Show HN: Deterministic objective Bayesian inference for spatial models [pdf]

To give some context, objective Bayesian inference refers to Bayesian analysis (i.e. integrating over the parameter space) using a prior that is design to represent "minimal information" (see [1], [2], and [3] for an overview). Particularly in cases where a model's likelihood function is not strongly peaked about a point, objective Bayesian inference can give better results than methods based off of point estimates like Maximum Likelihood [4].

Reference priors provides a general approach to construct so-called noninformative priors that are suitable for Objective Bayesian analysis ([5], [6]). The approach takes a practical viewpoint of noninformative priors and looks to build priors that are both tractable and provide good performance on frequentist coverage simulations. See Section 2 for a description of how the process and frequentist simulations work and [7] for examples with some basic models (e.g. why 1/σ^2 is the noninformative prior for the variance of normally distributed data with known mean).

[8] was the first to develop reference priors for Gaussian processes models, and [9] extended the work to handle Gaussian Processes with noise (or nugget effects).

The project I'm working on provides software and algorithms to do deterministic inference using the prior from [9]. Typically, such inference has been done using MCMC sampling algorithms; but my belief is that deterministic algorithms can give results that are more consistent, less sensitive to parameter tweaking, and more efficient, at the expense of some engineering cost and loss of generality.

For an example of how the algorithms work on a real-world data set of zinc measurements in a flood plain along the Meuse river [10], see https://github.com/rnburn/bbai/blob/master/example/11-meuse-...

References [1]: https://blogs.kent.ac.uk/jonw/files/2015/04/Berger2005.pdf [2]: https://projecteuclid.org/journals/bayesian-analysis/volume-... [3]: https://www.uv.es/~bernardo/OBayes.pdf [4]: https://projecteuclid.org/journals/statistical-science/volum... [5]: https://www2.stat.duke.edu/~berger/papers/ref-development.pd... [6]: https://www.uv.es/~bernardo/2009Annals.pdf [7]: https://github.com/rnburn/bbai/blob/master/example/09-covera... [8]: https://www.tandfonline.com/doi/abs/10.1198/0162145017533822... [9]: https://www.sciencedirect.com/science/article/pii/S0047259X1... [10]: https://cran.r-project.org/web/packages/gstat/vignettes/gsta...