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71 changes: 34 additions & 37 deletions joss_paper/paper.md
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index: 4
date: 2023-10-17
bibliography: references.bib
- \usepackage[margin=1in]{geometry}
header-includes:
- \usepackage{bm}
---

# Summary
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This work introduces `Taweret`, a Python package for Bayesian Model
Mixing that includes three novel approaches for combining models, each
of which defines the weight function in a unique way (see
Table [1](#tab:methodcomparison){reference-type="ref"
reference="tab:methodcomparison"} for a comparison of each method). This
Table [1]{label="methodcomparison"} for a comparison of each method). This
package has been developed as an integral piece of the Bayesian Analysis
of Nuclear Dynamics (BAND) collaboration's software. BAND is a
multi-institutional effort to build a cyber-infrastructure framework for
Expand Down Expand Up @@ -113,40 +113,37 @@ methods make it a marked improvement over `SAMBA`.

## Overview of methods

::: {#tab:methodcomparison}

+--------------------+---------+-----------+-----------+-----------+-------------------+--------------------+
| Method | Type | Number of | Number of | Number of | Weight | Calibration + |
| | | inputs | outputs | models | functions | mixing |
+:==================:+:=======:+:=========:+:=========:+:=========:+:=================:+:===================+
| Bivariate linear | Mean & | | | | Step, | |
| mixing | Density | 1 | $\geq 1$ | 2 | Sigmoid, | :heavy_check_mark: |
| | | | | | Asymmetric 2-step | |
+--------------------+---------+-----------+-----------+-----------+-------------------+--------------------+
|Multivariate mixing | Mean | 1 | 1 | $K$ | Precision | :x: |
| | | | | | weighting | |
+--------------------+---------+-----------+-----------+-----------+-------------------+--------------------+
| BART mixing | Mean | $\geq 1$ | 1 | $K$ | Regression | :x: |
| | | | | | trees | |
+====================+=========+===========+===========+===========+===================+====================+

: A summary of the three BMM approaches currently implemented in
`Taweret`. Note that $K\geq 2$. Following the method name and the type
of mixing model, the *Number of inputs* column details the dimensions
of the parameter which the mixing weights depend on (e.g., in
heavy-ion collisions this is the centrality bin); the *Number of
outputs* details how many observables the models themselves can have
to compute the model likelihood (e.g., in heavy-ion collisions this
can include charge multiplicities, transverse momentum distributions,
transverse momentum fluctuations, etc.); the *Number of models* column
details how many models the mixing method can combine; the *Weight
functions* column describes the available parameterization of how the
mixing weights depend on the input parameter (the one references in
the *Number of inputs* column); and, lastly, the *Calibration +
mixing* column indicates whether the model is cable of simultaneous
determining the model parameters and mixing weights.

:::
: A summary of the three BMM approaches currently implemented in
`Taweret`. Note that $K\geq 2$. Following the method name and the type
of mixing model, the *Number of inputs* column details the dimensions
of the parameter which the mixing weights depend on (e.g., in
heavy-ion collisions this is the centrality bin); the *Number of
outputs* details how many observables the models themselves can have
to compute the model likelihood (e.g., in heavy-ion collisions this
can include charge multiplicities, transverse momentum distributions,
transverse momentum fluctuations, etc.); the *Number of models* column
details how many models the mixing method can combine; the *Weight
functions* column describes the available parameterization of how the
mixing weights depend on the input parameter (the one references in
the *Number of inputs* column); and, lastly, the *Calibration +
mixing* column indicates whether the model is cable of simultaneous
determining the model parameters and mixing weights. []{label="methodcomparison"}

+---------------------+---------+-----------+-----------+-----------+---------------------+---------------+
| Method | Type | Number of | Number of | Number of | Weight | Calibration & |
| | | inputs | outputs | models | functions | mixing |
+:===================:+:=======:+:=========:+:=========:+:=========:+:===================:+:=============:+
| Bivariate linear | Mean & | 1 | $\geq 1$ | 2 | - Step, | |
| mixing | Density | | | | - Sigmoid, | |
| | | | | | - Asymmetric 2-step | |
+---------------------+---------+-----------+-----------+-----------+---------------------+---------------+
| Multivariate mixing | Mean | 1 | 1 | $K$ | Precision | |
| | | | | | weighting | |
+---------------------+---------+-----------+-----------+-----------+---------------------+---------------+
| BART mixing | Mean | $\geq 1$ | 1 | $K$ | Regression | |
| | | | | | trees | |
+---------------------+---------+-----------+-----------+-----------+---------------------+---------------+


### Bivariate linear mixing

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3 changes: 2 additions & 1 deletion joss_paper/references.bib
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Expand Up @@ -53,6 +53,7 @@ @phdthesis{Liyanage_thesis
URL = {http://rave.ohiolink.edu/etdc/view?acc_num=osu1689508609203123}
}


@inproceedings{BAND_Framework,
author = "{{Bayesian Analysis of Nuclear Dynamics (BAND) Framework project}}",
year="2020",
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year = {2022},
note = {R package version 3.18.17},
url = {https://CRAN.R-project.org/package=BMA},
}
}

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