calc_prediction_intervals {bartMachine} R Documentation

## 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{σ^2} estimate of the noise variance. We then sample normal_samples_per_gibbs_sample times from a N(\hat{y}, \hat{σ^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.

### 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

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)