If more people had been “mentally inoculated” somewhere during their education with a simple logical “vaccine” called a “Bayesian prior” we perhaps would not be in this current state of political craziness with elections and vaccine hesitancy.

Here is an “In the News” example: When thousands of signatures on mail-in ballots appear, to the untrained eye, to be different from some “official” signature from the same voters, which of these do you assume?

1. Massive voter fraud is occurring, enough to swing an election? Or…
2. The signatures of ordinary, rightful voters differ over time and among different legal documents?

A “prior” is an assumption on which you base a belief before you seek more evidence. How you frame that prior in your head, and then what you do to test your prior, will determine whether you will move your opinion toward more of a reality-based grounding, or whether you will let your prior take you into a rathole of conspiratorial thinking.

Bayesian priors are named after Thomas Bayes, the 18th-century creator of a simple, yet transformative, statistical method called Bayes Theorem. These are priors based on a probability guess using the best available existing evidence, if there is any. This sets the ground for an experiment or a high-quality search to find new data which would “improve” your probability guess, either up or down, using Bayes Theorem, which is a simple mathematical formula for updating that probability.

That “improved guess” (the posterior probability) in turn becomes the new prior for another round of testing. However, you don’t really even need to know the Bayes Theorem math to improve the accuracy of a well-grounded prior. Your brain is pretty good at doing this subconsciously to a “close enough” level without a calculator.

Here in Hurricane Country, we see this process repeated multiple times every year as new named tropical storms either evolve into full-fledged hurricanes or fizzle out. Hurricane forecasting models are essentially Bayesian priors generated from multiple computer simulations, each one predicting a probable path of each forming storm. Initially the models often disagree several days out, but as the days progress, the models merge into basic agreement.

Source: Ars Technica

And over the years, precisely because of this process, these Bayesian priors at the very early rumblings of each new tropical storm have become more and more accurate. Bayes Theorem moves you iteratively toward “better guesses” for improving your prophetic weather forecasting. Within a week after the forecast for Hurricane Irma below was published, the “loser models” were likely updated based on the new data and Bayes Theorem for better hurricane prediction the next time around.

Back to ballot signature fraud

If you are approaching the ballot signature challenge with absolutely no prior (literally) experience in signature matching, the differences in voters’ scrawls on signature lines can look very disturbing. But step back and form your assumption into a Bayesian prior. What percentage of apparently mismatched signatures are still those of valid voters? 90%? Or 50% Or 10% Take a stab.

The assumption of ignorance in a classic Bayes test would be to start at a 50-50 probability and cycle tests from there. This assumption is actually controversial among statisticians, but the point is that you need to start somewhere in order to move to the next stage, which is to construct an experiment that will quickly adjust that probability in one direction or another, as shown in the first diagram above.

Alternatively, you could improve your prior by asking an expert who has already run experiments on signature matching and begin your own testing of your assumption from there. The experts might not be exactly correct in their probabilities, but you likely have a much better prior from which to start.

The best experiments are those that would not necessarily support your position, but rather which would most definitively disprove it if they proved true. You could, for instance, take any signature verification process in use and pre-test it on a known data set of verified signatures before an election and see what kind of results you get. If your process “guesses wrong” too many times, then you likely need to adjust the process and you should be very suspicious of any ballots matched via this method.

Indeed, this testing is done all the time, especially as new computer-assisted signature matching computer software is proposed. Each well-constructed test will likely move the odds in one direction or another if you started with an inaccurate prior, a bad guess as to how the test would turn out.

Multiple tests on computer-automated verification of signatures have demonstrated over 95% accuracy, which sounds pretty good. Even then, the 5% bad guesses turn out by far to be mostly “Type I errors,” where a valid voter’s signature was rejected. Throwing out even 5% of “good votes” is not good public policy without contacting the voter, as you are denying the right to vote to legal voters based on their penmanship skills. [1] States such as California still rely mostly on a manual signature process, which has been pre-tested to demonstrate even higher accuracy, well over 99%. [2] In short, if your “Bayesian prior” assumption was that “50% of signature mismatches are fraud,” this very simple test would prove you wrong.

