gp_transition_matrixfor 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
Whereas the actual transition function moves the stock to a tight window around the high carrying capacity:
true transition function
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)
Fragility of parametric rigidity examples
- infer under BH and simulate under allee
- Infer ricker, simulate under BH
- Other examples?
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
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:
psgpProjected Spatial Gaussian Process (psgp) methods, Implements projected sparse Gaussian process kriging for the intamap package
spBayesspBayes fits univariate and multivariate spatial models with Markov chain Monte Carlo (MCMC).
rampsBayesian 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…
- another example (includes some data in the higher range) #7 06:49 pm 2012/12/11
- a simple multi-demensional example (no policy function yet) #7 06:43 pm 2012/12/11
- updated notes on mcmc approach #6 03:51 pm 2012/12/11
- transition matrix method for GP takes Ef, Cf explicitly now. 03:50 pm 2012/12/11
- GP that results in scorched earth fishing strategy 02:19 pm 2012/12/11