| Title: | Compute FAB (Frequentist and Bayes) Conformal Prediction Intervals |
| Version: | 1.0.4 |
| Description: | Computes and plots prediction intervals for numerical data or prediction sets for categorical data using prior information. Empirical Bayes procedures to estimate the prior information from multi-group data are included. See, e.g.,Bersson and Hoff (2022) <doi:10.48550/arXiv.2204.08122> "Optimal Conformal Prediction for Small Areas". |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| Imports: | sae (≥ 1.3), parallel, stats, graphics |
| Suggests: | knitr, devtools |
| NeedsCompilation: | yes |
| ByteCompile: | yes |
| VignetteBuilder: | knitr |
| URL: | https://github.com/betsybersson/fabPrediction |
| BugReports: | https://github.com/betsybersson/fabPrediction/issues |
| Packaged: | 2024-03-25 13:51:40 UTC; betsybersson |
| Author: | Elizabeth Bersson [aut, cre, cph] |
| Maintainer: | Elizabeth Bersson <elizabeth.bersson@duke.edu> |
| Depends: | R (≥ 3.5.0) |
| Repository: | CRAN |
| Date/Publication: | 2024-03-26 09:00:05 UTC |
Minnesota County Adjacency Matrix
Description
Adjacency matrix for MN counties based on group index that matches radon data.
Usage
data(W)
Format
A matrix.
Obtain a Bayesian prediction interval for categorical data
Description
This function computes the Bayesian prediction set for a multinomial conjugate family.
Usage
bayesMultinomialPrediction(
Y,
alpha = 0.15,
gamma = rep(1, length(Y)),
category_names = 1:length(Y)
)
Arguments
Y |
Observed data vector of length K containing counts of observations from each of the K categories |
alpha |
Prediction mis-coverage rate |
gamma |
Dirichlet prior concentration for the K categories |
category_names |
Category names (optional) |
Value
pred object
Obtain a Bayesian prediction interval
Description
This function computes a Bayesian prediction interval based on a normal model.
Usage
bayesNormalPrediction(Y, alpha = 0.15, mu = 0, tau2 = 1)
Arguments
Y |
Observed data vector |
alpha |
Prediction error rate |
mu |
Prior expected mean of the population mean |
tau2 |
Prior expected variance of the population mean |
Value
pred object
Obtain a distance-to-average conformal prediction interval
Description
This function computes a conformal prediction region under the distance-from-average non-conformity measure. That is, |a + bz*| <= |ci + di z^*| where i indexes training data.
Usage
dtaPrediction(Y, alpha = 0.15)
Arguments
Y |
Observed data vector |
alpha |
Prediction error rate |
Value
pred object
Create Identity Matrix
Description
This function returns an NxN identity matrix.
Usage
eye(N)
Arguments
N |
dimension of square matrix |
Value
NxN identity matrix
Obtain a FAB conformal prediction interval for categorical data
Description
This function computes a FAB conformal prediction set as described in Bersson and Hoff 2023.
Usage
fabCategoricalPrediction(
Y,
alpha = 0.15,
gamma = rep(1, length(Y)),
category_names = 1:length(Y)
)
Arguments
Y |
Observed data vector of length K containing counts of observations from each of the K categories |
alpha |
Prediction mis-coverage rate |
gamma |
Dirichlet prior concentration for the K categories |
category_names |
Category names (optional) |
Value
pred object
Obtain a FAB conformal prediction interval
Description
This function computes a FAB conformal prediction region as described in Bersson and Hoff 2022.
Usage
fabContinuousPrediction(Y, alpha = 0.15, mu = 0, tau2 = 1)
Arguments
Y |
Observed data vector |
alpha |
Prediction error rate |
mu |
Prior expected mean of the population mean |
tau2 |
Prior expected variance of the population mean |
Value
pred object
fabPrediction: Compute FAB Conformal Prediction Intervals
Description
A package for computing and plotting prediction intervals for numerical data or prediction sets for categorical data using prior information. Empirical Bayes procedures to estimate the prior information from multi-group data are included.
Author(s)
Elizabeth Bersson,
Maintainer: Elizabeth Bersson <elb75@duke.edu>
References
E. Bersson and P.D. Hoff. (2023) Frequentist Prediction Sets for Species Abundance using Indirect Information. Preprint.
E. Bersson and P.D. Hoff. (2023) Optimal Conformal Prediction for Small Areas. Journal of Survey Statistics and Methodology, forthcoming.
Obtain empirical Bayesian estimates for group j
Description
This function returns empirical Bayesian estimates for a specified group from the conjugate normal spatial Fay-Herriot model.
Usage
fayHerriotEB(j, Y, group, W = NA, X = NA)
Arguments
j |
Obtain EB values for group in index j- numeric value in group |
Y |
Data vector |
group |
index vecter of the same lenght as Y |
W |
Non-standardized adjacency matrix |
X |
Group-level covariates |
Value
empirical Bayesian estimates of population mean and it's variance
Obtain inital guess of MLE of the marginal Dirichlet-multinomial likelihood
Description
Method of moment matching to obtain an initial guess of the MLE, as in Minka (2000).
