Coupled to MCMC schemes for ABC
Description
This function implements three different algorithms to perform coupled to MCMC ABC.
Usage
1 2 3 
Arguments
method 
a character string indicating the ABCMCMC algorithm to be used. Possible values are 
model 
a 
prior 
a list of prior information. Each element of the list corresponds to a model parameter. The list element must be a vector whose first argument determines the type of prior distribution: possible values are 
summary_stat_target 
a vector containing the targeted (observed) summary statistics. 
prior_test 
a string expressing the constraints between model parameters.
This expression will be evaluated as a logical expression, you can use all the logical operators including 
n_rec 
a positive integer equal to the desired number of sampled points along the MCMC. 
n_between_sampling 
a positive integer equal to the desired spacing between sampled points along the MCMC. 
n_cluster 
a positive integer. If larger than 1 (the default value), 
use_seed 
logical. If 
verbose 
logical. 
dist_weights 
a vector containing the weights to apply to the distance between the computed and the targeted statistics. These weights can be used to give more importance to a summary statistisc for example. The weights will be normalized before applying them. If not provided, no weights will be applied. 
... 
Additional arguments can be passed depending on the choosen method (see below) 
Details
See the package's vignette for details on ABCMCMC.
Value
The returned value is a list containing the following components:
param 
The model parameters used in the 
stats 
The summary statistics obtained at the end of the 
dist 
The distance of the simulations to the data. 
stats_normalization 
The standard deviation of the summary statistics across the 
epsilon 
The final maximal distance between simulations and data in the retained sample of particles. 
nsim 
The number of 
n_between_sampling 
The spacing between two sampled points in the MCMC. 
computime 
The computing time to perform the simulations. 
min_stats 
The minimal values of each summary statistics during the calibration step, given when 
max_stats 
The maximal values of each summary statistics during the calibration step, given when 
lambda 
The lambda values of the BoxCox transformation, given when 
geometric_mean 
The geometric means, given when 
boxcox_mean 
The means of BoxCox transforms, given when 
boxcox_sd 
The standard deviations of BoxCox transforms, given when 
pls_transform 
The matrix of PLS transformation, given when 
numcomp 
The number of used components for the PLS transformation, given when 
Additional parameters
Depending on the choosen method, you can specify the following arguments:
 dist_max

a positive number, used when
method
is"Marjoram_original"
. This is the tolerance threshold used during the MCMC. If not provided by the user, it is automatically computed as half the distance between the first simulation and the target summary statistics and a warning is printed.  tab_normalization

a vector of the same length as
summary_stat_target
, used whenmethod
is"Marjoram_original"
. Each element contains a positive number by which each summary statistics must be divided before the computation of the Euclidean distance between simulations and data. If not provided by the user, the simulated summary statistics are divided by the target summary statistics and a warning is printed.  proposal_range

a vector of the same length as the number of model parameters, used when
method
is"Marjoram_original"
. Each element contains a positive number defining the range of MCMC jumps for each model parameter. If not provided by the user, a default value is used for each parameter and a warning is printed. The default value is 1/50 of the prior range for uniform distributions, 1/20 of the standard deviation of the prior distribution for normal distributions, 1/20 * exp ( sigma * sigma
for lognormal distributions where sigma is the standard deviation of the prior distribution in the log scale, and 1/20 of the inverse of the rate for exponential distributions.
 n_calibration

a positive integer, used when
method
is"Marjoram"
or"Wegmann"
. This is the number of simulations performed during the calibration step. Default value is 10000.  tolerance_quantile

a positive number between 0 and 1 (strictly), used when
method
is"Marjoram"
or"Wegmann"
. This is the percentage of simulations retained during the calibration step to determine the tolerance threshold to be used during the MCMC. Default value is 0.01.  proposal_phi

a positive number, used when
method
is"Marjoram"
or"Wegmann"
. This is a scaling factor defining the range of MCMC jumps. Default value is 1.  numcomp

a positive integer, used when
method
is"Wegmann"
. This is the number of components to be used for PLS transformations. Default value is 0 which encodes that this number is equal to the number of summary statistics.  seed_count

