I have read many articles about Bayesian thinking. Most of the time, they fall under 2 categories (or a mix of both).
- The first category of articles focuses on Bayes’ formula.
- The second category of articles focuses on the bayesian principle (without math).
But none focuses on a simple mental model that is 1) mentally easy to compute 2) accurate in assessing the probability of the posterior given some new information.
- Mentally easy to compute: Bayes’ formula is difficult to compute in your head.
- Accurate: The bayesian principle (without the math) doesn’t give accurate probabilities of the posterior.
While reading, what I wished to find was a simple bayesian mental model I can use in my head to make better decisions based on the guessed probabilities of particular events (even if it’s an approximation).
Will Startup X succeed?
H: startup X will succeed
d: Startup X got a series B funding
The prior is easy to grasp mentally. This is plain probability estimate of an initial belief.
There no difficulties to assign a rough probability to H. At least with a 10-20% variance.
E.g. I believe that startup X will not succeed (I assign a probability of success <50%. Easy). Based on rough statistics, I know that 9/10 startups fail. So my intuition will be ~10% success. Given the strong team behind the business, I will credit the startup with an additional 10% chance of success. Let’s say 20% chance of success.
So far, this prior estimate can be done mentally.
The rest of the equation
What is more difficult is to compute mentally the other part of the equation.
Indeed. Updating the initial belief in the light of new data, without the formula, fails to grasp the correct order of magnitude of the posterior.
E.g. If I believe startup X has 20% chance of success based on my prior belief and then I’m aware that startup X got a series B funding, this data favors the chance of success of startup X. But from 20% chance of success, should I believe startup X has now 35%, 45%, 55% or 80% chance of success?
The bayesian principle alone doesn’t give a sense of the correct order of magnitude of the posterior. Hence it is rather useless when it comes to mentally assessing the probability of a decision outcome.
Sure, using the formula, I can ballpark the probabilities for each term of the equation.
- H: Startup X will succeed
- ~H: Startup X will fail
- d: Startup X got a successful series B funding
- ~d: Startup X didn’t get a successful series B funding
With Bayes formula,
P(H|d) = [p(d|H) x p(H)] / [(p(d|H) x p(H)) + (p(d|~H) x p(~H))]
- p(H) = 20%
- p(~H) = 80%
- p(d|H) = 90% (rough estimate: startups who succeed have a high chance of having gotten a series B funding)
- p(d|~H) = 60% (rough estimate: startups who fail also get funding but probably didn’t make it until series B)
- p(H|d) = (90% x 20%) / [(90% x 20%) + (60% x 80%)]
- p(H|d) = 0.18 / (0.18 + 0.48)
- p(H|d) = 27%
Using the formula, we get a 27% chance of success. But:
- This result would have been difficult to compute in my head
- The result is surprisingly low to me.
Using the “Bayesian principle” (no math), I would have been biased. Even if startups tend to fail, a successful series B would have led me to believe that, now, this startup has a fair chance of success (at least around 50%).
- When no formula is involved (the “bayesian principle” only) I fail to assess the correct order of magnitude of the posterior.
- When math is involved, I find it very difficult to compute the posterior mentally.
- In both cases, it’s not really suitable for quick decision making.
What is your method to accurately “guesstimate” a decision using Bayes principle?