Run eDITH with BayesianTools

Function that runs a Bayesian sampler estimating parameters of an eDITH model

Usage

run_eDITH_BT(data, river, covariates = NULL, Z.normalize = TRUE,
           use.AEM = FALSE, n.AEM = NULL, par.AEM = NULL,
           no.det = FALSE, ll.type = "norm", source.area = "AG",
           mcmc.settings = NULL, likelihood = NULL, 
       prior = NULL, sampler.type = "DREAMzs",
           tau.prior = list(spec = "lnorm", a = 0, b = Inf, 
      meanlog = log(5), sd = sqrt(log(5) - log(4))),
           log_p0.prior = list(spec="unif",min=-20, max=0),
           beta.prior = list(spec="norm",sd=1),
           sigma.prior = list(spec="unif",min=0, max=max(data$values, na.rm = TRUE)),
           omega.prior = list(spec="unif",min=1, max=10*max(data$values, na.rm = TRUE)),
           Cstar.prior = list(spec="unif",min=0, max=max(data$values, na.rm = TRUE)),
       verbose = FALSE)

Arguments

data

eDNA data. Data frame containing columns ID (index of the AG node/reach where the eDNA sample was taken) and values (value of the eDNA measurement, expressed as concentration or number of reads).

river

A river object generated via aggregate_river.

covariates

Data frame containing covariate values for all river reaches. If NULL (default option), production rates are estimated via AEMs.

Z.normalize

Logical. Should covariates be Z-normalized?

use.AEM

Logical. Should eigenvectors based on AEMs be used as covariates? If covariates = NULL, it is set to TRUE. If TRUE and covariates are provided, AEM eigenvectors are appended to the covariates data frame.

n.AEM

Number of AEM eigenvectors (sorted by the decreasing respective eigenvalue) to be used as covariates. If par.AEM$moranI = TRUE, this parameter is not used. Instead, the eigenvectors with significantly positive spatial autocorrelation are used as AEM covariates.

par.AEM

List of additional parameters that are passed to river_to_AEM for calculation of AEMs. In particular, par.AEM$moranI = TRUE imposes the use of AEM covariates with significantly positive spatial autocorrelation based on Moran's I statistic.

no.det

Logical. Should a probability of non-detection be included in the model?

ll.type

Character. String defining the error distribution used in the log-likelihood formulation. Allowed values are norm (for normal distribution), lnorm (for lognormal distribution), nbinom (for negative binomial distribution) and geom (for geometric distribution). The two latter choices are suited when eDNA data are expressed as read numbers, while norm and lnorm are better suited to eDNA concentrations.

source.area

Defines the extent of the source area of a node. Possible values are "AG" (if the source area is the reach surface, i.e. length*width), "SC" (if the source area is the subcatchment area), or, alternatively, a vector with length river$AG$nodes.

mcmc.settings

List. It is passed as argument settings in runMCMC. Default is list(iterations = 2.7e6, burnin=1.8e6, message = TRUE, thin = 10).

likelihood

Likelihood function to be passed as likelihood argument to createBayesianSetup. If not specified, it is generated based on arguments no.det and ll.type. If a custom likelihood is specified, a custom prior must also be specified.

prior

Prior function to be passed as prior argument to createBayesianSetup. If not specified, it is generated based on the *.prior arguments provided. If a user-defined prior is provided, parameter names must be included in prior$lower, prior$upper (see example).

sampler.type

Character. It is passed as argument sampler in runMCMC.

tau.prior

List that defines the prior distribution for the decay time parameter tau. See details.

log_p0.prior

List that defines the prior distribution for the logarithm (in base 10) of the baseline production rate p0. See details. If covariates = NULL, this defines the prior distribution for the logarithm (in base 10) of production rates for all river reaches.

beta.prior

List that defines the prior distribution for the covariate effects beta. See details. If a single spec is provided, the same prior distribution is specified for all beta parameters. Alternatively, if spec (and the other arguments, if provided) is a vector with length equal to the number of covariates included, different prior distributions can be specified for the different beta parameters.

sigma.prior

List that defines the prior distribution for the standard deviation of the measurement error when ll.type is "norm" or "lnorm". It is not used if ll.type = "nbinom". See details.

omega.prior

List that defines the prior distribution for the overdispersion parameter omega of the measurement error when ll.type = "nbinom". It is not used if ll.type is "norm" or "lnorm". See details.

