detect_cp: Detect change points on time series.

In BayesChange: Bayesian Methods for Change Points Analysis

Detect change points on time series.

Description

The detect_cp function detect change points on univariate and multivariate time series.

Usage

detect_cp(
  data,
  n_iterations,
  n_burnin = 0,
  q = 0.5,
  params = list(),
  kernel,
  print_progress = TRUE,
  user_seed = 1234
)

Arguments

data	a vector or a matrix. If a vector the algorithm for univariate time series is used. If a matrix, where rows are the observations and columns are the times, then the algorithm for multivariate time series is used.
n_iterations	number of MCMC iterations.
n_burnin	number of iterations that must be excluded when computing the posterior estimate.
q	probability of performing a split at each iteration.
params	a list of parameters: If data is an univariate time series the following must be specified: a, b, c parameters of the Normal-Gamma prior for \mu and \lambda. prior_var_phi variance for the proposal in the N(0,\sigma^2_\phi) posterior estimate of \theta. par_theta_c parameter of the shifted Gamma prior of \theta. par_theta_d parameter of the shifted Gamma prior of \theta. If the time series is multivariate the following must be specified: m_0, k_0, nu_0, S_0 parameters for the Normal-Inverse-Wishart prior for (\mu,\lambda). prior_var_phi variance for the proposal in the N(0,\sigma^2_\phi) posterior estimate of \theta. par_theta_c parameter of the shifted Gamma prior of \theta. par_theta_d parameter of the shifted Gamma prior of \theta. If data are survival functions: M number of Monte Carlo iterations when computing the likelihood of the survival function. xi recovery rate fixed constant for each population at each time. a0,b0 parameters for the computation of the integrated likelihood of the survival functions. I0_var variance for the Metropolis-Hastings estimation of the proportion of infected at time 0. p prior average number of change points for each order.
kernel	can be "ts" if data are time series or "epi" if data are survival functions.
print_progress	If TRUE (default) print the progress bar.
user_seed	seed for random distribution generation.

Value

A DetectCpObj class object containing

• $data vector or matrix with the data.

• $n_iterations number of iterations.

• $n_burnin number of burn-in iterations.

• $orders matrix where each entries is the assignment of the realization to a block. Rows are the iterations and columns the times.

• $time computational time.

• $gammaMCMC traceplot for \gamma.

• $phi_MCMC_01 a 0/1 vector, the n-th element is equal to 1 if the proposed \gamma was accepted, 0 otherwise.

• $sigma_MCMC traceplot for \sigma.

• $sigma_MCMC_01 a 0/1 vector, the n-th element is equal to 1 if the proposed \sigma was accepted, 0 otherwise.

• $theta_MCMC traceplot for \theta.

• I0_MCMC traceplot for I_0.

• I0_MCMC_01 a 0/1 vector, the n-th element is equal to 1 if the proposed I_0 was accepted, 0 otherwise.

• kernel_ts if TRUE data are time series.

• kernel_epi if TRUE data are survival functions.

• $univariate_ts TRUE if data is an univariate time series, FALSE if it is a multivariate time series.

References

Martínez, A. F., & Mena, R. H. (2014). On a Nonparametric Change Point Detection Model in Markovian Regimes. Bayesian Analysis, 9(4), 823–858. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/14-BA878")}

Corradin, R., Danese, L., & Ongaro, A. (2022). Bayesian nonparametric change point detection for multivariate time series with missing observations. International Journal of Approximate Reasoning, 143, 26–43. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijar.2021.12.019")}

Corradin, R., Danese, L., KhudaBukhsh, W. R., & Ongaro, A. (2024). Model-based clustering of time-dependent observations with common structural changes. arXiv preprint arXiv:2410.09552.

Examples

## Univariate time series

data_vec <- as.numeric(c(rnorm(50,0,0.1), rnorm(50,1,0.25)))

out <- detect_cp(data = data_vec, n_iterations = 2500, n_burnin = 500,
                 params = list(a = 1, b = 1, c = 0.1), kernel = "ts")

print(out)

## Multivariate time series

data_mat <- matrix(NA, nrow = 3, ncol = 100)

data_mat[1,] <- as.numeric(c(rnorm(50,0,0.100), rnorm(50,1,0.250)))
data_mat[2,] <- as.numeric(c(rnorm(50,0,0.125), rnorm(50,1,0.225)))
data_mat[3,] <- as.numeric(c(rnorm(50,0,0.175), rnorm(50,1,0.280)))

out <- detect_cp(data = data_mat, n_iterations = 2500, n_burnin = 500,
                 params = list(m_0 = rep(0,3), k_0 = 0.25, nu_0 = 4,
                               S_0 = diag(1,3,3)), kernel = "ts")

print(out)


## Survival functions

data_mat <- matrix(NA, nrow = 1, ncol = 100)

betas <- c(rep(0.45, 25),rep(0.14,75))

inf_times <- sim_epi_data(10000, 10, 100, betas, 1/8)

inf_times_vec <- rep(0,100)
names(inf_times_vec) <- as.character(1:100)

for(j in 1:100){
 if(as.character(j) %in% names(table(floor(inf_times)))){
   inf_times_vec[j] = table(floor(inf_times))[which(names(table(floor(inf_times))) == j)]
 }
}

data_mat[1,] <- inf_times_vec

out <- detect_cp(data = data_mat, n_iterations = 500, n_burnin = 100,
                 params = list(M = 250, xi = 1/8, a0 = 40, b0 = 10), kernel = "epi")

print(out)

BayesChange documentation built on June 10, 2025, 9:09 a.m.