Terms are presented in the order they are introduced, except where it makes sense to place similar terms near each other.
| Filtering distribution |
The posterior distribution of hidden state \(x_t\) given observed data until time \(t\). Written \(P(x_t | y_{1:t})\). |
| Smoothing distribution |
The posterior distribution of hidden state \(x_t\) given all observed data. Written \(P(x_t|y_{1:T})\). |
| Introduction |
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| \(E[\cdot]\) |
The expectation operator. |
| \(C_t\) |
Reported cases on time-step \(t\). |
| \(I_t\) |
Infection incidence on time-step \(t\). |
| \(R_t\) |
The instantaneous reproduction number at time-step \(t\). |
| \(\omega_u\) |
The serial interval distribution. The probability that a secondary case was reported \(u\) days after the primary case. |
| \(g_u\) |
The generation time distribution. The probability that a secondary case was infected \(u\) days after the primary case. |
| \(\Lambda_t^c\) |
The force-of-infection derived from reported cases. Equals \(\sum_{u=1}^{u_{max}} C_{t-u} \omega_u\). |
| \(\Lambda_t\) |
The force-of-infection derived from infection incidence. Equals \(\sum_{u=1}^{u_{max}} I_{t-u} g_u\). |
| \(s:t\) |
Used as a subscript, refers to all indices between \(s\) and \(t\) (inclusive). |