2017/12/12 by Bram Thijssen, Thijssen, Bram, Lodewyk F.A. Wessels +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1712.04200
openalex publication_date 2017/12/12 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
An important feature of Bayesian statistics is the opportunity to do\nsequential inference: the posterior distribution obtained after seeing a\ndataset can be used as prior for a second inference. However, when Monte Carlo\nsampling methods are used for inference, we only have a set of samples from the\nposterior distribution. To do sequential inference, we then either have to\nevaluate the second posterior at only these locations and reweight the samples\naccordingly, or we can estimate a functional description of the posterior\nprobability distribution from the samples and use that as prior for the second\ninference. Here, we investigated to what extent we can obtain an accurate joint\nposterior from two datasets if the inference is done sequentially rather than\njointly, under the condition that each inference step is done using Monte Carlo\nsampling. To test this, we evaluated the accuracy of kernel density estimates,\nGaussian mixtures, vine copulas and Gaussian processes in approximating\nposterior distributions, and then tested whether these approximations can be\nused in sequential inference. In low dimensionality, Gaussian processes are\nmore accurate, whereas in higher dimensionality Gaussian mixtures or vine\ncopulas perform better. In our test cases, posterior approximations are\npreferable over direct sample reweighting, although joint inference is still\npreferable over sequential inference. Since the performance is case-specific,\nwe provide an R package mvdens with a unified interface for the density\napproximation methods.\n