Package 'familial'

Bayesian bootstrap

Description

Performs a Bayesian bootstrap for a statistic defined via a suitable function.

Usage

bayes.boot(x, fun, nboot = 1000, cluster = NULL, ...)

Arguments

x	a numeric vector to be passed as the first argument to fun
fun	the function to bootstrap; must accept data x and weights w (in that order), and return a data frame
nboot	the number of bootstraps to perform
cluster	an optional cluster for running bootstraps in parallel; must be set up using parallel::makeCluster
...	any other arguments for fun

Value

An object of class bayes.boot; a data frame with the following columns:

boot.id	the bootstrap iteration index
...	any columns returned by fun

Author(s)

Ryan Thompson <[email protected]>

Examples

set.seed(123)

boot <- bayes.boot(MASS::galaxies, fun = fit.family, nboot = 100)
head(boot)

---

Center test

Description

Performs a one- or two-sample test for a family of centers.

Usage

center.test(
  x,
  y = NULL,
  family = "huber",
  alternative = c("two.sided", "less", "greater"),
  mu = 0,
  paired = FALSE,
  nboot = 1000,
  loss = NULL,
  cluster = NULL,
  ...
)

Arguments

x	a numeric vector of data
y	an optional numeric vector of data
family	the family of centers; currently only allows 'huber' for Huber family
alternative	the form of the alternative hypothesis; must be one of 'two.sided' (default), 'greater', or 'less'
mu	the null value of the center for a one-sample test, or the null value of the center of differences for a paired two-sample test, or the null value of the difference of centers for an independent two-sample test; can be an interval
paired	a logical indicating whether to treat x and y as paired
nboot	the number of bootstraps to perform
loss	an optional c×2 matrix of losses incurred from an incorrect decision, where c is the number of candidate choices (typically c=3: H0, H1, or indeterminate)
cluster	an optional cluster for running bootstraps in parallel; must be set up using parallel::makeCluster
...	any other arguments

Details

Uses the Bayesian bootstrap to compute posterior probabilities for the hypotheses $\mathrm{H}_0:\mu(\lambda)=\mu_0$ for some $\lambda\in\Lambda$ vs. $\mathrm{H}_1:\mu(\lambda)\neq\mu_0$ for all $\lambda\in\Lambda$, where $\{\mu(\lambda):\lambda\in\Lambda\}$ is a family of centers.
The default loss matrix results in a decision whenever the posterior probability for one of the hypotheses is greater than 0.95 and otherwise is indeterminate.

Value

An object of class center.test; a list with the following components:

expected.loss	the expected loss, calculated by post-multiplying loss with prob
decision	the optimal decision given the expected loss
loss	the loss matrix
prob	the estimated posterior probabilities of the null and alternative
boot	the bootstrap output from bayes.boot
x	the x that was supplied
y	the y that was supplied
mu	the mu that was supplied
family	the family that was supplied

Author(s)

Ryan Thompson <[email protected]>

References

Thompson, R., Forbes, C. S., MacEachern, S. N., and Peruggia, M. (2023). 'Familial inference: Tests for hypotheses on a family of centres'. arXiv: 2202.12540.

Examples

set.seed(123)

test <- center.test(MASS::galaxies, mu = 21000, nboot = 100)
print(test)
plot(test)

cl <- parallel::makeCluster(2)
test <- center.test(MASS::galaxies, mu = 21000, nboot = 100, cluster = cl)
parallel::stopCluster(cl)
print(test)

---

Fit family

Description

Fits a family of centers.

Usage

fit.family(
  x,
  w = rep(1, length(x)),
  family = "huber",
  spread.fun = weighted.mad,
  eps = .Machine$double.eps
)

Arguments

x	a numeric vector of data
w	a numeric vector of weights
family	the location family; currently only allows 'huber' for Huber family
spread.fun	a function used for the spread of x; must accept data x and weights w (in that order), and return a numeric
eps	a numerical tolerance parameter

Value

An object of class fit.family; a data frame with the following columns:

mu	the fitted values
lambda	the thresholding parameter

Author(s)

Ryan Thompson <[email protected]>

Examples

fit <- fit.family(MASS::galaxies)
plot(fit)

---

Plot function for center.test object

Description

Plot the posterior distribution for the family of centers using a functional box plot.

Usage

## S3 method for class 'center.test'
plot(x, band = c(0.5, 0.75, 0.95), ninterp = 25, ...)

Arguments

x	an object of class center.test
band	a vector of band limits for the functional box plot
ninterp	the number of interpolation points for the functional box plot; more points lead to finer resolution of the plot at the expense of additional computation
...	any other arguments

Value

A plot of the posterior distribution.

Author(s)

Ryan Thompson <[email protected]>

---

Plot function for fit.family object

Description

Plot a fitted family.

Usage

## S3 method for class 'fit.family'
plot(x, y = NULL, ...)

Arguments

x	an object of class fit.family
y	an object of class fit.family
...	any other arguments

Value

A plot of the fitted family.

Author(s)

Ryan Thompson <[email protected]>

---

Print function for center.test object

Description

Print objects of class center.test.

Usage

## S3 method for class 'center.test'
print(x, ...)

Arguments

x	an object of class center.test
...	any other arguments

Value

The argument x.

Author(s)

Ryan Thompson <[email protected]>

---

Uniform Dirichlet distribution

Description

Random number generation for the uniform Dirichlet distribution (having all concentration parameters set to one).

Usage

rudirichlet(n, d)

Arguments

n	the number of observations
d	the number of dimensions

Value

A matrix; each row is a random draw and each column is a dimension.

Author(s)

Ryan Thompson <[email protected]>

---

Weighted statistics

Description

Assorted weighted statistics unavailable in base R.

Usage

weighted.median(x, w)

weighted.mad(x, w)

Arguments

x	a numeric vector of data
w	a numeric vector of weights

Value

A length-one numeric vector.

Author(s)

Ryan Thompson <[email protected]>

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