Run the MCMC for Bayesian trend filtering with a penalty on first (D = 1) or second (D = 2) differences of the log conditional expectation of a Negative Binomial distribution. The penalty is determined by the prior on the evolution errors, currently only the following options are available:
the dynamic horseshoe prior ('DHS');
the static horseshoe prior ('HS');
In each case, the evolution error is a scale mixture of Gaussians. Sampling is accomplished with a (parameter-expanded) Gibbs sampler, mostly relying on a dynamic linear model representation.
btf_nb(
y,
evol_error = "DHS",
D = 2,
nsave = 1000,
nburn = 1000,
nskip = 4,
mcmc_params = list("mu", "yhat", "evol_sigma_t2", "r", "dhs_phi", "dhs_mean"),
r_init = NULL,
r_sample = TRUE,
step = 1,
evol0_sample = FALSE,
evol0_sd = 10,
sigma_e = 1/sqrt(Nt),
chol0 = NULL,
computeDIC = TRUE,
offset = 0,
verbose = TRUE,
seed = NULL
)A named list with the following. One named element for each of the parameters specified in mcmc_params containing
the nsave posterior draws as a vector for scalar parameters and matrix for multivariate parameters.
An element named loglike containing a vector of the nsave evaluations of the log
likelihood of the data y with a Negative Binomial distribution defined by the current iteration conditional expectation + offset and overdispersion.
If computeDIC is TRUE, a named element for the computed value of DIC and effective parameters p_d for the data y
with a Negative Binomial distribution defined by the posterior mean of the conditional expectation + offset and posterior mean overdispersion.
the length T vector of time series observations; expected to be in the support of a Negative Binomial distribution
the evolution error distribution; must be one of 'DHS' (dynamic horseshoe prior; the default), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
degree of differencing (D = 0, D = 1, or D = 2)
number of MCMC iterations to record
number of MCMC iterations to discard (burnin)
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
character list of parameters for which we store the MCMC output; must be one or more of:
'mu' (conditional mean)
'yhat' (posterior predictive distribution)
'evol_sigma_t2' (evolution error variance)
'r' (overdispersion)
'dhs_phi' (DHS AR(1) coefficient)
'dhs_mean' (DHS AR(1) unconditional mean)
Defaults to everything.
numeric; initial value (defaults to 5) of MCMC sampling for
overdispersion parameter; must be an integer if r_sample is 'int_mh' or
NULL (initializes to default of 5)
logical; If TRUE (default), the overdispersion is sampled,
else it is fixed at r_init;
numeric (defaults to 1); step length of proposal distribution for
Metropolis-Hasting sampling of overdispersion parameter; ignored if r_sample is FALSE
logical; if TRUE (default), the prior variance of the initial D values of mu is sampled,
else it is fixed at evol0_sd
numeric; initial value (defaults to 10) or the fixed prior standard deviation
for the initial D values of mu
numeric; scale value (defaults to 1/sqrt(T)) for half-Cauchy prior on global variance parameter
logical; If anything except NULL (the default), the Cholesky term of the log volatility is precomputed
logical; if TRUE, compute the deviance information criterion DIC
and the effective number of parameters p_d
length T vector of offset values for the log conditional expectation
logical; If TRUE (the default), time remaining is printed to console
optional seed for random number generation for reproducible results