Run the MCMC algorithm for STAR given
a function to initialize model parameters; and
a function to sample (i.e., update) model parameters.
The transformation is modeled as an unknown, monotone function using I-splines. The Robust Adaptive Metropolis (RAM) sampler is used for drawing the parameter of the transformation function.
genMCMC_star_ispline(
y,
sample_params,
init_params,
lambda_prior = 1/2,
y_max = Inf,
nsave = 5000,
nburn = 5000,
nskip = 0,
save_y_hat = FALSE,
target_acc_rate = 0.3,
adapt_rate = 0.75,
stop_adapt_perc = 0.5,
verbose = TRUE
)A list with at least the following elements:
post.pred: draws from the posterior predictive distribution of y
post.sigma: draws from the posterior distribution of sigma
post.log.like.point: draws of the log-likelihood for each of the n observations
WAIC: Widely-Applicable/Watanabe-Akaike Information Criterion
p_waic: Effective number of parameters based on WAIC
post.g: draws from the posterior distribution of the transformation g
post.sigma.gamma: draws from the posterior distribution of sigma.gamma,
the prior standard deviation of the transformation g() coefficients
fitted.values: the posterior mean of the conditional expectation of the counts y
(NULL if save_y_hat=FALSE)
post.fitted.values: posterior draws of the conditional mean of the counts y
(NULL if save_y_hat=FALSE)
along with other elements depending on the nature of the initialization and sampling functions. See details for more info.
n x 1 vector of observed counts
a function that inputs data y and a named list
params containing at least
mu: vector of conditional means (fitted values)
sigma: the conditional standard deviation
coefficients: a named list of parameters that determine mu
and optionally a fourth element mu_test which contains the vector of conditional means
at test points. The output is an updated list params of samples from the full conditional posterior
distribution of coefficients and sigma (along with updates of mu and mu_test if applicable)
an initializing function that inputs data y
and initializes the named list params of mu, sigma, coefficients and mu_test (if desired)
the prior mean for the transformation g() is the Box-Cox function with
parameter lambda_prior
a fixed and known upper bound for all observations; default is Inf
number of MCMC iterations to save
number of MCMC iterations to discard
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
logical; if TRUE, compute and save the posterior draws of the expected counts, E(y), which may be slow to compute
target acceptance rate (between zero and one)
rate of adaptation in RAM sampler (between zero and one)
stop adapting at the proposal covariance at stop_adapt_perc*nburn
logical; if TRUE, print time remaining
If the coefficients list from init_params and sample_params contains a named element beta,
e.g. for linear regression, then the function output contains
coefficients: the posterior mean of the beta coefficients
post.beta: draws from the posterior distribution of beta
post.othercoefs: draws from the posterior distribution of any other sampled coefficients, e.g. variance terms
If no beta exists in the parameter coefficients, then the output list just contains
coefficients: the posterior mean of all coefficients
post.beta: draws from the posterior distribution of all coefficients
Additionally, if init_params and sample_params have output mu_test, then the sampler will output
post.predtest, which contains draws from the posterior predictive distribution at test points.