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Vector of continous responses for training data

Vector containing the number of observations per subject in the training data.

Vector of lengthlength(Y_train) that records which subject contributed each observation. Subjects should be numbered sequentially from 1 tolength(ni_train).

Matrix of covariates for training observations. Do not include intercept as the first column.

Matrix of continuous modifiers for training data. Note, modifiers must be rescaled to lie in the interval [-1,1]. Default is a 1x1 matrix, which signals that there are no continuous modifiers in the training data.

Integer matrix of categorical modifiers for training data. Note categorical levels should be 0-indexed. That is, if a categorical modifier has 10 levels, the values should run from 0 to 9. Default is a 1x1 matrix, which signals that there are no categorical modifiers in the training data.

Matrix of covariate for testing observations. Default is a 1x1 matrix, which signals that testing data is not provided.

Matrix of continuous modifiers for testing data. Default is a 1x1 matrix, which signals that testing data is not provided.

Integer matrix of categorical modifiers for testing data. Default is a 1x1 matrix, which signals that testing data is not provided.

Vector of logical values indicating whether cutpoints for each continuous modifier should be drawn from a continuous uniform distribution (TRUE) or a discrete set (FALSE) specified incutpoints_list. Default isTRUE for each variable inZ_cont_train

List of lengthncol(Z_cont_train) containing a vector of cutpoints for each continuous modifier. By default, this is set toNULL so that cutpoints are drawn uniformly from a continuous distribution.

List of lengthncol(Z_cat_train) containing a vector of levels for each categorical modifier. If the j-th categorical modifier contains L levels,cat_levels_list[[j]] should be the vector0:(L-1). Default isNULL, which corresponds to the case that no categorical modifiers are available.

List of adjacency matrices if any of the categorical modifiers are network-structured. Default isNULL, which corresponds to the case that there are no network-structured categorical modifiers.

Vector of logicals indicating whether each categorical modifier is network-structured. Default isrep(FALSE, times = ncol(Z_cat_train)).

Logical, indicating whether or not to perform variable selection in each tree ensemble based on a sparse Dirichlet prior rather than uniform prior; see Linero 2018. Default isTRUE

Initial auto-correlation parameter for compound symmetry error structure. Must be between 0 and 1. Default is 0.9.

Number of trees in each ensemble. Default is 50.

Prior mean for jumps/leaf parameters. Default is 0 for each beta function. If supplied, must be a vector of length1 + ncol(X_train).

Prior standard deviation for jumps/leaf parameters. Default is1/sqrt(M) for each beta function. If supplied, must be a vector of length1 + ncol(X_train).

Degrees of freedom for scaled-inverse chi-square prior on sigma^2. Default is 3.

Scale hyperparameter for scaled-inverse chi-square prior on sigma^2. Default places 90% prior probability that sigma is less thansd(Y_train).

Number of posterior draws to return. Default is 1000.

Number of MCMC iterations to be treated as "warmup" or "burn-in". Default is 1000.

Number of post-warmup MCMC iteration by which to thin. Default is 1.

Logical, indicating whether to return all posterior samples. Default isTRUE. IfFALSE, only posterior mean is returned.

Logical, indicating whether or not to save a text-based representation of the tree samples. This representation can be passed topredict_flexBART to make predictions at a later time. Default isFALSE.

Logical, inciating whether to print progress to R console. Default isTRUE.

As the MCMC runs, a message is printed everyprint_every iterations. Default isfloor( (nd*thin + burn)/10) so that only 10 messages are printed.

Mean of the training observations (needed bypredict_VCBART)

Standard deviation of the training observations (needed bypredict_VCBART)

Vector of means of columns ofX_train, including the intercept (needed bypredict_VCBART).

Vector of standard deviations ofX_trian, including the intercept (needed bypredict_VCBART).

Vector containing posterior mean of evaluations of regression function E[y|x,z] on training data.

Matrix withlength(Y_train) rows andncol(X_train)+1 columns containing the posterior mean of evaluations of each coefficient function evaluated on the training data. Each row corresponds to a training set observation and each colunn corresponds to a coefficient function. Note the first column is for the intercept function.

Matrix withnd rows andlength(Y_train) columns. Each row corresponds to a posterior sample of the regression function E[y|x,z] and each column corresponds to a training set observation. Only returned ifsave_samples == TRUE.

