Nonparametric Bayes Notes

  • Code gp_transition_matrix for generic multi-dimensional case

Understanding Gaussian Process performance

If the estimated recruitment dynamics correspond to population dynamics that are non-persistent (might call this non self-sustaining, but in a rather stricter sense than when Reed (1979) introduced that term), and if no reward is offered at the terminal time point for a standing stock (zero scrap value), the GP dictates the rather counter-intuitive practice of simply removing the stock entirely.

Exploring this by comparing evolution of the probability density for the population size under the transition function. Consider this example from a May1979 model (full run in may1979-example.md): The Gaussian process infers a rather pessemistic evolution of the probabilty density (grey distribution becomes black distribution when unharvested, 20 years (OptTime)):

GP transition function

plot of chunk gp-F-sim
plot of chunk gp-F-sim

Whereas the actual transition function moves the stock to a tight window around the high carrying capacity:

true transition function

plot of chunk par-F-sim
plot of chunk par-F-sim

Often this results in a policy function that harvests all the fish, since they won’t persist. Exploring approaches to avoid such solutions, such as adding a reward for leaving some standing stock at the boundary time (issue #10).

Multi-species examples (issue #7)

multidimensional.md

Fragility of parametric rigidity examples

  • infer under BH and simulate under allee
  • Infer ricker, simulate under BH
  • Other examples?

MCMC

Examples of controlling priors, resulting posteriors. See yesterday’s notes for details

additional R software support

Have been focusing recently on the MCMC implementation for treed Gaussian Processes, provided in the tgp package.

Lots of various implementations of Gaussian Proccesses in R in geospatial stats packages (e.g. Kriging implementations) including some the offer fully heirachical Bayesian approaches with a variety of twists:

  • psgp Projected Spatial Gaussian Process (psgp) methods, Implements projected sparse Gaussian process kriging for the intamap package
  • gstat
  • geoR
  • spBayes spBayes fits univariate and multivariate spatial models with Markov chain Monte Carlo (MCMC).
  • ramps Bayesian geostatistical modeling of Gaussian processes using a reparameterized and marginalized posterior sampling (RAMPS) algorithm designed to lower autocorrelation in MCMC samples. Package performance is tuned for large spatial datasets.

From the commit log…