Han Solo and Bayesian Priors

You also need to consider the survivorship bias of a story from a long time ago in a galaxy far, far away.<p>All the other potential stories where the protagonist predictably wins the Darwin Award would be too uninteresting to reach us over such an immense time and distance.

C3PO&#x27;s estimation would have been a lot more useful if he&#x27;d calculated <i>their</i> odds.<p>Also his calculation suggests there&#x27;s a strong open data regime in the empire, which is a nice thought.

I like the concept, it&#x27;s a cool way of introducing Bayesian probabilities!<p>The conclusion strikes me as overly confident, though. It implies that if we had 100 Han Solo&#x27;s, we are <i>very</i> confident that about 3&#x2F;4 of them are going to make it through. This comes about because it uses this:<p><i>We&#x27;re going to say that C3PO has records of two people surviving and 7,440 people ending their trip through the asteroid field in a glorious explosion.</i><p>as data for Han&#x27;s odds of making it. But 100 out-of-shape people dying on the ascent of Mount Everest does not tell us anything about the odds for someone who is very fit.<p>I would rather model that there is no one true probability of making it through - it&#x27;s going to be dependent on the pilot. Mediocre pilots might have odds in the neighborhoud of 1&#x2F;3720, but there is presumably a lot of variance depending on skill, and my prior belief is that Han would wind up in the upper end of the distribution.

The 75% result (chance to survive) seems about right, but the confidence in this result seems completely unnatural. The sharp peak in the posterior plot suggests that I have nailed down the exact probability to +&#x2F;- 2%. No way.

Thought experiment: imagine there is a second robot, C4P1, on one of the TIE fighters. He independently comes up with an estimate of 10,000:1 for Han&#x27;s death. Are we now going to slide our estimate all the way down? Or, what if C3P0&#x27;s line was revised to say 1,000,000:1? Would the author now say, &#x27;whelp, I was pretty confident at 20,000:1, but now that C3PO&#x27;s number is so much bigger than mine, I guess Han&#x27;s gonna die&#x27;?

I think this is the kind of analysis you need instead:<p><a href="http:&#x2F;&#x2F;tvtropes.org&#x2F;pmwiki&#x2F;pmwiki.php&#x2F;Main&#x2F;PlotArmor" rel="nofollow">http:&#x2F;&#x2F;tvtropes.org&#x2F;pmwiki&#x2F;pmwiki.php&#x2F;Main&#x2F;PlotArmor</a>

Original source: <a href="http://www.countbayesie.com/blog/2015/2/18/hans-solo-and-bayesian-priors" rel="nofollow">http:&#x2F;&#x2F;www.countbayesie.com&#x2F;blog&#x2F;2015&#x2F;2&#x2F;18&#x2F;hans-solo-and-bay...</a>

Does the author have something backwards or do I?<p>P(RateOfSuccess|Successes) = Beta(α,β)<p>&quot;In Bayesian terms, C3PO&#x27;s estimate of the true rate of success given observed data is referred to as the likelihood.&quot;<p>BUT we know likelihood(rateofsuccess|data) = probability(data|rate of success).<p>I am confused.

One factor seems missing: the deviation of Han&#x27;s skills from that of the average pilot. Does C3PO take it into account in his likelihood? Do we take it into account in our probability of success? Although I do get the point, it seems there&#x27;s often something of that sort, a simplification, in that kind of bayesian reasoning.

Someone needs to do this with Game of Thrones characters. Everything I thought about important characters&#x27; survival chances turned upside down as I watched it.