Inductive Probabilistic Reasoning

The world is less parsimonious than most scientists believe …

Inductive Probabilistic Reasoning+ (IPR) quite simply states: If “70% of A’s are B’s" and “a is in A” then “a is in B with a probability of 70%.” So if 70% of patients with mental impairment have Alzheimer’s then if we find a patient with mental impairment there is a 70% chance he or she has Alzheimer’s.

For Inductive Probabilistic Reasoning to work we must first generalize. We generalize what it means to have mental impairment (A), and we generalize what it means to have Alzheimer’s (B). Just because the math worked for those first clinicians who came up with the 70% doesn’t mean it will work for subsequent clinicians. There are a thousand variations on what we deem mental impairment (A). And there are many interpretations on the clinical symptoms required for Alzheimer’s (B). We generalize the probabilities using The Principle of Indifference. We assume that each and every event has same probability of occurring.

Inductive Probabilistic Reasoning forms the basis of the funnel approach in science. The funnel approach is a stepwise approach where we start with a very broad population and in each step we try to eliminate as many paths as possible, and we eliminate based on probabilities. It’s a last man standing approach. It means a lot of work goes on before your R&D product reaches the consumer, and only then it fails. Good products may never see the light of day because they are never queried in consumers. They didn’t make it past the early probabilities. The funnel approach to R&D was born as a tactic to cut down on waste and to reduce costs. But it opens the possibility we may be throwing out the baby with the bath water.

We have a series of rooms, each with different textured walls. In the first room we have a big pile of mud. Both the texture of the wall and the mud have been specially formulated to maximize the chance that mudballs made from the pile will stick to the wall. We start making mudballs and throwing them against the wall. Some of our team uses an overhand pitch, others use gentle underhand lobs. A couple of team members are quite innovative in how they throw the mudball to maximize its chance of sticking.

The second team peels the mudballs off the wall in the first room that have stuck. ‘What about this one that is only half-stuck?’ ‘Leave it, the competition is also busy throwing mudballs and we’ll fall behind is we consider every partial success.’ So the second team lobs, pitches and heaves the mudballs onto their specially textured wall. ‘These mudballs don’t seem to have the right heft!’ ‘Just keep throwing them!’ In the end only half of the mudballs stick, the mud is starting to dry out.

The third team comes and peels the mudballs stuck to the second wall. They are to throw these at the their specially designed wall. ‘Hey, what about these few mudballs that stick but don’t seem to leave any stain?’ ‘That’s interesting, but we’re only interested in whether or not they were stuck to the wall.’ The third team finds that none of the mudballs stick to their wall. They try again, but the mud’s really starting to dry out now. They wonder if perhaps adding a bit of water to the surface of the balls might make them stick better, but the balls start to disintegrate. The project is brought to a halt.

So IPR means 70% of the mudballs (A) stick to the first wall (B), and only 35% (A’) to the second wall (B’), and then 0% to the third wall. Our third wall (C’) it turns out did not have a single texture: those wascally humans. It should be clear to the reader there are other ways of finding mudballs that stick to all the walls, and perhaps even do not leave stains on the walls. For example, we might follow the room scenario 1-3-2-3-1-2-3. More mudballs make it to room 3 in this scenario.

IPR is very much intertwined with ad hoc hypotheses creation. In the first room I hypothesized that 100% of my mudballs would stick, based on cohesion, moisture, grain size, and a host of other physical characteristics of the mud. My wall was designed so my mud should always stick. But it didn’t. So I come up with an alternative hypothesis. There was just too much variability in the texture of the wall. That’s why we saw so many mudballs that only partially stuck. Where the texture was good, then it stuck. That’s why we only got 70%. I create a new ad hoc hypothesis. We test the texture of the wall and find that indeed it is varied, but the variations are finely mixed within otherwise well-textured spaces. There is nothing obviously different about the texture of the wall where a mudball stuck and where one didn’t stick. So it must be the mud. I hypothesis the mud was not mixed well enough, or that some of the ingredients were out-of-spec. So I begin a microscopic review of mudballs that stick vs. didn’t stick. Again, no difference. It must be the pitcher. No difference. It must be some combination of pitcher and location in the room, the size of the mudball, differences in ambient condition from the beginning to the end of the test, ad infinitum. The ad hoc hypothesis creation is a never-ending cycle. And now onto the second room…

Of course if one or two mudballs had stuck to the last wall it would be quite a story you could weave. You go down through the funnels and you explain why these one or two made it through to the end. You weave a narrative that makes it all sound exceptionally good and so logical. It’s very easy to weave a narrative for a mudball that makes it past all the hurdles. In the pharmaceutical industry successful drugs often end up treating a medical condition for which they never were originally intended. That last wall won’t have the texture for which we end up licensing our mudballs.

Also, if my mudball sticks to all the walls I assume I have a mudball that will always stick to the last wall. And we know that’s not true because my last wall is quite special. As a matter of fact, it would almost be better to have a mudball that sticks many times to my last wall, even if it didn’t stick to any of the other walls. I say almost because if I can’t weave a story then the stickiness on that last wall doesn’t matter:

The mechanism of mudball sticking is currently unknown on smooth textured walls.

And the FDA will never approve your mudball for that smooth textured wall without a convincing narrative.

Further Reading