Package {MRS}

Multi Resolution Scanning for one-way ANDOVA using the multi-scale Beta-Binomial model

Description

This function executes the Multi Resolution Scanning algorithm to detect differences across the distributions of multiple groups having multiple replicates.

Usage

andova(
  X,
  G,
  H,
  n_groups = length(unique(G)),
  n_subgroups = NULL,
  Omega = "default",
  K = 6,
  init_state = c(0.8, 0.2, 0),
  beta = 1,
  gamma = 0.07,
  delta = 0.4,
  eta = 0,
  alpha = 0.5,
  nu_vec = 10^(seq(-1, 4)),
  return_global_null = TRUE,
  return_tree = TRUE,
  n_post_samples = 0,
  baseline = 0,
  method = "newton",
  n_grid_theta = 4
)

Arguments

Value

An mrs object.

References

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
n = 1000
M = 5
class_1 = sample(M, n, prob= 1:5, replace=TRUE  )
class_2 = sample(M, n, prob = 5:1, replace=TRUE )

Y_1 = rnorm(n, mean=class_1, sd = .2)
Y_2 = rnorm(n, mean=class_2, sd = .2)

X = matrix( c(Y_1, Y_2), ncol = 1)
G = c(rep(1,n),rep(2,n))
H = sample(3,2*n, replace = TRUE  )

ans = andova(X, G, H)
ans$PostGlobNull
plot1D(ans)

Multi Resolution Scanning

Description

This function executes the Multi Resolution Scanning algorithm to detect differences across multiple distributions.

Usage

mrs(
  X,
  G,
  n_groups = length(unique(G)),
  Omega = "default",
  K = 6,
  init_state = NULL,
  beta = 1,
  gamma = 0.3,
  delta = NULL,
  eta = 0.3,
  alpha = 0.5,
  return_global_null = TRUE,
  return_tree = TRUE,
  n_post_samples = 0,
  baseline = 0,
  min_n_node = 0
)

Arguments

Value

An mrs object.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Examples

set.seed(12345)
n = 20
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
ans = mrs(X=X, G=G)

Plot regions of the representative tree in 1D

Description

This function visualizes the regions of the representative tree of the output of the mrs function. For each region the posterior probability of difference (PMAP) or the effect size is plotted.

Usage

plot1D(
  ans,
  type = "prob",
  group = 1,
  dim = 1,
  regions = rep(1, length(ans$RepresentativeTree$Levels)),
  legend = FALSE,
  main = "default",
  abs = TRUE,
  eff_scale = "lor"
)

Arguments

Value

Invisibly returns NULL. The function is called for its side effect of drawing a one-dimensional multiresolution map on the current graphics device. The plotted regions encode posterior probabilities of a difference when type = "prob", or the selected group's effect sizes when type = "eff".

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
p = 1
n1 = 200
n2 = 200
mu1 = matrix( c(0,10), nrow = 2, byrow = TRUE)
mu2 = mu1; mu2[2] = mu1[2] + .01
sigma = c(1,.1)

Z1 = sample(2, n1, replace=TRUE, prob=c(0.9, 0.1))
Z2 = sample(2, n2, replace=TRUE, prob=c(0.9, 0.1))
X1 = mu1[Z1] + matrix(rnorm(n1*p), ncol=p)*sigma[Z1]
X2 = mu2[Z2] + matrix(rnorm(n2*p), ncol=p)*sigma[Z1]
X = rbind(X1, X2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=10)
plot1D(ans, type = "prob")
plot1D(ans, type = "eff")

Plot one-dimensional windows selected by Bayesian FDR

Description

Selects representative-tree windows whose posterior alternative probabilities satisfy a requested Bayesian false discovery rate, then displays them with plot1D.

Usage

plot1DSigWindows(ans_mrs, fdr = 0.1, precision = 0.001, ...)

Arguments

Value

Invisibly, a list containing the selected node indices and threshold.

Plot regions of the representative tree in 2D

Description

This function visualizes the regions of the representative tree of the output of the mrs function.

