Let’s back up and take the outside view.

I dug up a somewhat sloppily produced pdf published by the who that purports to be a changelog of variant classifications. The list seems incomplete, because there are variants that change classification before being assigned a classification, and some variants are assigned a classification but then don’t get mentioned in the rest of the document, which spans more than two years.

Here is a brief summary of the relevant variant changes listed in the document.

• There are 28 variants that entered the list as variants under monitoring.
• Of these, 4 were upgraded to variants of interest.
• Another 20 were de-escalated, meaning they ceased being under monitoring without entering a higher severity class.

We can sense some complications in this, like how the fate of four variants is unknown. In survival analysis, we say that the data is censored.1¹ Additionally, there is one variant that was upgraded to voi from vum without first entering as vum, and four variants that were de-escalated from vum without entering as vum. This is known as truncation. We could use tools from survival analysis to deal with this, but we will – at least for now – focus on the specific question asked on Metaculus, assume the effects of censoring and truncation are relatively small and look just at the cases for which we know the full timeline.

• 24 variants enter under monitoring, of which
• 4 are eventually upgraded to variants of interest.

We can already provide a very naïve estimate for the base rate here. When a variant enters under monitoring, we have – thanks to Laplace’s law of succession – a posterior of

\[\frac{4+1}{24+2} \approx 19 \%\]

probability that it eventually becomes a variant of interest. Already, this is lower than the community 35 %.

But it doesn’t account for the time horizon of the question! Some of those 19 % of variants will be upgraded to a variant of interest only after the question time horizon is over, which means they don’t count for our forecast. What’s the timeline of upgrades? The variants under monitoring that became variants of interest stayed under monitoring for

This means that even assuming that a variant becomes a variant of interest eventually, there’s only about a 70 % chance that it happens within 44 days of listing.2² Linear interpolation between 50 % at 22 days and 75 % at 49 days. You might find it odd that I dare linearly interpolate an empirical distribution of just four values, but as we’ll see later, the distribution of monitoring times also for de-escalated variants is fairly linear, which lends credibility to the method.

So in total, the probability that a variant is upgraded to a variant of concern within 44 days of being listed as a variant of concern is 19 % × 70 % = 14 %. This probably suffices as a first forecast, but it doesn’t tell us anything about how to update our forecast as time passes.

Note that the variants that were upgraded were under monitoring for an average of 37 days. The variants that are under monitoring but get de-escalated stay under monitoring for an average of 119 days! For every day that passes and a variant is not upgraded, that should slightly increase our belief that this variant belongs to the group that will eventually be de-escalated.

We can compute this using Bayes’ rule in its odds form:

\[o(u \mid T > t) = \frac{P(T > t \mid u)}{P(T > t \mid \neg u)} o(u)\]

where \(u\) is the hypothesis “BA.2.86 will eventually be upgraded” and \(T > t\) is the observation “BA.2.86 has been under monitoring for at least \(t\) days”.

It helps here to know that

\[o(E) = \frac{P(E)}{1 - P(E)}\]

and conversely

\[P(E) = \frac{o(E)}{1+o(E)}\]

Applying this, we’ll learn the odds that BA.2.86 will eventually be upgraded given that it has been under monitoring for \(t\) days, and then we will recompute this for each day that passes.

We already know our prior odds \(o(u)\) – that’s the 19 % probability we computed before, an odds of 0.23.

Tabulation of forecast for my own convenience.