Cstar.prior

List that defines the prior distribution for the Cstar parameter controlling the probability of no detection. It is only used if no.det = TRUE. See details.

verbose

Logical. Should console output be displayed?

Details

The arguments of the type *.prior consist in the lists of arguments required by dtrunc (except the first argument x).

By default, AEMs are computed without attributing weights to the edges of the river network. Use e.g. par.AEM = list(weight = "gravity") to attribute weights.

Value

A list with objects:

param_map

Vector of named parameters corresponding to the maximum a posteriori estimate. It is the output of the call to MAP.

p_map

Vector of best-fit eDNA production rates corresponding to the maximum a posteriori parameter estimate param_map. It has length equal to river$AG$nNodes.

C_map

Vector of best-fit eDNA values (in the same unit as data$values, i.e. concentrations or read numbers) corresponding to the maximum a posteriori parameter estimate param_map. It has length equal to river$AG$nNodes.

probDet_map

Vector of best-fit detection probabilities corresponding to the maximum a posteriori parameter estimate param_map. It has length equal to river$AG$nNodes. If a custom likelihood is provided, this is a vector of null length (in which case the user should calculate the probability of detection independently, based on the chosen likelihood).

cI

Output of the call to getCredibleIntervals.

gD

Output of the call to gelmanDiagnostics.

covariates

Data frame containing input covariate values (possibly Z-normalized).

source.area

Vector of source area values.

outMCMC

Object of class mcmcSampler returned by the call to runMCMC.

Moreover, arguments ll.type (possibly changed to "custom" if a custom likelihood is specified), no.det and data are added to the list.

Examples

data(wigger)
data(dataC)
data(dataRead)

# reduce number of iterations for illustrative purposes 
# (use default mcmc.settings to ensure convergence)
settings.short <- list(iterations = 1e3, thin = 10)
set.seed(1)
out <- run_eDITH_BT(dataC, wigger, mcmc.settings = settings.short)
#> Covariates not specified. Production rates will be estimated
#>                       based on the first n.AEM = 26 AEMs. 
#> 
 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  1718.183 1854.383 1815.865 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  1747.124 1860.675 1856.744 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  1751.218 1860.362 1858.926 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  1860.589 1860.362 1866.549 Please wait! 

#> runMCMC terminated after 1.947seconds
#> gelmanDiagnostics could not be calculated, possibly there is not enoug variance in your MCMC chains. Try running the sampler longer

# \donttest{
library(rivnet)
# best-fit (maximum a posteriori) map of eDNA production rates
plot(wigger, out$p_map)


# best-fit map (maximum a posteriori) of detection probability
plot(wigger, out$probDet_map)



# compare best-fit vs observed eDNA concentrations
plot(out$C_map[dataC$ID], dataC$values,
  xlab="Modelled (MAP) concentrations", ylab="Observed concentrations")
abline(a=0, b=1) 


## fit eDNA read number data - use AEMs as covariates
out <- run_eDITH_BT(dataRead, wigger, ll.type = "nbinom",
  par.AEM = list(weight = "gravity"),
  mcmc.settings = settings.short) # use default mcmc.settings to ensure convergence
#> Covariates not specified. Production rates will be estimated
#>                       based on the first n.AEM = 26 AEMs. 
#> 
 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  -686.9741 -665.4549 -898.7046 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  -604.4475 -612.4648 -784.337 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  -435.4761 -500.5367 -738.2181 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  -435.4761 -500.5367 -738.2181 Please wait! 

