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Update phi parameterisation #487

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Oct 25, 2023
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Update NEWS.md
Co-authored-by: Sebastian Funk <sebastian.funk@lshtm.ac.uk>
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seabbs and sbfnk authored Oct 24, 2023
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## Model changes

* Updated the parameterisation of the overdispersion term `phi` to be `phi = 1 / sqrt_phi ^ 2` rather than the previous parameterisation `phi = 1 / sqrt(sqrt_phi)` based on the suggested prior [here](https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations#story-when-the-generic-prior-fails-the-case-of-the-negative-binomial) and the performance benefits seen in the `epinowcast` package (see [here](https://github.com/epinowcast/epinowcast/blob/8eff560d1fd8305f5fb26c21324b2bfca1f002b4/inst/stan/epinowcast.stan#L314)). By @seabbs in # and reviewed by @sbfnk.
* Updated the parameterisation of the dispersion term `phi` to be `phi = 1 / sqrt_phi ^ 2` rather than the previous parameterisation `phi = 1 / sqrt(sqrt_phi)` based on the suggested prior [here](https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations#story-when-the-generic-prior-fails-the-case-of-the-negative-binomial) and the performance benefits seen in the `epinowcast` package (see [here](https://github.com/epinowcast/epinowcast/blob/8eff560d1fd8305f5fb26c21324b2bfca1f002b4/inst/stan/epinowcast.stan#L314)). By @seabbs in # and reviewed by @sbfnk.

# EpiNow2 1.4.0

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