GMCMC.RdThese functions provide a quite general infrastructure for sampling BAMLSS. The default proposal function is based on iteratively weighted least squares (IWLS), however, each model term may have a different updating function, see the details.
## Sampler functions:
sam_GMCMC(x, y, family, start = NULL, weights = NULL, offset = NULL,
n.iter = 1200, burnin = 200, thin = 1, verbose = TRUE,
step = 20, propose = "iwlsC_gp", chains = NULL, ...)
GMCMC(x, y, family, start = NULL, weights = NULL, offset = NULL,
n.iter = 1200, burnin = 200, thin = 1, verbose = TRUE,
step = 20, propose = "iwlsC_gp", chains = NULL, ...)
## Propose functions:
GMCMC_iwls(family, theta, id, eta, y, data,
weights = NULL, offset = NULL, ...)
GMCMC_iwlsC(family, theta, id, eta, y, data,
weights = NULL, offset = NULL, zworking, resids, rho, ...)
GMCMC_iwlsC_gp(family, theta, id, eta, y, data,
weights = NULL, offset = NULL, zworking, resids, rho, ...)
GMCMC_slice(family, theta, id, eta, y, data, ...)For function bfit() the x list, as returned from function
bamlss.frame, holding all model matrices and other information that is used for
fitting the model. For the updating functions an object as returned from function
smooth.construct or smoothCon.
The model response, as returned from function bamlss.frame.
A bamlss family object, see family.bamlss.
A named numeric vector containing possible starting values, the names are based on
function parameters.
Prior weights on the data, as returned from function bamlss.frame.
Can be used to supply model offsets for use in fitting,
returned from function bamlss.frame.
Sets the number of MCMC iterations.
Sets the burn-in phase of the sampler, i.e., the number of starting samples that should be removed.
Defines the thinning parameter for MCMC simulation. E.g., thin = 10 means,
that only every 10th sampled parameter will be stored.
Print information during runtime of the algorithm.
How many times should algorithm runtime information be printed, divides n.iter.
Sets the propose function for model terms, e.g. for a term s(x) in the model
formula. Per default this is set to "iwlsC", a character pointing to the set of propose
functions, see above. Other options are "iwls" and "slice", however, this is
more experimental and should not be set by the user. Another option is to pass a full propose
function which should be used for each model term, the structure of propose functions is
described in the details below. Model terms may also have different propose functions, see
the example section.
How many chains should be started? Chains a sampled sequentially!
The current state of parameters, provided as a named list. The first level
represents the parameters of the distribution, the second level the parameters of
the model terms. E.g., using the gaussian_bamlss family object
theta[["mu"]][["s(x)"]] extracts the current state of a model term "s(x)"
of the "mu" parameter. Extraction is done with the id argument.
The parameter identifier, a character vector of length 2. The first character specifies the current distributional parameter, the second the current model term.
The current value of the predictors, provided as a named list, one list entry
for each parameter. The names correspond to the parameter names in the family object,
see family.bamlss. E.g., when using the gaussian_bamlss family
object, the current values for the mean can be extracted by eta\$mu and for the
standard deviation by eta\$sigma.
An object as returned from function
smooth.construct or smoothCon. The object is
preprocessed by function bamlss.engine.setup.
Preinitialized numeric vector of length(y), only for internal usage.
Preinitialized numeric vector of length(y), only for internal usage.
An environment, only for internal usage.
Arguments passed to function bamlss.engine.setup and to the
propose functions.
The sampler function sam_GMCMC() cycles through all distributional parameters and corresponding
model terms in each iteration of the MCMC chain. Samples of the parameters of a model term (e.g.,
s(x)) are generated by proposal functions, e.g. GMCMC_iwls().
The default proposal function that should be used for all model terms is set with argument
propose. For smooth terms, e.g. terms created with function s, if
a valid propose function is supplied within the extra xt list, this propose function will
be used. This way each model term may have its own propose function for creating samples
of the parameters. See the example section.
The default proposal function GMCMC_iwlsC_gp allows for general priors for the
smoothing variances and general penalty functions. Samples of smoothing variances are computed
using slice sampling. Function GMCMC_iwlsC samples smoothing variances of univariate terms
assuming an inverse gamma prior. Terms of higher dimensions use again slice sampling for creating
samples of smoothing variances.
Function GMCMC_iwls is similar to function GMCMC_iwlsC but uses plain R code.
Function GMCMC_slice applies slice sampling also for the regression coefficients and
is therefore relatively slow.
The function returns samples of parameters, depending on the return value of the propose functions
other quantities can be returned. The samples are provided as a mcmc matrix.
If chains > 1, the samples are provided as a mcmc.list.
Umlauf N, Klein N, Zeileis A (2016). Bayesian Additive Models for Location Scale and Shape (and Beyond). (to appear)
if (FALSE) ## Simulated data example illustrating
## how to call the sampler function.
## This is done internally within
## the setup of function bamlss().
d <- GAMart()
f <- num ~ s(x1, bs = "ps")
bf <- bamlss.frame(f, data = d, family = "gaussian")
#> Error in eval(expr, envir, enclos): object 'd' not found
## First, find starting values with optimizer.
opt <- with(bf, bfit(x, y, family))
#> Error in eval(expr, envir, enclos): object 'bf' not found
## Sample.
samps <- with(bf, sam_GMCMC(x, y, family, start = opt$parameters))
#> Error in eval(expr, envir, enclos): object 'bf' not found
plot(samps)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'samps' not found