Generate Simulated Datasets with Change Points in Covariance Matrix

Description

This function generates simulated datasets that include change points in the covariance matrix for change point detection. Users can specify various parameters to control the dataset size, dimension, size of signal, and change point locations. The generated datasets include datasets with and without change points, allowing for comparisons in simulation studies.

Usage

generate_cov_datasets(
  n,
  p,
  signal_size,
  sparse = TRUE,
  single_point = round(n/2),
  multiple_points = c(round(n/4), round(2 * n/4), round(3 * n/4)),
  type = c(1, 2, 3, 4, 5)
)

Arguments

Value

A 3D array containing the generated datasets. Each slice represents a different dataset type.

Examples

# Generate a default dataset
datasets <- generate_cov_datasets(100, 50, 1)

null_data <- datasets[,,1]
single_many_data <- datasets[,,3]

Generate Simulated Datasets with Change Points in Mean Vector

Description

This function generates simulated datasets that include change points in the mean vector for change point detection. Users can specify various parameters to control the dataset size, dimension, size of signal, and change point locations. The generated datasets include datasets with and without change points, allowing for comparisons in simulation studies.

Usage

generate_mean_datasets(
  n = 500,
  p = 200,
  signal_size = 1,
  pre_proportion = 0.4,
  pre_value = 0.3,
  single_point = round(n/2),
  multiple_points = c(round(n/4), round(2 * n/4), round(3 * n/4)),
  type = c(1, 2, 3, 4, 5)
)

Arguments

Value

A 3D array containing the generated datasets. Each slice represents a different dataset type.

Examples

# Generate a default dataset
datasets <- generate_mean_datasets(100, 50, 1)

null_data <- datasets[,,1]
single_many_data <- datasets[,,3]

Majority Rule for Multiscale approach using mxPBF Results

Description

This function implements a majority rule-based post-processing approach to identify common change points across multiple window sizes from mxPBF results.

Usage

majority_rule_mxPBF(res_mxPBF)

Arguments

Value

A vector of final detected change points that are common across multiple windows based on majority rule.

Examples

n <- 500
p <- 200
signal_size <- 1
pre_value <- 0.3
pre_proportion <- 0.4
given_data <- generate_mean_datasets(n, p, signal_size, pre_proportion, pre_value,
single_point = 250, multiple_points = c(150,300,350), type = 5)
nws <- c(25, 60, 100)
alps <- seq(1,10,0.05)
res_mxPBF <- mxPBF_mean(given_data, nws, alps)
majority_rule_mxPBF(res_mxPBF)

Multivariate Normal Random Number Generator

Description

Generates random numbers from a multivariate normal distribution with specified mean and covariance matrix using a C++ implementation.

Usage

mvrnorm_cpp(n = 1, mu, Sigma)

Arguments

Value

A numeric matrix where each row is a random sample from the multivariate normal distribution.

Examples

# Example usage
mu <- c(0, 0)
Sigma <- matrix(c(1, 0.5, 0.5, 1), 2, 2)
mvrnorm_cpp(5, mu, Sigma)

Change Point Detection in Mean Structure using Maximum Pairwise Bayes Factor (mxPBF)

Description

This function detects change points in both mean and covariance structure of multivariate Gaussian data using the Maximum Pairwise Bayes Factor (mxPBF). The function selects alpha that controls the empirical False Positive Rate (FPR), as suggested in the paper. The function conducts a multiscale approach using the function.

Usage

mxPBF_combined(
  given_data,
  nws,
  alps,
  a0 = 0.01,
  b0 = 0.01,
  FPR_want = 0.05,
  n_sample = 300,
  n_cores = 1
)

Arguments

Value

A list provided. Each element in the list contains:

Result_cov

A list result from the mxPBF_cov() function.

Result_mean

A list result from the mxPBF_mean() function applied to each segmented data.

Change_points_cov

Locations of detected change points identified by mxPBF_cov() function.

Change_points_mean

Locations of detected change points identified by mxPBF_mean() function.