Usage
initMoM(D)
Arguments
D |
matrix (JxK) of counts; each row is a sample from a MN distribution with K categories |
Value
Hessian
Obtain a pivot prediction interval
Description
This function computes a prediction interval under assumed normality.
Usage
normalPrediction(Y, alpha = 0.15)
Arguments
Y |
Observed data vector |
alpha |
Prediction error rate |
Value
pred object
Plot a 'pred' object constructed for a categorical response
Description
Plot a 'pred' object constructed for a categorical response
Usage
## S3 method for class 'pred'
plot(x, ...)
Arguments
x |
pred object- a list classified as pred containing objects data and bound |
... |
additional parameters passed to the default plot method |
Value
capability to plot pred object. More details: the command 'plot(obj)' plots the empirical densities of each category. Mass denoted in red indicates inclusion in the prediction set
Obtain empirical Bayesian estimates for conjugate normal spatial Fay-Herriot model
Description
This function returns plug-in values for a conjugate normal spatial Fay-Herriot model.
Usage
pluginValues(Y, group, W = NA, X = NA)
Arguments
Y |
Data vector |
group |
Group membership of each entry in Y |
W |
Adjacency matrix |
X |
Group-level covariates |
Value
plug-in values of spatial Fay-Herriot model
Obtain gradient of the marginal Dirichlet-multinomial likelihood
Description
Obtain gradient of the marginal Dirichlet-multinomial likelihood
Usage
polyaGradient(D, gamma, Nj = rowSums(D), K = ncol(D))
Arguments
D |
matrix (JxK) of counts; each row is a sample from a MN distribution with K categories |
gamma |
current value of prior concentration parameter |
Nj |
sample sizes of the J groups |
K |
number of categories |
Value
gradient
Obtain Hessian of the marginal Dirichlet-multinomial likelihood
Description
Obtain Hessian of the marginal Dirichlet-multinomial likelihood
Usage
polyaHessian(D, gamma, Nj = rowSums(D), K = ncol(D))
Arguments
D |
matrix (JxK) of counts; each row is a sample from a MN distribution with K categories |
gamma |
current value of prior concentration parameter |
Nj |
sample sizes of the J groups |
K |
number of categories |
Value
Hessian
Obtain MLE of marginal Dirichlet-multinomial likelihood
Description
This function retuns the MLE of the prior concentration from a marginal Dirichlet-multinomial likelihood. Default method iterates a Newton-Raphson algorithm until convergence.
Usage
polyaMLE(
D,
init = NA,
method = "Newton_Raphson",
epsilon = 1e-04,
print_progress = FALSE
)
Arguments
D |
matrix (JxK) of counts; each row is a sample from a MN distribution with K categories |
init |
If NA, use method moment matching procedure to obtain good init values |
method |
"Newton_Raphson", "fixed_point", "separate", "precision_only" |
epsilon |
convergence diagnostic |
print_progress |
if TRUE, print progress to screen |
Value
mle of prior concentration from marginal Dirichlet-multinomial likelihood
Wrapper to obtain a prediction interval for continuous data
Description
This function computes a prediction interval from a number of methods.
Usage
predictionInterval(Y, method = "FAB", alpha = 0.15, mu = 0, tau2 = 1)
Arguments
Y |
Observed data vector |
method |
Choice of prediction method. Options include FAB, DTA, direct, Bayes. |
alpha |
Prediction error rate |
mu |
Prior expected mean of the population mean |
tau2 |
Prior expected variance of the population mean |
Value
pred object containing prediction interval bounds and interval coverage
Examples
# example data
data(radon)
y_county9 = radon$radon[radon$group==9]
fab.region = predictionInterval(y_county9,
method = "FAB",
alpha = .15,
mu = 0.5,tau2 = 1)
fab.region$bounds
plot(fab.region)
Wrapper to obtain a prediction set for categorical data
Description
This function computes a prediction set from a number of methods.
Usage
predictionSet(
Y,
method = "FAB",
alpha = 0.15,
gamma = rep(1, length(Y)),
category_names = 1:length(Y)
)
Arguments
Y |
Observed data vector |
method |
Choice of prediction method. Options include FAB, direct, Bayes. |
alpha |
Prediction mis-coverage rate |
gamma |
Dirichlet prior concentration for FAB/Bayes methods |
category_names |
Category names (optional) |
Value
pred object containing prediction set and interval coverage
Examples
# obtain example categorical data
set.seed(1)
prob = rdirichlet(50:1)
y = rmultinom(1,15,prob)
fab.set = predictionSet(y,
method = "FAB",
gamma = c(50:1))
plot(fab.set)
Minnesota Radon Data
Description
Data from a national US EPA survey of household radon values. County index contained in group column.
Usage
data(radon)
Format
A matrix.
Source
References
US Environmental Protection Agency (1992) National residential radon survey: summary report. Washington, DC; DOI EPA402-R-92-011.
Generate a random sample from a Dirichlet distribution
Description
Generate a random sample from a Dirichlet distribution
Usage
rdirichlet(gamma)
Arguments
gamma |
Prior concentration vector of length K |
Value
a vector of length K that is a random sample from a Dirichlet distribution
Row standardize a matrix
Description
Row standardize a matrix
Usage
row_standardize(W)
Arguments
W |
matrix |
Value
row-standardized matrix