Implemented in BUGS/allen.md

- [x] Inverse gamma priors on variances 36888da
- [x] Uniform prior on standard deviations 75df941
- [x] Mean plot for parametric fit 75df941
[x] Convergence diagnostics for both parametric and nonparametric MCMC, using similar visual layout 75df941

Oh, Jeromy Anglim has a rather nice collection of jags links

## On Variance Priors for the Parametric MCMC

- Gelman recommends uniform priors on standard deviations for the noise terms: in the
`.bugs`

file we have

```
stdQ ~ dunif(0,100)
stdR ~ dunif(0,100)
# as "precision" tau instead of stdev sigma
iQ <- 1/(stdQ*stdQ);
iR <- 1/(stdR*stdR);
```

Where these enter the model as

```
for(t in 1:(N-1)){
mu[t] <- x[t] + exp(r0 * (1 - x[t]/K)* (x[t] - theta) )
x[t+1] ~ dnorm(mu[t],iQ)
}
for(t in 1:(N)){
y[t] ~ dnorm(x[t],iR)
}
```

Note that `dnorm`

in JAGS notation is defined in terms of the mean and the precision (reciprocal of the variance), rather than standard deviation (e.g. in R’s `dnorm`

function), see the JAGS manual, particularly Table 6.1 pg 29, below. Note that the standard deviation has the uniform prior, not the precision.

- Also try inverse gamma priors,

```
iQ ~ dgamma(0.0001,0.0001)
iR ~ dgamma(0.0001,0.0001)
```

(Precision is Gamma distributed when the variances are inverse-gamma distributed.

- Both are quite uniformative, results appear quite comparable.

## Markov Chain Monte Carlo Convergence Analysis

- Add for both parametric and non-parametric cases
- Extra long runs before finalizing analysis
- Some examples with R code

A variety of tools from `coda`

package. Of course these methods are designed from toy problems and cannot guarentee convergence.

- Traceplots, density plots
- Running mean, autocorrelation plots
`autocorr.plot`

- Metropolis acceptance/rejection rate
`rejectionRate`

- Multiple chain diagonostics: Gelman-Rubin
`gelman.diag`

,`gelman.plot`

- Geweke (compare means between different sections)
`geweke.diag`

- Raferty-Lewis
`raferty.diag`

- Heidelberg and Welch
`heidel.diag`