nsRFA (version 0.5-8)

BayesianMCMC: Bayesian MCMC frequency analysis

Description

Bayesian Markov Chain Monte Carlo algorithm for flood frequency analysis with historical information.

Usage

BayesianMCMC (xcont, xhist=NA, infhist=NA, suphist=NA, nbans=NA, seuil=NA,
               nbpas=1000, nbchaines=3, confint=c(0.05, 0.95), dist="GEV",
               parameters0=NA, varparameters0=NA)
 ## S3 method for class 'BayesianMCMC':
plot(x, which=1, ask=FALSE, ...)
 ## S3 method for class 'BayesianMCMC':
print(x, ...)

Arguments

x

object of class BayesianMCMC, output of function BayesianMCMC

xcont

vector of systematic data

xhist

vector of historical data

infhist

inferior limit for historical data

suphist

superior limit for historical data

nbans

period (in years) over which the threshold has been exceeded by historical data

seuil

threshold exceeded by historical data

nbpas

number of iterations for the MCMC algorithm

nbchaines

number of chains for the MCMC algorithm

confint

confidence limits for the flood quantiles

dist

distribution: normal "NORM", log-normal with 2 parameters "LN", Exponential "EXP", Gumbel "GUMBEL", Generalized Extreme Value "GEV", Generalized Logistic "GENLOGIS", Generalized

parameters0

initial values of the parameters for the MCMC algorithm

varparameters0

initial values of the parameter variances for the MCMC algorithm

which

a number of a vector of numbers that defines the graph to plot (see details)

ask

if TRUE, the interactive mode is run

...

other arguments

Value

• BayesianMCMC returns the following values:

  parameters matrix (nbpas)x(nbchaines) with the simulated sets of parameters with the MCMC algorithm;

  parametersML set of parameters correspondent to the maximum likelihood;

  returnperiods return periods for which quantilesML and intervals are calculated;

  quantilesML quantiles correspondent to returnperiods for the distribution whose parameters are parametersML;

  intervals confidence intervals for the quantiles quantilesML for limits confint;

  varparameters matrix (nbpas)x(nbchaines)x(number of parameters) with the simulated variances for the MCMC algorithm;

  vraisdist likelihoods for the sets parameters;

  plot.BayesianMCMC plots the following figures:

  1 data as plotting position, fitted distribution (maximum likelihood) and confidence intervals;

  2 diagnostic plot of the MCMC simulation (parameters);

  3 diagnostic plot of the MCMC simulation (likelyhood and MCMC acceptance rate);

  3 posterior distribution of parameters obtained with the MCMC simulation (cloud plots);

See Also

.

Examples

set.seed(2988)
serie <- rand.GEV(120, xi=40, alfa=20, k=-0.4)
serie100 <- serie[1:100]
serie100[serie100 < 250] <- NA
serie20 <- serie[101:120]
serie <- c(serie100, serie20)


plot(serie, type="h", ylim=c(0, 600), xlab="", ylab="Annual flood peaks [m3/s]", lwd=3)
abline(h=0)
points(serie100, col=2)

# Using only sistematic data
only_sist <- BayesianMCMC (xcont=serie20, xhist=NA, infhist=NA, suphist=NA, 
                           nbans=NA, seuil=NA,
                           nbpas=5000, nbchaines=3, 
                           confint=c(0.05, 0.95), dist="GEV")
plot(only_sist, which=c(1:3), ask=TRUE, ylim=c(1,600))



# Adding the information that the threshold 250 m3/s was exceeded 3 times in the past 100 years
with_hist_thresh <- BayesianMCMC (xcont=serie20, xhist=NA, infhist=rep(250,3), suphist=NA, 
                                  nbans=100, seuil=250,
                                  nbpas=5000, nbchaines=3, 
                                  confint=c(0.05, 0.95), dist="GEV")
plot(with_hist_thresh, which=c(1:3), ask=TRUE, ylim=c(1,600))



# Assuming that the 3 historical events are known with high uncertainty
with_hist_limits <- BayesianMCMC (xcont=serie20, xhist=NA, infhist=c(320,320,250), suphist=c(360,400,270), 
                                  nbans=100, seuil=250,
                                  nbpas=5000, nbchaines=3, 
                                  confint=c(0.05, 0.95), dist="GEV")
plot(with_hist_limits, which=c(1:3), ask=TRUE, ylim=c(1,600))



# Assuming that the 3 historical events are perfectly known
with_hist_known <- BayesianMCMC (xcont=serie20, xhist=serie100[!is.na(serie100)], infhist=NA, suphist=NA, 
                                 nbans=100, seuil=250,
                                 nbpas=5000, nbchaines=3, 
                                 confint=c(0.05, 0.95), dist="GEV")
plot(with_hist_known, which=c(1:3), ask=TRUE, ylim=c(1,600))