#> runMCMC terminated after 2.116seconds
#> gelmanDiagnostics could not be calculated, possibly there is not enoug variance in your MCMC chains. Try running the sampler longer

## use user-defined covariates
covariates <- data.frame(urban = wigger$SC$locCov$landcover_1,
                         agriculture = wigger$SC$locCov$landcover_2,
                         forest = wigger$SC$locCov$landcover_3,
                         elev = wigger$AG$Z,
                         log_drainageArea = log(wigger$AG$A))
             
out.cov <-   run_eDITH_BT(dataC, wigger, covariates, 
  mcmc.settings = settings.short) # use default mcmc.settings to ensure convergence
#> 
 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  1879.684 1875.527 1892.416 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  1889.913 1878.238 1892.246 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  1889.309 1888.549 1890.724 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  1898.566 1889.417 1891.649 Please wait! 

#> runMCMC terminated after 1.157seconds

# use user-defined covariates and AEMs
out.covAEM <-   run_eDITH_BT(dataC, wigger, covariates, 
  use.AEM = TRUE, par.AEM = list(weight = "gravity"),
  mcmc.settings = settings.short) # use default mcmc.settings to ensure convergence  
#> 
 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  1746.426 -29078.04 1805.56 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  1762.692 1822.293 1807.302 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  1792.439 1822.293 1807.302 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  1792.439 1822.293 1807.302 Please wait! 

#> runMCMC terminated after 2.185seconds
#> gelmanDiagnostics could not be calculated, possibly there is not enoug variance in your MCMC chains. Try running the sampler longer

# use AEMs with significantly positive spatial autocorrelation
out.AEM.moran <- run_eDITH_BT(dataC, wigger, use.AEM = TRUE,
  par.AEM = list(weight = "gravity", moranI = TRUE), 
  mcmc.settings = settings.short) # use default mcmc.settings to ensure convergence 
#> Covariates not specified. Production rates will be estimated
#>                       based on the first n.AEM = 26 AEMs. 
#> 
 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  1606.697 1600.336 -180806.9 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  1611.237 1607.149 -119385.3 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  1607.692 1607.149 -119319.6 Please wait! 

 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  1608.786 1628.349 -119319.6 Please wait! 

#> runMCMC terminated after 7.716seconds
#> gelmanDiagnostics could not be calculated, possibly there is not enoug variance in your MCMC chains. Try running the sampler longer

## use posterior sample to specify user-defined prior
library(BayesianTools)
data(outSample)
pp <- createPriorDensity(outSample$outMCMC)
# Important! add parameter names to objects lower, upper
names(pp$lower) <- names(pp$upper) <- colnames(outSample$outMCMC$chain[[1]])[1:8] 
# the three last columns are for log-posterior, log-likelihood, log-prior 
out.new <- run_eDITH_BT(dataC, wigger, covariates, prior = pp, 
  mcmc.settings = settings.short)
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 Running DREAM-MCMC, chain  1 iteration 300 of 1002 . Current logp  1277.972 998.5392 1194.398 Please wait! 

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#> 
 Running DREAM-MCMC, chain  1 iteration 600 of 1002 . Current logp  1444.823 1017.773 1358.49 Please wait! 

#> Warning: NaNs produced
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#> 
 Running DREAM-MCMC, chain  1 iteration 900 of 1002 . Current logp  1444.823 1284.865 1365.387 Please wait! 

#> Warning: NaNs produced
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#> 
 Running DREAM-MCMC, chain  1 iteration 1002 of 1002 . Current logp  1444.823 1495.063 1388.418 Please wait! 

#> runMCMC terminated after 3.522seconds
#> gelmanDiagnostics could not be calculated, possibly there is not enoug variance in your MCMC chains. Try running the sampler longer
  
# }