calc_prediction_intervals: 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.

Value

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

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.

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

Examples

Run this code

## 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)

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