Reference for Bayesian statistical methods in high dimensional settings

Question

I am starting to get a knowledge about the Bayesian methods in high dimensional settings. The following two references are what I am getting at.

Hjort, Nils Lid. "Bayesian approaches to non-and semiparametric density estimation." Preprint series. Statistical Research Report http://urn. nb. no/URN: NBN: no-23420 (1994).

Müller, Peter, and Fernando A. Quintana. "Nonparametric Bayesian data analysis." Statistical science (2004): 95-110.

Interestingly enough, most Bayesian nonparametrics/parametrics reference did not mention high dimensional setting in full details. The only work that I know of is Chap.9 of :

Ghosh, Jayanta K., Mohan Delampady, and Tapas Samanta. An introduction to Bayesian analysis: theory and methods. Springer Science & Business Media, 2007.

This is a nice short chapter with emphasis in classical hypothesis testing. However, its material is obviously a bit out-dated given the research progress in this field. A book-length treatment assuming a relatively high-level of pre-knowledge is

Frigessi, Arnoldo, et al., eds. Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014. Vol. 11. Springer, 2016.

And most high-dimensional related introduction did not give enough time to Bayesian modelling in high dimensional setting.

My question is: Are there any reference/introductory paper that allows readers to grasp a panoramic view of Bayesian procedures in high dimensional settings? Preferably it should be readable and gives a big picture instead of falling into too much technicalities.

Thanks,

Answer 1

Because it has been nine months, I want to start by answering, "No." But I want to hear about it if there's a great survey paper or book!

Then I want to point out two papers that introduce methods for parametric Bayesian modeling in high dimensions.

First, Expectation Propagation can help by using a distributed system for doing parametric Bayesian inference on "big data", including high dimensionality ("hundreds of dimensions").

"Expectation Propagation as a Way of Life". Gelman et al., 2017 http://www.stat.columbia.edu/~gelman/research/unpublished/ep_arxiv.pdf

Also, Stochastic Variational Inference can handle high dimensional data.

"Stochastic Variational Inference". Hoffman, Blei, Wang, and Paisley, 2013 https://arxiv.org/pdf/1206.7051.pdf