Thread by @balajis

In 2009, it was unlikely that BTC would cross $100k. But conditional on BTC having *already crossed* $10k, it was more likely to cross $100k.

On Dec 1, 2019 it was unlikely the virus would cross 100k cases. But having *accelerated* past 10k, it was more likely to cross 100k.

Of course, the dynamics of prices & cases are different, but both are often modeled as stochastic processes: prices as GBMs, epidemics as SEIR[S].

At the beginning the parameters of these stochastic processes are unknown. But as data comes in, parameter estimates update.

Now, because we can't run these experiments over again, the utility of these models is more limited than (eg) physics.

That is, there's only one multi-year rise of Bitcoin, only one #covid2019 epidemic (thankfully!). But you can do as many inclined plane experiments as you want.

Still, given assumptions, the math gives you probabilities that you can use to hedge against various outcomes. What they are best for is formalizing the *non-obvious* consequences of assumptions.

Given that X(t) got to 10k, how much more likely is it that it gets to 100k?

Some links:

1) BTC prices: blockchain.com/charts/market-…
2) JHU dashboard: gisanddata.maps.arcgis.com/apps/opsdashbo…
3) Geometric Brownian Motions: en.wikipedia.org/wiki/Geometric…
4) SEIR[S]: institutefordiseasemodeling.github.io/Documentation/…
5) Level crossings:
6) Excursion probabilities: en.wikipedia.org/wiki/Excursion…