- 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

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?

## 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…

- 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