Bayesian Spatial Analysis of Hardwood Tree Counts in Forests via MCMC

Parallelising MCMC via Random Forests

For Bayesian computation in big data contexts, the divide-and-conquer MCMC concept splits the whole data set into batches, runs MCMC algorithms separately over each batch to produce samples of parameters, and combines them to produce an approximation of the target distribution. In this article, we embed random forests into this framework and use each subposterior/partial-posterior as a proposal distribution to implement importance sampling. Unlike the existing divide-and-conquer MCMC, our methods are based on scaled subposteriors, whose scale factors are not necessarily restricted to being equ…

通过随机森林代理的延迟接受序贯蒙特卡洛方法加速贝叶斯系统发育推断

Accelerating Bayesian Phylogenetic Inference via Delayed Acceptance Sequential Monte Carlo with Random Forest Surrogates

本文提出利用机器学习预测树移动对似然函数的影响，设计延迟接受MCMC核，结合序贯蒙特卡洛框架，提升系统发育推断效率。

Modelling Spatial Compositional Data: Reconstructions of past land cover and uncertainties

In this paper, we construct a hierarchical model for spatial compositional data, which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past $6\,000$ years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to…

$R^*$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges asymptotically to the posterior distribution, but this provides no guarantees about its performance in finite time. The predominant method for monitoring convergence is to run multiple chains and monitor individual chains' characteristics and compare these to the population as a whole: if within-chain and between-chain summaries are comparable, then this is tak…

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influen…

面向大型空间数据的快速变分贝叶斯方法

Fast Variational Bayes for Large Spatial Data

针对大规模地理空间数据分析，提出快速变分贝叶斯方法spVarBayes，通过变分法与闭式更新替代自动微分，在保持与MCMC软件spNNGP相当准确性的同时显著提升了计算速度。