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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. See timeMAXdata.

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 the sampleFit element of the returned object, and ar e in relation with the ind_miss incex vector which give their position in the data 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 by sampling. Caution: for now the parameter names do not match the parameter names of the TVGEVBayes 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 the terms hence conforms to what would be obtained using lm 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).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 3.5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.35 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> 
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.3e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.
#> 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
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.
#> Chain 4: Adjust your expectations accordingly!
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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).
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#> Chain 1: Adjust your expectations accordingly!
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#> 
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 2).
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#> Chain 2: Gradient evaluation took 3.3e-05 seconds
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#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 3.4e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.34 seconds.
#> Chain 3: Adjust your expectations accordingly!
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#> 
#> SAMPLING FOR MODEL 'TVGEVCensor' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 3e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.
#> Chain 4: Adjust your expectations accordingly!
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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()`).