The goal of this is to create a Julia package which will allow the user to fit a data set with one independent variable to a model with N parameters, and to do so while taking accound the uncertainties in the independent and dependent variables.
I'll use a time series as an example to frame the discussion.
The user supplies
- a time sequence together with the uncertainty at each time,
- a set of measurements, [y] together with their uncertainties,
- a model function with N parameters with which to fit the data
- whether to smooth the data before fitting the code will return the best fit model parameters, and will determine the uncertainty by creating M bootstrapped data sets and refitting to each. The uncertainty in the N parameters is determined by the standard deviation of the M bootstrapped data set parameter values.
Then, this code is used to plot the data along with 1$\sigma$ and 3$\sigma$ confidence bands.