Bayesian Inference for some Time-Varying Models with Generalized Extreme Value Margins
TVGEVBayes.Rd
Bayesian inference for some Time-Varying models with GEV margins.
Usage
TVGEVBayes(
data,
timeMAXdata = NULL,
date,
response,
design = NULL,
loc = ~1,
scale = ~1,
shape = ~1,
prior = NULL,
blockDuration = "year",
sampleMiss = FALSE,
trace = 0,
...
)
Arguments
- data
A data frame containing at least the two variables: response and date, with arbitrary names.
- timeMAXdata
When given, this must be an object with class
"timeMAXdata"
specifying the largest observations for the block maxima on one or several periods, usually historical periods. SeetimeMAXdata
.- date, response
The names of the data and the response variables as in
TVGEV
.- design
A call that defines a design matrix with some functions of the
Date
variable as its columns.- loc, scale, shape
Formulas for the GEV parameters.
- prior
Not allowed yet.
- blockDuration
Not used yet.
- sampleMiss
Logical. If
TRUE
the missing values for the response are sampled. They appear in thesampleFit
element of the returned object, and ar e in relation with theind_miss
incex vector which give their position in thedata
element.- trace
Integer level of verbosity.
- ...
Further arguments to be passed to the
sampling
of the rstan package.
Value
An object with (S3) class "TVGEVBayes"
. This is
mainly a list with the following items
stanFit The object with class
"stanfit"
returned bysampling
. Caution: for now the parameter names do not match the parameter names of theTVGEVBayes
object.MCMC The array of MCMC iterates with the warm-up iterations discarded. The dimensions are: MCMC iterate, chain and parameter. The parameters have names using prefixes
"mu"
,"sigma"
and"xi"
. The remaining part of the names is given by theterms
hence conforms to what would be obtained usinglm
with the same formula. However an exception is for the intercepts. For instance the name"mu_(Intercept)"
will be replaced by"mu_0"
.
Details
The Bayesian inference relies on Markov Chain Monte Carlo (MCMC) sampling performed thanks to a Stan code. The Stan code needs to be compiled, which requires computing time.
Examples
df <- within(TXMax_Dijon, Date <- as.Date(sprintf("%4d-01-01", Year)))
## We now that a high temperature occured 1922-05-24, see
## Infoclimat where the observations "Donnees Offcielle Meteo-France"
## https://www.infoclimat.fr/climatologie/normales-records/1981-2010/dijon-longvic/valeurs/07280.html
tMD <- timeMAXdata("1922_1922" = list("1922-05-24" = c(34.4, Inf)))
## "1923_1923" = list("1923-09-01" = c(34.0, Inf)))
fit <- TVGEVBayes(data = df,
timeMAXdata = tMD,
date = "Date", response = "TXMax",
design = breaksX(date = Date, breaks = "1970-01-01", degree = 1),
loc = ~ t1 + t1_1970, scale = ~ 1, shape = ~ 1,
seed = 1234)
#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000102 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.02 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 2).
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 3).
#> Chain 3:
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#> Chain 3: Adjust your expectations accordingly!
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 4).
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#> Chain 4: Gradient evaluation took 3.1e-05 seconds
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#> Chain 4: Elapsed Time: 1.817 seconds (Warm-up)
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#> Chain 4:
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
## plot the regression mean with its 95% confidence intervals, as
## coputed using the \code{fitted method}.
autoplot(fit) + ggtitle("Kink design \"breaksX\": posterior mean")
#> Warning: Removed 9 rows containing missing values (`geom_point()`).
#> Warning: Removed 95 rows containing missing values (`geom_segment()`).
#> Warning: Removed 9 rows containing missing values (`geom_segment()`).
##' Return levels
autoplot(RL(fit)) + ggtitle("Kink design \"breaksX\": return levels")
autoplot(RL(fit, level = 0.95, smooth = TRUE)) +
ggtitle("Kink design \"breaksX\": return levels")
## predictive distribution: by default for the next block
autoplot(predict(fit)) +
ggtitle("Kink design \"breaksX\": prediction for next block")
## change the period.
autoplot(predict(fit, newTimeRange = "2020_2049")) +
ggtitle("Kink design \"breaksX\": prediction for \"2020_2049\"")
if (FALSE) {
library(shinystan)
my_sso <- launch_shinystan(fit$stanFit)
}
fit2 <- TVGEVBayes(data = df,
timeMAXdata = tMD,
date = "Date", response = "TXMax",
design = natSplineX(date = Date, knots = "1970-01-01",
boundaryKnots = c("1920-01-01", "2017-01-01")),
loc = ~ ns1 + ns2 + ns3 - 1, scale = ~ 1, shape = ~ 1,
seed = 2345)
#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 4.7e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.47 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 2).
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 3).
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#> Chain 3: Gradient evaluation took 3.4e-05 seconds
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#> Chain 3: Adjust your expectations accordingly!
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#>
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 4).
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#> Chain 4: Gradient evaluation took 3e-05 seconds
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#> Warning: There were 3 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
autoplot(fit2) + ggtitle("Natural spline design: posterior mean")
#> Warning: Removed 9 rows containing missing values (`geom_point()`).
#> Warning: Removed 95 rows containing missing values (`geom_segment()`).
#> Warning: Removed 9 rows containing missing values (`geom_segment()`).