Hello everyone,
I’m working on a biological experiment where I have a small time series consisting of 7 data points. The data represent a growth and decay process, and I have the following information:
Time points:
t_data <- seq(0, 7, by = 1) # Time points: 0.0, 1.0, ..., 7.0
Observations:
n_data <- c(0.00, 0.72, 1.00, 0.89, 0.21, 0.32, 0.03, 0.00)
The first value at t = 0 is always 0 for every experiment, and the data represent a growth phase (from 0 to 1) followed by a decay phase.
Additionally, I have the standard errors (noise in n_data). As an example:
sigma <- 0.15 * n_data
I’d like to generate bootstrapped samples from this time series (similar time series, just at the given points), but I need to take into account both the standard errors (for uncertainty in the measurements) and the autocorrelation between the observations. I have thought about estimating a covariance matrix using ACF or maybe a gaussian process for a bayesian approach, but I am not sure.
Specifically, my questions is: How can I generate bootstrapped samples in R while accounting for both the measurement errors and the autocorrelation structure in the data? Any recommendations on R packages or functions that could help with this process?
Thank you for any suggestions or examples you can provide!