I am showing below comments, questions and answers. Readers are welcome to send me their own version of replies to my comments and questions.

Are we all classified as “doomed”, “immune”, “causative”, or preventive?

Comment #1: Having been taught that uncertainty (and even “of the degree of uncertainty”) is always present in scientific inference, I was trying to find one among the limitations:

What is the value of the entire exercise if “doomed, immune, causative, and preventive” do not exist? What if causal parameters are a property of a world constructed with indeterministic causation? What if the outcome of an individual is a random variable when exposed and a random variable when unexposed? I guess that at the end we are uncertain whether the bounds are certain or not--even without additional constraints.

Response: Certainly, like every other method, this one is only as good as its assumptions. You question whether people really belong to deterministic causal types. There is certainly no way to resolve this question. All I can say is that it seems to make sense to me, and others. Your supposition that outcomes are truly random events seems completely outside the realm of any real world experience I've ever had. Randomness doesn't exist outside of the quantum realm. Randomness can ~seem~ to occur, but this is likely due to unobserved causes. Perhaps, "happenstance" or "coincidence" is a better term than random.

Comment: Like many others, I prefer to think that no miracle has transformed indeterminism at the micro-cosmos into determinism at the macro-cosmos. But I don't know the answer. I am not aware of methods to know whether the outcome of a person is deterministic or indeterministic, but I do have some theories to explain when our mind is convinced that the outcome was deterministic. As we know, intuition and psychology are not reliable means to discover hidden reality.

Comment #2: Quote: “Stochastic variability can be introduced to the extent that the observed population is a random sample of a hypothetical superpopulation. In this case, the cell frequencies are sampled and the resulting constraints have a random component, which can be modeled using Markov Chain Monte Carlo methods”.

With reference to the quote: To where do we take the bounds, once computed? To which population? How do we use them to infer anything about any other population, which likely contain a different, unknown distribution, of the four types? What sort of inference do we have beyond the finite population at hand? Nothing? To a hypothetical super-population? What is the formal definition of this entity and why do I care about ITS causal parameter?

Response: …bounds for the exposed population, which is typical in epidemiology. Similar bounds could be computed for the unexposed or total population or to an external population. If an external population is required, additional assumptions will likely be needed to gain informative bounds.

Comment: It seems to me that if the world is deterministic, it is bad news to all causal inference. It is very difficult to explain how knowledge from a study may be exported outside of the study.