I have noted in the past that mail-in votes, so much criticized in this last election go-round, are often much easier to audit (assuming a “real CPA-type” audit, not the amateurish Arizona thing) post-election than are many of the in-person systems currently in place. You simply set up a reasonable “Bayesian prior” estimate, and using proven statistical sampling methods, a small number of randomly selected ballots (rather than “recount them all”) will either validate or challenge your prior assumption. Numerous “real audits” consistently validate ballot signatures at a very high level, and even then, most “rejections” are, in the end, those Type I error “real voters” with bad handwriting.

Bayesian priors and vaccines

I will be the first to grant that getting a vaccine injection can be a scary experience if you have not had a shot since the multiple vaccine injections you had to get before attending grade school, or the many vaccinations (up to 17) that you may have received while serving in the U.S. military forces. The three Covid-19 vaccination alternatives have experienced an unusually-high level of vaccine resistance in the United States, despite over 200 million Americans and over 3.5 billion people worldwide having received at least one shot.

You might phrase your Bayesian prior in any one of a number of ways. Start out by saying: Given what I know NOW…

1. What is the percentage chance that this vaccine will cause me permanent harm? Or…
2. What is the percentage chance that this vaccine will prevent my hospitalization or death from Covid-19?

Let’s say that your prior estimates that you have a 1-out-of-100 chance of being permanently harmed by a Covid vaccination. That would mean that you would need to find evidence that two million Americans, or 35 million people worldwide, have already been harmed by the vaccination. If you can’t find data to support that (and you won’t), then you need to ratchet down your prior odds considerably and try again. If you keep repeating this process, and follow the data rather than an anecdote you read on Facebook, your “prior odds” will keep dropping well into the “negligible” level.

If, on the other hand, what if you were to guess that the vaccination would give you a 95% chance of preventing hospitalization or death from Covid? The Centers for Disease Control has estimated that, so far, 6.2 million people have been hospitalized, and over 700,000 have died from Covid. Given a U.S. population of 331.5 million people, this indicates that around 2% of the U.S. population have already been hospitalized for Covid, both before and after vaccinations have become widely available.

But how many of these hospitalized people were vaccinated? The CDC currently counts only about 32,000 people out of about 187 million vaccinated Americans who have been hospitalized or died from Covid, with people over 65 making up 85% of these deaths and two-thirds of the hospitalizations. Run that through your calculator: 32,000 divided by 187,000,000. That is about 0.02%, or 100 times less than the total hospitalized percentage.

And so, for my #2 prior above, I need to “up the percentage” of my Bayesian prior well past a 99% probability that the vaccine will keep me out of the hospital and the grave. And the shot is free. Quite the deal!

Inject your brain

The next time you engage in a conversation about a controversial subject, stop and ask yourself, “What are my priors?” What kind of betting odds would be required to assume that my priors are true, and how would I go about confirming or challenging those odds? Purposefully “inject this vaccine” into your own head.

Some of the world’s top neuroscientists posit that the human brain is itself constantly performing a neurochemical form of Bayesian analysis via the “probability voting” of millions of neurons firing near-simultaneously (or not). New input from your senses is constantly updating the “Bayesian priors” coming from your memories, and in the process new memories (new priors) are formed. Every time you swing a baseball bat or attempt to parallel park your brain is being updated with new probabilities to become your new, updated priors the next time you are in a similar situation.

And so, here you are, doing Bayesian statistics constantly in your head and you weren’t even a math major.

Notes:

1. As far as I can determine, my Florida county matches my mail-in ballot signature to a signature that I had entered at the DMV office using a plastic stylus on “hinky” credit-card-style pad. I look at my not-so-good driver’s license signature and try to match it when I sign my ballot.
2. Here is part of the California manual signature validation process. Note that by law “the basic presumption that the signature on the petition or ballot envelope is the voter’s signature”:
   • Slant of the signature.
   • Signature is printed or in cursive.
   • Size, proportions, or scale.
   • Individual characteristics, such as how the “t’s” are crossed, “i’s” are dotted, or loops are made on the letters f, g, j, y, or z.
   • Spacing between the letters within the first and/or last name and between first and last name.
   • Line direction.
   • Letter formations.
   • Proportion or ratio of the letters in the signature.Initial strokes and connecting strokes of the signature.
   • Similar endings such as an abrupt end, a long tail, or loop back around.
   • Speed of the writing.
   • Presence or absence of pen lifts.
   • Misspelled names.

Related posts:

• Type I versus Type II errors in election security
• Governance via unamusing anecdote
• Bad habits and the Bayesian brain