LD50_MHmcmc: Metropolis-Hastings algorithm for LD50

In HelpersMG: Tools for Environmental Analyses, Ecotoxicology and Various R Functions

Metropolis-Hastings algorithm for LD50

Description

Run the Metropolis-Hastings algorithm for tsd.
Deeply modified from a MCMC script by Olivier Martin (INRA, Paris-Grignon).
The number of iterations is n.iter+n.adapt+1 because the initial likelihood is also displayed.
I recommend that thin=1 because the method to estimate SE uses resampling.
If initial point is maximum likelihood, n.adapt = 0 is a good solution.
To get the SE from result_mcmc <- tsd_MHmcmc(result=try), use:
result_mcmc$BatchSE or result_mcmc$TimeSeriesSE
The batch standard error procedure is usually thought to be not as accurate as the time series methods.
Based on Jones, Haran, Caffo and Neath (2005), the batch size should be equal to sqrt(n.iter).
Jones, G.L., Haran, M., Caffo, B.S. and Neath, R. (2006) Fixed Width Output Analysis for Markov chain Monte Carlo , Journal of the American Statistical Association, 101:1537-1547.
coda package is necessary for this function.
The parameters intermediate and filename are used to save intermediate results every 'intermediate' iterations (for example 1000). Results are saved in a file of name filename.
The parameter previous is used to indicate the list that has been save using the parameters intermediate and filename. It permits to continue a mcmc search.
These options are used to prevent the consequences of computer crash or if the run is very very long and processes at time limited.

Usage

LD50_MHmcmc(
  result = stop("A result of LD50() fit must be provided"),
  n.iter = 10000,
  parametersMCMC = NULL,
  n.chains = 1,
  n.adapt = 0,
  thin = 1,
  trace = FALSE,
  batchSize = sqrt(n.iter),
  adaptive = FALSE,
  adaptive.lag = 500,
  adaptive.fun = function(x) {
     ifelse(x > 0.234, 1.3, 0.7)
 },
  intermediate = NULL,
  filename = "intermediate.Rdata",
  previous = NULL
)

Arguments

result	An object obtained after a SearchR fit
n.iter	Number of iterations for each step
parametersMCMC	A set of parameters used as initial point for searching with information on priors
n.chains	Number of replicates
n.adapt	Number of iterations before to store outputs
thin	Number of iterations between each stored output
trace	True or False, shows progress
batchSize	Number of observations to include in each batch fo SE estimation
adaptive	Should an adaptive process for SDProp be used
adaptive.lag	Lag to analyze the SDProp value in an adaptive content
adaptive.fun	Function used to change the SDProp
intermediate	Period for saving intermediate result, NULL for no save
filename	If intermediate is not NULL, save intermediate result in this file
previous	Previous result to be continued. Can be the filename in which intermediate results are saved.

Details

LD50_MHmcmc runs the Metropolis-Hastings algorithm for LD50 (Bayesian MCMC)

Value

A list with resultMCMC being mcmc.list object, resultLnL being likelihoods and parametersMCMC being the parameters used

Author(s)

Marc Girondot [e-mail]

See Also

Other LD50 functions: LD50(), LD50_MHmcmc_p(), logLik.LD50(), plot.LD50(), predict.LD50()

Examples

## Not run: 
library("HelpersMG")
data <- data.frame(Doses=c(80, 120, 150, 150, 180, 200),
Alive=c(10, 12, 8, 6, 2, 1),
Dead=c(0, 1, 5, 6, 9, 15))
LD50_logistic <- LD50(data, equation="logistic")
pMCMC <- LD50_MHmcmc_p(LD50_logistic, accept=TRUE)
# Take care, it can be very long
result_mcmc_LD50 <- LD50_MHmcmc(result=LD50_logistic, 
		parametersMCMC=pMCMC, n.iter=10000, n.chains = 1,  
		n.adapt = 0, thin=1, trace=1000, adaptive=TRUE, )
# summary() permits to get rapidly the standard errors for parameters
summary(result_mcmc_LD50)
plot(x=result_mcmc_LD50, parameters="S", scale.prior=TRUE, las=1)
plot(result_mcmc_LD50, parameters="S", scale.prior=TRUE, las=1, xlim=c(-20, 20))
plot(result_mcmc_LD50, parameters="P", scale.prior=TRUE, las=1)
1-rejectionRate(as.mcmc(result_mcmc_LD50))
raftery.diag(as.mcmc(result_mcmc_LD50))
heidel.diag(as.mcmc(result_mcmc_LD50))

#### Example with Uniforms priors

pMCMC <- structure(list(Density = c("dunif", "dunif"), 
Prior1 = c(77.6216005852911, -31.0438095277258), 
Prior2 = c(310.486402341165, 31.0438095277258), 
SDProp = c(2, 0.5), 
Min = c(77.6216005852911, -31.0438095277258), 
Max = c(310.486402341165, 31.0438095277258), 
Init = c(155.243201170582, -15.5219047638629)), 
row.names = c("P", "S"), class = "data.frame")
result_mcmc_LD50 <- LD50_MHmcmc(result=LD50_logistic, 
		parametersMCMC=pMCMC, n.iter=10000, n.chains = 1,  
		n.adapt = 0, thin=1, trace=1000, adaptive=TRUE, )
# summary() permits to get rapidly the standard errors for parameters
summary(result_mcmc_LD50)
plot(x=result_mcmc_LD50, parameters="S", scale.prior=TRUE, las=1)
plot(result_mcmc_LD50, parameters="S", scale.prior=TRUE, las=1, xlim=c(-40, 40))
plot(result_mcmc_LD50, parameters="P", scale.prior=TRUE, las=1)
1-rejectionRate(as.mcmc(result_mcmc_LD50))
raftery.diag(as.mcmc(result_mcmc_LD50))
heidel.diag(as.mcmc(result_mcmc_LD50))


## End(Not run)

HelpersMG documentation built on Sept. 12, 2024, 9:35 a.m.