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spelling fixes #263

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Dec 17, 2024
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2 changes: 1 addition & 1 deletion model_definition.md
Original file line number Diff line number Diff line change
Expand Up @@ -265,7 +265,7 @@ We use informative priors for parameters that have been well characterized in th
| Total genomes shed per infected individual | $\log_{10}[G] \sim \mathrm{Normal}(9, 2)$ | Watson et al 2023[^Watson] |
| Initial infections per capita $I_0$ | $I_0 \sim \mathrm{Beta}(1 + k i_\mathrm{est}, 1 + k (1-i_\mathrm{est}))$ | where $i_\mathrm{est}$ is the sum of the last 7 days of hospital admissions, divided by jurisdiction population, and divided by the prior mode for $p_\mathrm{hosp}$, and $k = 5$ is a parameter governing the informativeness ("certainty") of the Beta distribution |
| Initial exponential growth rate | $r \sim \mathrm{Normal}(0, 0.01)$ | Chosen to assume flat dynamics prior to observations |
| Infection feedback term | $\gamma \sim \mathrm{logNormal}(4.50, 0.64)$ | Weakly informative prior chosen to have a mode of 90 in natural scale, based on posterior estimates of the infection feedback from model fits from March 2023 to March 2024 in a Alaska, Massachsuettes, New Jersey, New Hampshire, and Washington |
| Infection feedback term | $\gamma \sim \mathrm{logNormal}(4.50, 0.64)$ | Weakly informative prior chosen to have a mode of 90 in natural scale, based on posterior estimates of the infection feedback from model fits from March 2023 to March 2024 in Alaska, Massachusetts, New Jersey, New Hampshire, and Washington |
| Day of the week effects | $\frac{\vec{\omega}}{7} \sim \mathrm{Dirichlet}(5, 5, 5, 5, 5, 5, 5)$ | Weakly informative prior with a mode at even daily reporting (no effects) |
| Standard deviation of the log of the site-lab level multiplier $M_{ij}$ | $\sigma_m \sim \mathrm{Normal}(0, 0.25) $ | Weakly informative prior chosen to allow average magnitude of concentrations to be either similar or different among individual sites, depending on data |
| Modal site-level observation standard deviation | $\hat{\sigma}\_c \sim \mathrm{Normal}(1,1)$ | Weakly informative prior chosen to allow the mode to be either small or large |
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