Array of dimension withnd xlength(Y_train) xncol(X_train)+1 containing posterior samples of evaluations of the coefficient functions. The first dimension corresponds to posterior samples/MCMC iterations, the second dimension corresponds to individual training set observations, and the third dimension corresponds to coefficient functions. Only returned ifsave_samples == TRUE.

Vector containing posterior mean of evaluations of regression function E[y|x,z] on testing data.

Matrix withnrow(X_test) rows andncol(X_testn)+1 columns containing the posterior mean of evaluations of each coefficient function evaluated on the training data. Each row corresponds to a training set observation and each colunn corresponds to a coefficient function. Note the first column is for the intercept function.

Matrix withnd rows andnrow(X_test) columns. Each row corresponds to a posterior sample of the regression function E[y|x,z] and each column corresponds to a testing set observation. Only returned ifsave_samples == TRUE.

Array of sizend xnrow(X_test) xncol(X_test)+1 containing posterior samples of evaluations of the coefficient functions. The first dimension corresponds to posterior samples/MCMC iterations, the second dimension corresponds to individual training set observations, and the third dimension corresponds to coefficient functions. Only returned ifsave_samples == TRUE.

Vector containing ALL samples of the residual standard deviation, including warmup.

Vector containing ALL samples of the auto-correlation parameter rho, including warmup.

Array of sizend x R xncol(X)+1 that counts the number of times a variable was used in a decision rule in each posterior sample of each ensemble. Here R is the total number of potential modifiers (i.e.R = ncol(Z_cont_train) + ncol(Z_cat_train)).

Ifsparse=TRUE, an array of sizend x Rncol(X)+1 containing samples of the variable splitting probabilities.

A list (of lengthnd) of lists (of lengthncol(X_train)+1) of character vectors (of lengthM) containing textual representations of the regression trees. The string for the s-th sample of the m-th tree in the j-th ensemble is contaiend intrees[[s]][[j]][m]. These strings are parsed bypredict_VCBART to reconstruct the C++ representations of the sampled trees.

Vector of continous responses for training data

Vector containing the number of observations per subject in the training data.

Vector of lengthlength(Y_train) that records which subject contributed each observation. Subjects should be numbered sequentially from 1 tolength(ni_train).

Matrix of covariates for training observations. Do not include intercept as the first column.

Matrix of continuous modifiers for training data. Note, modifiers must be rescaled to lie in the interval [-1,1]. Default is a 1x1 matrix, which signals that there are no continuous modifiers in the training data.

Integer matrix of categorical modifiers for training data. Note categorical levels should be 0-indexed. That is, if a categorical modifier has 10 levels, the values should run from 0 to 9. Default is a 1x1 matrix, which signals that there are no categorical modifiers in the training data.

Matrix of covariate for testing observations. Default is a 1x1 matrix, which signals that testing data is not provided.

Matrix of continuous modifiers for testing data. Default is a 1x1 matrix, which signals that testing data is not provided.

Integer matrix of categorical modifiers for testing data. Default is a 1x1 matrix, which signals that testing data is not provided.

Vector of logical values indicating whether cutpoints for each continuous modifier should be drawn from a continuous uniform distribution (TRUE) or a discrete set (FALSE) specified incutpoints_list. Default isTRUE for each variable inZ_cont_train

List of lengthncol(Z_cont_train) containing a vector of cutpoints for each continuous modifier. By default, this is set toNULL so that cutpoints are drawn uniformly from a continuous distribution.

List of lengthncol(Z_cat_train) containing a vector of levels for each categorical modifier. If the j-th categorical modifier contains L levels,cat_levels_list[[j]] should be the vector0:(L-1). Default isNULL, which corresponds to the case that no categorical modifiers are available.

List of adjacency matrices if any of the categorical modifiers are network-structured. Default isNULL, which corresponds to the case that there are no network-structured categorical modifiers.

Vector of logicals indicating whether each categorical modifier is network-structured. Default isrep(FALSE, times = ncol(Z_cat_train)).

Logical, indicating whether or not to perform variable selection in each tree ensemble based on a sparse Dirichlet prior rather than uniform prior; see Linero 2018. Default isTRUE

Number of trees in each ensemble. Default is 50.

Prior mean for jumps/leaf parameters. Default is 0 for each beta function. If supplied, must be a vector of length1 + ncol(X_train).

