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=1…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 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(TS−t|μZ,σZ)
Relevant priors are:
μζ∼Normal(0,1)σζ∼HalfNormal(0,1)φ∼HalfNormal(0,1)σ∼HalfNormal(0,1)