Table 2 Prior distributions
From: Impact of the Euro 2020 championship on the spread of COVID-19
Variable | Meaning | Prior distribution | Equation |
|---|---|---|---|
coff | Off-diagonal term of non-football related interaction matrix | \({{{{{{{\rm{Beta}}}}}}}}\left(\alpha=8,\beta=8\right)\) | (6) |
ωgender | The fraction of female participation in football related gatherings compared to the total participation | \({{{{{{{\rm{Beta}}}}}}}}\left(\alpha=10,\beta=20\right)\) | (9) |
\(\Delta {R}_{{{{{{{{\rm{match}}}}}}}}}^{{{{{{{{\rm{mean}}}}}}}}}\) | Mean gathering-related match effect | \({{{{{{{\mathcal{N}}}}}}}}\left(\mu=0,\sigma=5\right)\) | (14) |
\(\Delta {R}_{{{{{{{{\rm{stadium}}}}}}}}}^{{{{{{{{\rm{mean}}}}}}}}}\) | Mean effect of hosting a match at the stadium | \({{{{{{{\mathcal{N}}}}}}}}\left(\mu=0,\sigma=5\right)\) | (19) |
σα | Prior value of the deviation from the mean match effect | \({{{{{{{\rm{HalfNormal}}}}}}}}\left(\sigma=5\right)\) | (16) |
σβ | Prior value of the deviation from the mean stadium effect | \({{{{{{{\rm{HalfNormal}}}}}}}}\left(\sigma=5\right)\) | (21) |
R0 | Value of Rbase(t) at t = 0 | \({{{{{{{\rm{LogNormal}}}}}}}}\left(\mu=1,\sigma=1\right)\) | (23) |
σΔγ | Prior value of the effect of the change points of the base reproduction number | \({{{{{{{\rm{HalfCauchy}}}}}}}}\left(0.5\right)\) | (26) |
ln | Length of the change point n | \(\log \left(1+\exp \left({{{{{{{\mathcal{N}}}}}}}}\left(4,1\right)\right)\right)\) | (27) |
dn | Date of the change point n | \(\,{{\mbox{27th May 2021}}}\,+10\cdot n+{{{{{{{\mathcal{N}}}}}}}}\left(0,3.5\right)\) | (29) |
ΔR0,noise | Value of ΔRnoise(t) at t = 0 | \({{{{{{{\mathcal{N}}}}}}}}\left(\mu=0,\sigma=0.1\right)\) | (32) |
\({\sigma }_{\Delta \tilde{\gamma }}\) | Prior value of the effect of the change points of the reproduction number of other non-balanced transmission | \({{{{{{{\rm{HalfCauchy}}}}}}}}\left(0.2\right)\) | (35) |
\({\tilde{l}}_{n}\) | Length of the non-balanced transmission change point n | \(\log \left(1+\exp \left({{{{{{{\mathcal{N}}}}}}}}\left(4,1\right)\right)\right)\) | (36) |
\({\tilde{d}}_{n}\) | Date of the non-balanced transmission change point n | \(\,{{\mbox{27th May 2021}}}\,+10\cdot n+{{{{{{{\mathcal{N}}}}}}}}\left(0,3.5\right)\) | (38) |
D | Median of the latent period and reporting delay kernel | \(\log ({{{{{{{\mathcal{N}}}}}}}}(\mu=\exp ({\bar{D}}_{{{{{{{{\rm{country}}}}}}}}}),\sigma={\sigma }_{\log \bar{D}}))\) | (41) |
σD | Standard deviation of the delay kernel | \({{{{{{{\mathcal{N}}}}}}}}(\mu=0.2\cdot {\bar{D}}_{{{{{{{{\rm{country}}}}}}}}},\sigma=0.08\cdot {\bar{D}}_{{{{{{{{\rm{country}}}}}}}}})\) | (43) |
\({r}_{{{{{{{{\rm{base}}}}}}}},d}^{{{{\dagger}}} }\) | Prior fraction of the logit-transformed weekday dependent delay | ||
σr | Prior deviation of the different weekdays from the prior of the fraction of delayed cases | \({{{{{{{\rm{HalfCauchy}}}}}}}}\left(1\right)\) | (51) |
e | Prior deviation of each day from the weekday dependent delay | \({{{{{{{\rm{HalfCauchy}}}}}}}}\left(0.2\right)\) | (52) |
κ | Overdispersion of the observed cases around the expected number of cases | \({{{{{{{\rm{HalfCauchy}}}}}}}}\left(20\right)\) | (54) |
