ObservationSchemes.jl
This is a utility package belonging to a suite of packages in JuliaDiffusionBayes. Its purpose is to provide a systematic way of encoding discrete-time observations for stochastic processes. However, in principle, it can also be used in more general contexts, for observations that were not generated by stochastic processes.
The underlying idea behind the package is to provide a set of decorators that may be used to equip each data-point separately, and in doing so, describe how a given data-point has been recorded. This flexible framework can be used to define complex observation schemes in a simple way.
The following types of observations can be defined with this package:
- Exact observations of all or a subset of all coordinates of the underlying process
- Linear translations of the underlying process, disturbed by Gaussian noise
- First-passage time observations
- First-passage time observations with additional resetting events
- Non-linearly (or linearly) transformed observations with Gaussian or non-Gaussian noise
- Parameterized versions of all observation types above
Additionally, the package provides functionality to couple multiple observations together, so as to define:
- Multiple observations of a single process
- Multiple observations of multiple processes, coming possibly from different laws that share subsets of parameters (mixed-effect models)
Finally, we provide infrastructure for defining priors over starting points. In particular we add concrete implementations of
- Degenerate priors corresponding to fixed starting points
- Gaussian priors
Depending on your intended use of this package you might choose to start at different places:
- For a quick overview of ObservationSchemes.jl's main functionality see Get started
- For a systematic introduction to all functionality introduced in this package see the Manual
- For a didactic introduction to problems that can be solved using ObservationSchemes.jl see the Tutorials
- If you have a problem that you think can be addressed with this package, then check out the How-to guides to see if the answer is already there.