bsm_bc: Bayesian spline model with a Box-Cox transformation

In SeBR: Semiparametric Bayesian Regression Analysis

Bayesian spline model with a Box-Cox transformation

Description

MCMC sampling for Bayesian spline regression with a (known or unknown) Box-Cox transformation.

Usage

bsm_bc(
  y,
  x = NULL,
  x_test = x,
  psi = NULL,
  lambda = NULL,
  sample_lambda = TRUE,
  nsave = 1000,
  nburn = 1000,
  nskip = 0,
  verbose = TRUE
)

Arguments

y	n x 1 vector of observed counts
x	n x 1 vector of observation points; if NULL, assume equally-spaced on [0,1]
x_test	n_test x 1 vector of testing points; if NULL, assume equal to x
psi	prior variance (inverse smoothing parameter); if NULL, sample this parameter
lambda	Box-Cox transformation; if NULL, estimate this parameter
sample_lambda	logical; if TRUE, sample lambda, otherwise use the fixed value of lambda above or the MLE (if lambda unspecified)
nsave	number of MCMC iterations to save
nburn	number of MCMC iterations to discard
nskip	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
verbose	logical; if TRUE, print time remaining

Details

This function provides fully Bayesian inference for a transformed spline model via MCMC sampling. The transformation is parametric from the Box-Cox family, which has one parameter lambda. That parameter may be fixed in advanced or learned from the data.

Value

a list with the following elements:

• coefficients the posterior mean of the regression coefficients

• fitted.values the posterior predictive mean at the test points x_test

• post_theta: nsave x p samples from the posterior distribution of the regression coefficients

• post_ypred: nsave x n_test samples from the posterior predictive distribution at x_test

• post_g: nsave posterior samples of the transformation evaluated at the unique y values

• post_lambda nsave posterior samples of lambda

• model: the model fit (here, sbsm_bc)

as well as the arguments passed in.

Note

Box-Cox transformations may be useful in some cases, but in general we recommend the nonparametric transformation (with Monte Carlo, not MCMC sampling) in sbsm.

Examples

# Simulate some data:
n = 100 # sample size
x = sort(runif(n)) # observation points

# Transform a noisy, periodic function:
y = g_inv_bc(
  sin(2*pi*x) + sin(4*pi*x) + rnorm(n, sd = .5),
             lambda = .5) # Signed square-root transformation

# Fit the Bayesian spline model with a Box-Cox transformation:
fit = bsm_bc(y = y, x = x)
names(fit) # what is returned
round(quantile(fit$post_lambda), 3) # summary of unknown Box-Cox parameter

# Plot the model predictions (point and interval estimates):
pi_y = t(apply(fit$post_ypred, 2, quantile, c(0.05, .95))) # 90% PI
plot(x, y, type='n', ylim = range(pi_y,y),
     xlab = 'x', ylab = 'y', main = paste('Fitted values and prediction intervals'))
polygon(c(x, rev(x)),c(pi_y[,2], rev(pi_y[,1])),col='gray', border=NA)
lines(x, y, type='p')
lines(x, fitted(fit), lwd = 3)

SeBR documentation built on June 17, 2025, 1:07 a.m.