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This model deals with the problem of nowcasting, or adjusting for right-truncation in reported count data. This occurs when the quantity being observed, for example cases, hospitalisations or deaths, is reported with a delay, resulting in an underestimation of recent counts. The estimate_truncation() model attempts to infer parameters of the underlying delay distributions from multiple snapshots of past data. It is designed to be a simple model that can integrate with the other models in the package and therefore may not be ideal for all uses. For a more principled approach to nowcasting please consider using the epinowcast package.

Given snapshots $$C^{i}_{t}$$ reflecting reported counts for time $$t$$ where $$i=1\ldots S$$ is in order of recency (earliest snapshots first) and $$S$$ is the number of past snapshots used for estimation, we try to infer the parameters of a discrete truncation distribution $$\zeta(\tau | \mu_{\zeta}, \sigma_{\zeta})$$ with corresponding probability mass function $$Z(\tau | \mu_{\zeta}$$).

The model assumes that final counts $$D_{t}$$ are related to observed snapshots via the truncation distribution such that

$$$C^{i < S)_{t}_\sim \mathcal{NegBinom}\left(Z (T_i - t | \mu_{Z}, \sigma_{Z}) D(t) + \sigma, \varphi\right)$$$

where $$T_i$$ is the date of the final observation in snapshot $$i$$, $$Z(\tau)$$ is defined to be zero for negative values of $$\tau$$ and $$\sigma$$ is an additional error term.

The final counts $$D_{t}$$ are estimated from the most recent snapshot as

$$$D_t = \frac{C^{S}}{Z (T_\mathrm{S} - t | \mu_{Z}, \sigma_{Z})}$$$

Relevant priors are:

\begin{align} \mu_\zeta &\sim \mathrm{Normal}(0, 1)\\ \sigma_\zeta &\sim \mathrm{HalfNormal}(0, 1)\\ \varphi &\sim \mathrm{HalfNormal}(0, 1)\\ \sigma &\sim \mathrm{HalfNormal}(0, 1) \end{align}