Classic Bayesian decision theory helps us make the best decisions assuming we have knowledge of several things. For instance, to decide if a given sample is good or bad, we need to know the expected fraction of bad samples in the whole population. We also need to know the properties of the method we use to make the decision. All methods will have some rate of false positives and false negatives.
We also need to have a payoff matrix. What is the cost of making a wrong decision if the sample is good and what is the cost of making a wrong decision is the sample is bad? What is the benefit in each case?
A typical example of this process might be trying to decide if a biopsy sample is cancerous or not. We have four possible results: (1) It is cancerous and we correctly identify it; (2) It is cancerous and we misidentify it; (3) It is normal and we correctly identity it; (4) It is normal and we misidentify it. Since cancer is well studied, we know before making the test that the sample has a given probability of being cancerous. Assume we also know the rates of false negatives and false positives for this test. But we are not done. In addition, we also know (at least approximately) the payoff matrix.
If the patient has cancer and we do not catch it, the patient might die due to lack of care. If the patient does not have cancer and we conclude falsely that cancer is present, then expensive, potentially dangerous treatments might follow along with mental distress. If the patient has cancer and we catch it, effective treatment might follow. If the patient does not have cancer and we agree, then the world is good. The simple Bayesian formulas give us the probability of making the correct decision weighted by the payoff matrix.
This might sound too complicated, but it’s straightforward. In daily life, we approximate this formal process without thinking. Before making a decision based on observations, we might consider the likelihood that we are right and the probability that the event we think we witnessed is correct. Is a streak across the sky a meteor or an alien landing from outer space? Meteors are common; aliens are not. Of course, this informal method is often biased and improperly applied, leading to spurious decisions such as racial prejudice.
Which brings us to the more interesting problem that we all face daily: How do we make rational decisions in the absence of sufficient knowledge? When you drive a car in traffic, formal Bayesian decision theory will not help you make an immediate decision to avoid objects falling off the car in front of you. In an emergency, we must respond quickly. How do we do it?
Often we make immediate decisions based on experience and later go back to gather more data to help make better decisions in the future. An example of this from the previous post in this series is whether to accept the duality hypothesis of mind and brain. In essence, are our beings completely described by the neurochemical working of our physical brains, or is there something in addition that defines us? That something else is often called a soul. Do souls exist? Most people make a decision one way or the other with grossly inadequate data.
To remedy this lack and put that decision on a more solid basis, some investigators have gone to great lengths to find scientific evidence that could be used to determine if souls exist. One that I am particularly fond of is a determined quest to measure the weight of people as they died. Dr. Duncan MacDougall hypothesized that a soul had weight, and since the soul is thought to leave a body at death, a sensitive scale could detect its departure from a dying person. In the early 20th century, he actually put dying patients on a sensitive scale (volunteers?) and made careful measurements of their weight when they died. He correctly found a slow loss of weight due to normal breathing and loss of moisture as they were lying on his scales, but most surprising was his conclusion that, at death, his subjects lost an average of 21 grams (about half an ounce) and that could be attributed to the departure of a soul since no other source of the loss was apparent. He even repeated his tests with dying dogs, which are assumed to not have souls, and found no loss of weight on dying in agreement with his hypothesis.
Subsequent studies found serious flaws in his techniques and conclusions. His results have been soundly refuted. There is a large literature based on this study. A movie, 21 Grams, was named for the weight of a soul. Note that refuting his work does not mean the concept of souls is refuted; it just means that if they exist, they were not weighed by him. In other words, he failed to support, but did not refute, his hypothesis.
From a decision making point of view, we should consider the good doctor to be a minor hero. Unwilling to simply accept or reject the hypothesis of duality, he set out to find dispassionate evidence. Even though his studies were flawed and probably biased by his personal beliefs, they were reasonably thought out and actually provoked further studies — and even this article.
The next time you are subjected to a harangue about either religion or politics with your oppressor stoutly affirming what is right — without scientific evidence — remember Dr. MacDougall, who took the higher road and at least attempted to put his personal decisions on a firm scientific footing by increasing his knowledge of the underlying phenomena. That he did this rather than blindly accept an unsupported hypothesis is to be commended even if his final analysis was flawed. Seekers who are willing to put their beliefs to scientific scrutiny are our most valuable asset.