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# Summary

`UnfoldSim.jl` is a Julia package for simulating multivariate time series, with a focus on EEG, especially event-related potentials (ERPs). The user provides four ingredients: 1) an experimental design, with both categorical and continuous variables, 2) event basis functions specified via linear or hierarchical models, 3) an inter-event onset distribution, and 4) a noise specification. `UnfoldSim.jl` then simulates continuous EEG signals with potentially overlapping events. Multi-channel support via EEG-forward models is available as well. `UnfoldSim.jl` is modular, providing intuitive entrance points for individual customizations. The user can implement custom designs, components, onset distributions or noise types to tailor the package to their needs. This allows support even for other modalities, e.g. single-voxel fMRI or pupil dilation signals.
`UnfoldSim.jl` is a Julia package for simulating multivariate time series, with a focus on EEG, especially event-related potentials (ERPs). The user provides four ingredients: 1) an experimental design, with both categorical and continuous variables, 2) event basis functions specified via linear or hierarchical models, 3) an inter-event onset distribution, and 4) a noise specification. `UnfoldSim.jl` then simulates continuous EEG signals with potentially overlapping events. Multi-channel support via EEG-forward models is available as well. `UnfoldSim.jl` is modular, allowing users to implement custom designs, components, onset distributions or noise types to tailor the package to their needs. This allows support even for other modalities, e.g. single-voxel fMRI or pupil dilation signals.

# Statement of Need
In our work (e.g. @ehinger2019unfold, @dimigen2021regression), we often analyze data containing (temporally) overlapping events (e.g. stimulus onset and button press, or consecutive eye-fixations), non-linear effects, and complex experimental designs. For a multitude of reasons, we often need to simulate such kind of data: Simulated EEG data is useful to test preprocessing and analysis tools, validate statistical methods, illustrate conceptual issues, test toolbox functionalities, and find limitations of traditional analysis workflows. For instance, such simulation tools allow for testing the assumptions of new analysis algorithms and testing their robustness against any violation of these assumptions.
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To generate complex activations, it is possible to specify a vector of `<:AbstractComponents`.

## Inter-onset distributions
The inter-onset distribution defines the distance between events in the continuous (EEG) signal. Currently, `UniformOnset` and `LogNormalOnset` are implemented. By adjusting the distribution's parameters, one indirectly controls the amount of overlap between the event-related responses. \autoref{fig_onset_distributions} illustrates the parameterization of the two implemented distributions.
The inter-onset distribution defines the distance between events in the continuous (EEG) signal. Currently, `UniformOnset` and `LogNormalOnset` are implemented (see \autoref{fig_onset_distributions}). By adjusting the distribution's parameters, one indirectly controls the amount of overlap between the event-related responses.

![Illustration of the inter-onset distributions. The colours indicate different sets of parameter values. Please note that for the lognormal distribution, the parameters are defined on a logarithmic scale, while the distribution is shown on a linear scale. \label{fig_onset_distributions}](plots/onset_distributions.svg){height="180pt"}

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# Package references
Please note that we list only the main dependencies here, but the dependencies of the dependencies can be found in the respective `Manifest.toml` files. Furthermore, please note that we only list rather than cite the packages for which we could not find any citation file or instruction.

**Julia** [@Julia-2017], **DataFrames.jl** [@JSSv107i04], **Distributions.jl** [@Distributions.jl-2019; @JSSv098i16], **Documenter.jl** [@Documenter_jl], **DSP.jl**[@simon_kornblith_2023_8344531], **FileIO.jl**, **Glob.jl**, **HDF5.jl**, **HypothesisTests.jl**, **ImageFiltering.jl**, **Literate.jl**, **LiveServer.jl**, **Makie.jl** [@DanischKrumbiegel2021], **MixedModels.jl** [@douglas_bates_2023_10268806], **MixedModelsSim.jl** [@phillip_alday_2024_10669002], **Parameters.jl**, **PrettyTables.jl** [@ronan_arraes_jardim_chagas_2023_10214175], **ProjectRoot.jl**, **SignalAnalysis.jl**, **Statistics.jl**, **StableRNGs.jl**, **StatsBase.jl**, **StatsModels.jl**, **TimerOutputs.jl**, **ToeplitzMatrices.jl**, **Unfold.jl** [@ehinger2019unfold], **UnfoldMakie.jl** [@mikheev_2023_10235220]
**Julia** [@Julia-2017], **DataFrames.jl** [@JSSv107i04], **Distributions.jl** [@Distributions.jl-2019; @JSSv098i16], **Documenter.jl** [@Documenter_jl], **DSP.jl** [@simon_kornblith_2023_8344531], **FileIO.jl**, **Glob.jl**, **HDF5.jl**, **HypothesisTests.jl**, **ImageFiltering.jl**, **Literate.jl**, **LiveServer.jl**, **Makie.jl** [@DanischKrumbiegel2021], **MixedModels.jl** [@douglas_bates_2023_10268806], **MixedModelsSim.jl** [@phillip_alday_2024_10669002], **Parameters.jl**, **PrettyTables.jl** [@ronan_arraes_jardim_chagas_2023_10214175], **ProjectRoot.jl**, **SignalAnalysis.jl**, **Statistics.jl**, **StableRNGs.jl**, **StatsBase.jl**, **StatsModels.jl**, **TimerOutputs.jl**, **ToeplitzMatrices.jl**, **Unfold.jl** [@ehinger2019unfold], **UnfoldMakie.jl** [@mikheev_2023_10235220]

# References

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