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sbfnk committed Oct 16, 2023
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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](https://package.epinowcast.org) 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 $Z(\tau | \mu_{\zeta}$.
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

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