calc_prediction_intervals {bartMachine}

Calculate Prediction Intervals

Description

Generates prediction intervals for \hat{y} for a specified set of observations.

Usage

calc_prediction_intervals(bart_machine, new_data, 
pi_conf = 0.95, num_samples_per_data_point = 1000)

Arguments

bart_machine

An object of class “bartMachine”.

new_data

A data frame containing observations at which prediction intervals for \hat{y} are to be computed.

pi_conf

Confidence level for the prediction intervals. The default is 95%.

num_samples_per_data_point

The number of samples taken from the predictive distribution. The default is 1000.

Details

Credible intervals (see calc_credible_intervals) are the appropriate quantiles of the prediction for each of the Gibbs samples post-burn in. Prediction intervals also make use of the noise estimate at each Gibbs sample and hence are wider. For each Gibbs sample, we record the \hat{y} estimate of the response and the \hat{\sigma^2} estimate of the noise variance. We then sample normal_samples_per_gibbs_sample times from a N(\hat{y}, \hat{\sigma^2}) random variable to simulate many possible disturbances for that Gibbs sample. Then, all normal_samples_per_gibbs_sample times the number of Gibbs sample post burn-in are collected and the appropriate quantiles are taken based on the confidence level, pi_conf.

Value

Returns a matrix of the lower and upper bounds of the prediction intervals for each observation in new_data.

Note

This function is parallelized by the number of cores set in set_bart_machine_num_cores.

Author(s)

Adam Kapelner and Justin Bleich

References

Adam Kapelner, Justin Bleich (2016). bartMachine: Machine Learning with Bayesian Additive Regression Trees. Journal of Statistical Software, 70(4), 1-40. doi:10.18637/jss.v070.i04

See Also

calc_credible_intervals, bart_machine_get_posterior

Examples

## Not run: 
#generate Friedman data
set.seed(11)
n  = 200 
p = 5
X = data.frame(matrix(runif(n * p), ncol = p))
y = 10 * sin(pi* X[ ,1] * X[,2]) +20 * (X[,3] -.5)^2 + 10 * X[ ,4] + 5 * X[,5] + rnorm(n)

##build BART regression model
bart_machine = bartMachine(X, y)

#get prediction interval
pred_int = calc_prediction_intervals(bart_machine, X)
print(head(pred_int))

## End(Not run)