Usage

plot2D(
  ans,
  type = "prob",
  data.points = "all",
  background = "none",
  group = 1,
  dim = c(1, 2),
  levels = sort(unique(ans$RepresentativeTree$Levels)),
  regions = rep(1, length(ans$RepresentativeTree$Levels)),
  legend = FALSE,
  main = "default",
  abs = TRUE
)

Arguments

Value

Invisibly returns NULL. The function is called for its side effect of drawing one panel for each selected tree level on the current graphics device. Rectangles encode posterior probabilities or effect sizes; optional points and a smoothed background show the observed data.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plot2D(ans, type = "prob", legend = TRUE)

plot2D(ans, type="empty", data.points = "differential",
 background = "none")

plot2D(ans, type="none", data.points = "differential",
 background = "smeared", levels = 4)

Plot nodes of the representative tree

Description

This function visualizes the representative tree of the output of the mrs function. For each node of the representative tree, the posterior probability of difference (PMAP) or the effect size is plotted. Each node in the tree is associated to a region of the sample space. All non-terminal nodes have two children obtained by partitioning the parent region with a dyadic cut along a given direction. The numbers under the vertices represent the cutting direction.

Usage

plotTree(
  ans,
  type = "prob",
  group = 1,
  legend = FALSE,
  main = "",
  node.size = 5,
  abs = TRUE
)

Arguments

Value

Invisibly returns NULL. The function is called for its side effect of drawing the representative binary partition tree on the current graphics device. Node size and color encode posterior probabilities or effect sizes, and labels beneath non-terminal nodes identify split directions.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
p = 2
n1 = 200
n2 = 200
mu1 = matrix( c(9,9,0,4,-2,-10,3,6,6,-10), nrow = 5, byrow=TRUE)
mu2 = mu1; mu2[2,] = mu1[2,] + 1

Z1 = sample(5, n1, replace=TRUE)
Z2 = sample(5, n2, replace=TRUE)
X1 = mu1[Z1,] + matrix(rnorm(n1*p), ncol=p)
X2 = mu2[Z2,] + matrix(rnorm(n2*p), ncol=p)
X = rbind(X1, X2)
colnames(X) = c(1,2)
G = c(rep(1, n1), rep(2,n2))

ans = mrs(X, G, K=8)
plotTree(ans, type = "prob", legend = TRUE)

Print summary of a mrs object

Description

This function prints a summary of the output of the mrs function. It provides the marginal prior and posterior of the null and the top regions of the representative tree.

Usage

## S3 method for class 'summary.mrs'
print(x, ...)

Arguments

Value

Invisibly returns NULL. The method is called for its side effect of printing the global prior and posterior null probabilities and, when present, the selected differential regions with their posterior alternative probabilities, effect sizes, region bounds, and split directions.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
x = mrs(X=X, G=G)
fit = summary(x, rho = 0.95, abs_eff = 1)
print(fit)

Summary of a mrs object

Description

This function summarizes the output of the mrs function. It provides the marginal prior and posterior null and the top regions of the representative tree.

Usage

## S3 method for class 'mrs'
summary(object, rho = 0.5, abs_eff = 0, sort_by = "eff", ...)

Arguments

Value

A list with information about the top regions.

References

Soriano J. and Ma L. (2017). Probabilistic multi-resolution scanning for two-sample differences. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi:10.1111/rssb.12180

Ma L. and Soriano J. (2018). Analysis of distributional variation through multi-scale Beta-Binomial modeling. Journal of Computational and Graphical Statistics, 27(3), 529–541. doi:10.1080/10618600.2017.1402774

Examples

set.seed(12345)
n = 100
p = 2
X = matrix(c(runif(p*n/2),rbeta(p*n/2, 1, 4)), nrow=n, byrow=TRUE)
G = c(rep(1,n/2), rep(2,n/2))
object = mrs(X=X, G=G)
fit = summary(object, rho = 0.5, abs_eff = 0.1)