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Model definition: estimate_truncation()

This is a work in progress. Please consider submitting a PR to improve it.

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 Cit reflecting reported counts for time t where i=1S 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 ζ(τ|μζ,σζ) with corresponding probability mass function Z(τ|μζ).

The model assumes that final counts Dt are related to observed snapshots via the truncation distribution such that

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

where Ti is the date of the final observation in snapshot i, Z(τ) is defined to be zero for negative values of τ and σ is an additional error term.

The final counts Dt are estimated from the most recent snapshot as

Dt=CSZ(TSt|μZ,σZ)

Relevant priors are:

μζNormal(0,1)σζHalfNormal(0,1)φHalfNormal(0,1)σHalfNormal(0,1)