a positive integer, the initial seed value provided to the function
model
(ifuse_seed=TRUE
). This value is incremented by 1 at each call of the functionmodel
.  progress_bar

logical,
FALSE
by default. IfTRUE
,ABC_mcmc
will output a bar of progression with the estimated remaining computing time. Option not available with multiple cores.  max_pick

a positive number, the max number of fails when moving particle inside the prior. Enabled only if inside_prior is to
TRUE
.10000
by default.
Author(s)
Franck Jabot, Thierry Faure and Nicolas Dumoulin
References
Marjoram, P., Molitor, J., Plagnol, V. and Tavar\'e, S. (2003) Markov chain Monte Carlo without likelihoods. PNAS, 100, 15324–15328.
Wegmann, D., Leuenberger, C. and Excoffier, L. (2009) Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood. Genetics, 182, 12071218.
See Also
binary_model
, binary_model_cluster
, ABC_rejection
, ABC_emulation
, ABC_sequential
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81  ## Not run:
##### EXAMPLE 1 #####
#####################
## the model has two parameters and outputs two summary statistics.
## defining a simple toy model:
toy_model<function(x){ c( x[1] + x[2] + rnorm(1,0,0.1) , x[1] * x[2] + rnorm(1,0,0.1) ) }
## define prior information
toy_prior=list(c("unif",0,1),c("normal",1,2))
# a uniform prior distribution between 0 and 1 for parameter 1, and a normal distribution
# of mean 1 and standard deviation of 2 for parameter 2.
## define the targeted summary statistics
sum_stat_obs=c(1.5,0.5)
## to perform the Marjoram et al. (2003)'s method:
##
ABC_Marjoram_original<ABC_mcmc(method="Marjoram_original", model=toy_model, prior=toy_prior,
summary_stat_target=sum_stat_obs)
ABC_Marjoram_original
## artificial example to perform the Marjoram et al. (2003)'s method, with modifications
# drawn from Wegmann et al. (2009) without BoxCox and PLS transformations.
##
ABC_Marjoram<ABC_mcmc(method="Marjoram", model=toy_model, prior=toy_prior,
summary_stat_target=sum_stat_obs)
ABC_Marjoram
## artificial example to perform the Wegmann et al. (2009)'s method.
##
ABC_Wegmann<ABC_mcmc(method="Wegmann", model=toy_model, prior=toy_prior,
summary_stat_target=sum_stat_obs)
ABC_Wegmann
##### EXAMPLE 2 #####
#####################
## this time, the model is a C++ function packed into a R function  this time,
# the option 'use_seed' must be turned to TRUE.
## define prior information
trait_prior=list(c("unif",3,5),c("unif",2.3,1.6),c("unif",25,125),c("unif",0.7,3.2))
trait_prior
## define the targeted summary statistics
sum_stat_obs=c(100,2.5,20,30000)
## artificial example to perform the Marjoram et al. (2003)'s method.
##
n=10
ABC_Marjoram_original<ABC_mcmc(method="Marjoram_original", model=trait_model,
prior=trait_prior, summary_stat_target=sum_stat_obs, n_rec=n, use_seed=TRUE)
ABC_Marjoram_original
## artificial example to perform the Marjoram et al. (2003)'s method, with modifications
# drawn from Wegmann et al. (2009) without BoxCox and PLS transformations.
##
n=10
n_calib=10
tol_quant=0.2
ABC_Marjoram<ABC_mcmc(method="Marjoram", model=trait_model, prior=trait_prior,
summary_stat_target=sum_stat_obs, n_rec=n, n_calibration=n_calib,
tolerance_quantile=tol_quant, use_seed=TRUE)
ABC_Marjoram
## artificial example to perform the Wegmann et al. (2009)'s method.
##
n=10
n_calib=10
tol_quant=0.2
ABC_Wegmann<ABC_mcmc(method="Wegmann", model=trait_model, prior=trait_prior,
summary_stat_target=sum_stat_obs, n_rec=n, n_calibration=n_calib,
tolerance_quantile=tol_quant, use_seed=TRUE)
ABC_Wegmann
## End(Not run)

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