MCMCc4photo: Markov chain Monte Carlo for C4 photosynthesis parameters
In BioCro: Simulation of Biomass Crops

Description Usage Arguments Value References Examples

This function implement Markov chain Monte Carlo methods for the C4 photosynthesis model of Collatz et al. The chain is constructed using a Gaussian random walk. The value of this function is in the possibility of examining the empirical posterior distribution (i.e. vectors) of the vmax and alpha parameters. Notice that you will get different results each time you run it.

MCMCc4photo(data, niter = 20000, op.level=1, ivmax = 39, ialpha = 0.04, ikparm =
           0.7, itheta = 0.83, ibeta = 0.93, iRd = 0.8, Catm = 380, b0 = 0.08,
           b1 = 3, stress = 1, ws = c("gs", "vmax"), scale = 1,
           sds = c(1, 0.005, 0.5), prior=c(39,10,0.04,0.02,3,1))

`data`	observed assimilation data, which should be a data frame or matrix. The first column should be observed net assimilation rate (micro mol per meter squared per second). The second column should be the observed quantum flux (micro mol per meter squared per second). The third column should be observed temperature of the leaf (Celsius). The fourth column should be the observed relative humidity in proportion (e.g. 0.7).
`niter`	number of iterations to run the chain for (default = 20000).
`op.level`	should be 1 (default) for optimization of vmax and alpha and 2 for optimization of vmax, alpha and rd.
`ivmax`	initial value for Vcmax (default = 39).
`ialpha`	initial value for alpha (default = 0.04).
`ikparm`	initial value for kparm (default = 0.7). Not optimized at the moment.
`itheta`	initial value for theta (default = 0.83). Not optimized at the moment.
`ibeta`	initial value for beta (default = 0.93). Not optimized at the moment.
`iRd`	initial value for dark respiration (default = 0.8).
`Catm`	see `c4photo` function.
`b0`	see `c4photo` function.
`b1`	see `c4photo` function.
`stress`	see `c4photo` function.
`ws`	see `c4photo` function.
`scale`	This scale parameter controls the size of the standard deviations which generate the moves in the chain.
`sds`	Finer control for the standard deviations of the proposal distributions. The first element is for vmax, the second for alpha and the third for rd. The proposed elements are forced to be positive as negative parameters are not meaningful.
`prior`	Vector of length 6 with first element prior mean for vmax, second element prior standard deviation for vmax, third element prior mean for alpha, fourth element prior standard deviation for alpha, fifth element prior mean for rd and sixth element for prior standard deviation for rd.

an object of class MCMCc4photo with components

`accept`	number of accepted moves in the chain.
`resuMC`	matrix of dimensions `niter` by 3 containing the values for Vmax and alpha and the RSS in each iteration of the chain.

Brooks, Stephen. (1998). Markov chain Monte Carlo and its application. The Statistician. 47, Part 1, pp. 69-100.

## Not run: 
## Using Beale, Bint and Long (1996)
data(obsBea)

## Different starting values
resB1 <- MCMCc4photo(obsBea, 100000, scale=1.5)
resB2 <- MCMCc4photo(obsBea, 100000, ivmax=25, ialpha=0.1, scale=1.5)
resB3 <- MCMCc4photo(obsBea, 100000, ivmax=45, ialpha=0.02, scale=1.5)

## Use the plot function to examine results
plot(resB1,resB2,resB3)
plot(resB1,resB2,resB3,plot.kind="density",burnin=1e4)

## It is possible to plot the predicted and observed for one object

data(aq)
aq5 <- subset(aq, ID == 5)
res.aq5 <- MCMCc4photo(aq5[,3:6], 1e4, scale=1.5)
## The line below takes a long time because it runs a prediction
## for each of the possible values for the parameters
plot(res.aq5, plot.kind = "OandF", burnin=1e3)


## End(Not run)