Prior standard deviation for jumps/leaf parameters. Default is1/sqrt(M) for each beta function. If supplied, must be a vector of length1 + ncol(X_train).

Degrees of freedom for scaled-inverse chi-square prior on sigma^2. Default is 3.

Scale hyperparameter for scaled-inverse chi-square prior on sigma^2. Default places 90% prior probability that sigma is less thansd(Y_train).

Number of posterior draws to return. Default is 1000.

Number of MCMC iterations to be treated as "warmup" or "burn-in". Default is 1000.

Number of post-warmup MCMC iteration by which to thin. Default is 1.

Logical, indicating whether to return all posterior samples. Default isTRUE. IfFALSE, only posterior mean is returned.

Logical, indicating whether or not to save a text-based representation of the tree samples. This representation can be passed topredict_flexBART to make predictions at a later time. Default isFALSE.

Logical, inciating whether to print progress to R console. Default isTRUE.

As the MCMC runs, a message is printed everyprint_every iterations. Default isfloor( (nd*thin + burn)/10) so that only 10 messages are printed.

Mean of the training observations (needed bypredict_VCBART)

Standard deviation of the training observations (needed bypredict_VCBART)

Vector of means of columns ofX_train, including the intercept (needed bypredict_VCBART).

Vector of standard deviations ofX_trian, including the intercept (needed bypredict_VCBART).

Vector containing posterior mean of evaluations of regression function E[y|x,z] on training data.

Matrix withlength(Y_train) rows andncol(X_train)+1 columns containing the posterior mean of evaluations of each coefficient function evaluated on the training data. Each row corresponds to a training set observation and each colunn corresponds to a coefficient function. Note the first column is for the intercept function.

Matrix withnd rows andlength(Y_train) columns. Each row corresponds to a posterior sample of the regression function E[y|x,z] and each column corresponds to a training set observation. Only returned ifsave_samples == TRUE.

Array of dimension withnd xlength(Y_train) xncol(X_train)+1 containing posterior samples of evaluations of the coefficient functions. The first dimension corresponds to posterior samples/MCMC iterations, the second dimension corresponds to individual training set observations, and the third dimension corresponds to coefficient functions. Only returned ifsave_samples == TRUE.

Vector containing posterior mean of evaluations of regression function E[y|x,z] on testing data.

Matrix withnrow(X_test) rows andncol(X_testn)+1 columns containing the posterior mean of evaluations of each coefficient function evaluated on the training data. Each row corresponds to a training set observation and each colunn corresponds to a coefficient function. Note the first column is for the intercept function.

Matrix withnd rows andnrow(X_test) columns. Each row corresponds to a posterior sample of the regression function E[y|x,z] and each column corresponds to a testing set observation. Only returned ifsave_samples == TRUE.

Array of sizend xnrow(X_test) xncol(X_test)+1 containing posterior samples of evaluations of the coefficient functions. The first dimension corresponds to posterior samples/MCMC iterations, the second dimension corresponds to individual training set observations, and the third dimension corresponds to coefficient functions. Only returned ifsave_samples == TRUE.

Vector containing ALL samples of the residual standard deviation, including warmup.

Array of sizend x R xncol(X)+1 that counts the number of times a variable was used in a decision rule in each posterior sample of each ensemble. Here R is the total number of potential modifiers (i.e.R = ncol(Z_cont_train) + ncol(Z_cat_train)).

Ifsparse=TRUE, an array of sizend x Rncol(X)+1 containing samples of the variable splitting probabilities.

A list (of lengthnd) of lists (of lengthncol(X_train)+1) of character vectors (of lengthM) containing textual representations of the regression trees. The string for the s-th sample of the m-th tree in the j-th ensemble is contaiend intrees[[s]][[j]][m]. These strings are parsed bypredict_VCBART to reconstruct the C++ representations of the sampled trees.

A list returned byVCBART_ind orVCBART_cs

Matrix of continuous modifiers at which you wish to evaluate the covariate effect functions. Default is a 1x1 matrix, which signals that no continuous modifiers are required for these evaluations.

Integer matrix of categorical modifiers at which you wish to evaluate the covariate effect functions. Default is a 1x1 matrix, which signals that no continuous modifiers are required for these evaluations.

Boolean indicating whether the code should print its progress (TRUE). Default isTRUE.

An array, returned byVCBART_ind,VCBART_cs, orpredict_betas of posterior samples of coefficient function evaluations