Uncertainty in Epidemiology

Uncertainty arises from making decisions with incomplete information

We treat the modeller’s role as making an estimate $a$ of some unknown quantity $z$, which induces a loss $\ell(a,z)$. We show that the choice of $\ell(a,z)$ defines the measure of uncertainty, while the model defines the missing data.

The missing data determines how much uncertainty can be reduced

In machine learning, irreducible uncertainty is usually what would remain with unlimited data. An epidemic only happens once, so we instead define the missing data as data that could practically be collected. Uncertainty that these data would remove is reducible, and the rest is irreducible.

Reasoning about the data quantifies reducible uncertainty

The missing data are typically unknown in advance. The chosen model makes implicit assumptions about these, allowing us to quantify the expected uncertainty reduction, and thus estimate the value of collecting more data.

More data isn’t guaranteed to reduce uncertainty

New data can contradict what has already been observed, thus increasing uncertainty. Ideally, new data would be expected to reduce uncertainty, and we show that coherence (the assumptions in the predictive model match the assumptions in the fitting model) is the required condition.

EpiEstim [3] and EpiFilter [4] are two widely used tools for tracking how fast an epidemic is spreading. Each depends on a smoothing parameter that users usually leave at its default. We developed efficient methods for fitting these from the data, showing marked improvements in calibration and timeliness [5].

We used the fact that the sum of the log one-step-ahead predictive probabilities is equivalent to the model likelihood. Adapting the models to produce one-step-ahead predictions resulted in computationally efficient ways of calculating likelihoods, thus allowing us to find the posterior distribution of the smoothing parameters.

This work improves the robustness and timeliness of existing popular methods.