blr {bsamGP}  R Documentation 
This function fits a Bayesian linear regression model using scale invariant prior.
blr(formula, data = NULL, mcmc = list(), prior = list(), marginal.likelihood = TRUE)
formula 
an object of class “ 
data 
an optional data frame. 
mcmc 
a list giving the MCMC parameters.
The list includes the following integers (with default values in parentheses):

prior 
a list giving the prior information. The list includes the following parameters
(default values specify the noninformative prior):

marginal.likelihood 
a logical variable indicating whether the log marginal likelihood is calculated. 
This generic function fits a Bayesian linear regression model using scale invariant prior.
Let y_i
and w_i
be the response and the vector of parametric predictors, respectively.
The model for regression function is as follows.
y_i = w_i^T\beta + \epsilon_i, ~ i=1,\ldots,n,
where the error terms \{\epsilon_i\}
are a random sample from a normal distribution, N(0,\sigma^2)
.
The conjugate priors are assumed for \beta
and \sigma
:
\beta  \sigma \sim N(m_{0,\beta}, \sigma^2V_{0,\beta}), \quad \sigma^2 \sim IG\Big(\frac{r_{0,\sigma}}{2}, \frac{s_{0,\sigma}}{2}\Big)
An object of class blm
representing the Bayesian spectral analysis model fit.
Generic functions such as print
and fitted
have methods to show the results of the fit.
The MCMC samples of the parameters in the model are stored in the list mcmc.draws
and
the posterior samples of the fitted values are stored in the list fit.draws
.
The output list also includes the following objects:
post.est 
posterior estimates for all parameters in the model. 
lmarg 
log marginal likelihood. 
rsquarey 
correlation between 
call 
the matched call. 
mcmctime 
running time of Markov chain from 
#####################
# Simulated example #
#####################
# Simulate data
set.seed(1)
n < 100
w < runif(n)
y < 3 + 2*w + rnorm(n, sd = 0.8)
# Fit the model with default priors and mcmc parameters
fout < blr(y ~ w)
# Summary
print(fout); summary(fout)
# Fitted values
fit < fitted(fout)
# Plots
plot(fout)