Examples

nws <- c(25, 60, 100)
alps <- seq(1,10,0.05)
## H0 data
mu1 <- rep(0,10)
sigma1 <- diag(10)
X <- mvrnorm_cpp(500, mu1, sigma1)
res1 <- mxPBF_combined(X, nws, alps)

## H1 data
mu2 <- rep(1,10)
sigma2 <- diag(10)
for (i in 1:10) {
  for (j in i:10) {
    if (i == j) {
    next
    } else {
    cov_value <- rnorm(1, 1, 1)
    sigma2[i, j] <- cov_value
    sigma2[j, i] <- cov_value
    }
  }
}
sigma2 <- sigma2 + (abs(min(eigen(sigma2)$value))+0.1)*diag(10) # Make it nonsingular
Y1 <- mvrnorm_cpp(150, mu1, sigma1)
Y2 <- mvrnorm_cpp(150, mu2, sigma1)
Y3 <- mvrnorm_cpp(200, mu2, sigma2)
Y <- rbind(Y1, Y2, Y3)
res2 <- mxPBF_combined(Y, nws, alps)

Change Point Detection in Covaraiance Structure using Maximum Pairwise Bayes Factor (mxPBF)

Description

This function detects change points in the covariance structure of multivariate Gaussian data using the Maximum Pairwise Bayes Factor (mxPBF). The function selects alpha that controls the empirical False Positive Rate (FPR), as suggested in the paper. One can conduct a multiscale approach using the function majority_rule_mxPBF().

Usage

mxPBF_cov(
  given_data,
  nws,
  alps,
  a0 = 0.01,
  b0 = 0.01,
  FPR_want = 0.05,
  n_sample = 300,
  n_cores = 1
)

Arguments

Value

A list of length equal to the number of window sizes provided. Each element in the list contains:

Change_points

Locations of detected change points.

Bayes_Factors

Vector of calculated Bayes Factors for each middle points.

Selected_alpha

Optimal alpha value selected based on the method that controls the empirical FPR.

Window_size

Window size used for change point detection.

Examples

nws <- c(25, 60, 100)
alps <- seq(1,10,0.05)
## H0 data
mu <- rep(0,10)
sigma1 <- diag(10)
X <- mvrnorm_cpp(500, mu, sigma1)
res1 <- mxPBF_cov(X, nws, alps)

## H1 data
mu <- rep(0,10)
sigma2 <- diag(10)
for (i in 1:10) {
  for (j in i:10) {
    if (i == j) {
    next
    } else {
    cov_value <- rnorm(1, 1, 1)
    sigma2[i, j] <- cov_value
    sigma2[j, i] <- cov_value
    }
  }
}
sigma2 <- sigma2 + (abs(min(eigen(sigma2)$value))+0.1)*diag(10) # Make it nonsingular
Y1 <- mvrnorm_cpp(250, mu, sigma1)
Y2 <- mvrnorm_cpp(250, mu, sigma2)
Y <- rbind(Y1, Y2)
res2 <- mxPBF_cov(Y, nws, alps)

Change Point Detection in Mean Structure using Maximum Pairwise Bayes Factor (mxPBF)

Description

This function detects change points in the mean structure of multivariate Gaussian data using the Maximum Pairwise Bayes Factor (mxPBF). The function selects alpha that controls the empirical False Positive Rate (FPR), as suggested in the paper. One can conduct a multiscale approach using the function majority_rule_mxPBF().

Usage

mxPBF_mean(given_data, nws, alps, FPR_want = 0.05, n_sample = 300, n_cores = 1)

Arguments

Value

A list of length equal to the number of window sizes provided. Each element in the list contains:

Change_points

Locations of detected change points.

Bayes_Factors

Vector of calculated Bayes Factors for each middle points.

Selected_alpha

Optimal alpha value selected based on the method that controls the empirical FPR.

Window_size

Window size used for change point detection.

Examples

nws <- c(25, 60, 100)
alps <- seq(1,10,0.05)
## H0 data
mu1 <- rep(0,10)
sigma <- diag(10)
X <- mvrnorm_cpp(500, mu1, sigma)
res1 <- mxPBF_mean(X, nws, alps)

## H1 data
mu2 <- rep(1,10)
sigma <- diag(10)
Y <- rbind(mvrnorm_cpp(250,mu1,sigma), mvrnorm_cpp(250,mu2,sigma))
res2 <- mxPBF_mean(Y, nws, alps)