Strength in Numbers

How much does a snowflake weigh? How about a drop of water? If you’ve ever shoveled snow, or picked up a large jug of water, you know that the weight adds up. The same principle holds true with evaluating evidence. When starting an analysis, we often find little hints that slightly support one hypothesis over the other. Many people might think that these clues wouldn’t really have an impact. Or they might assume that a piece of evidence with a significant influence on the hypotheses renders other evidence meaningless.

However, just like snow, those little pieces of evidence can add up. It’s hard to shovel up thousands of snowflakes at a time (even though individually they’re almost weightless). Likewise, enough evidence pointing in the same direction can have a weighty influence (even if each individual “proof” is not that strong independently).


Adding up the Evidence

For example, imagine that you have two boxes in front of you. Box A is filled with balls: ⅔ of the balls are white and ⅓ are black.  Box B is also filled with balls, but with the opposite distribution: ⅔ black and ⅓ white. You pick a box randomly, not knowing whether it’s Box A (mostly white balls) or Box B (mostly black balls). You draw a ball from the box 50 times (returning the ball each time). Each time you record the color of the ball you pulled out. Out of the 50 times you drew a ball, you got a white ball 30 times.

Does this mean that Box A is more likely to be the one with ⅔ white balls? And if so, then by how much?

Well, it’s actually about a thousand times more likely that Box A is the one with ⅔ white balls. This is a much higher probability than intuition would lead us to expect! Most people guess that it’s around 70%. And even those who think it’s higher don’t come close to the real likelihood (99.9%). Each individual ball drawn has a relatively modest influence, but compounded after 50 draws, the impact is very significant.


Rootclaim’s Bayesian Analysis

In other words, enough little clues can make a big difference, even though each piece of evidence on its own doesn’t tip the scales significantly. However, it can be difficult and counter-intuitive to properly evaluate the different pieces of evidence. That’s one advantage of the Bayesian model–it lets you know when all those little clues are significant enough to overturn the starting assumption. Rootclaim’s unique methodology helps compensate for the cognitive biases that make computing likelihoods accurately so difficult.


What Happened to MH370?

Malaysia Airlines Flight 370 went missing on March 8, 2014, sparking the most extensive search for a plane in history. To date, the plane and its 239 passengers remain missing, with only a few pieces of the plane having been recovered. Theories trying to explain what happened to the plane range from the mundane (pilot suicide or mechanical failure) to the paranormal (alien abductions).


The Pilot Probably Did It

The Rootclaim analysis of MH370 finds that the most likely explanation is pilot suicide, at more than an 80% likelihood. And that’s despite the initial likelihood being higher for fire or maintenance issues–both more common causes of fatal plane crashes. In fact, when considering pieces of “key evidence”–those pieces of evidence identified as having particularly significant differences between the different hypotheses–the pilot suicide hypothesis is only a bit more likely than the copilot suicide hypothesis. 

The rest of the evidence is what causes the odds of the pilot suicide hypothesis to be the most plausible explanation. The other 28 pieces of evidence combined point overwhelmingly towards pilot suicide as the explanation. Each individual piece of evidence only helps a small bit. But all together, they make the difference in determining the outcome of the analysis.