse problems provides a powerful framework for inferring unknown parameters from noisy observations. Among the computationally most challenging statistical inference problems are problems with intractable likelihoods, especially if no unbiased likelihood estimator is available. We focus on...
Josef Martínek, Julian Hofstadler, Alexander M. G. Cox et al.· 0 citations
Statistical analysis of spatial point patterns often needs to deal with heterogeneous structures in intensity function estimation with possibly high‐dimensional covariate space. Likelihood based inference for spatial point process models needs to address the challenges in evaluating the multidimensional integral of...
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference---Markov chain Monte Carlo (MCMC)---is sequential, yields correlated samples, and must be rerun for each new observation. Conditional flow matching offers an amortized alternative: a...
Jan Blechschmidt, O. Ernst, Moritz Poguntke et al.· 0 citations
Bayesian nonparametric regression methods have wide applications in statistics and machine learning, but inference can often be expensive or require approximations. This paper introduces a class of recursive moment function updates which are closed form, interpretable, expedient, and fully quantify Bayesian uncertainty...
Peter Liu, Andrew Yiu, Edwin Fong· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
