Perusall Comment Degree of Belief Discussion

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Chapter 8
When and How Will You Die?
It is difficult to make predictions, especially about the future.
— Niels Bohr (probably)
In our first Big Question, we began to look at individual differences between people or what
statisticians call variation within a population. If there is no variation—like in the bizarro world
where everyone orients their toilet paper in the “under” orientation—then there is nothing to
talk about, at least not statistically speaking. There is, however, considerable variation in health
outcomes and human lifespan. Lots to talk about there. In our next Big Question, we ask “when
and how will you die?” and “what, if anything, can you do about it?”
What kind of question is, “when and how will you die?” Well, according to some of my colleagues,
it is a morbid question. Feelings aside, we might say that it sounds like a prediction question, since
it is about the future. So to explore this big question, we will need to understand what it means in
general to make a forecast about some future event. We’ll also find it useful to distinguish between
predictions that are or are not explanatory. Most efforts in health sciences attempt to explain
relationships between behavioral and genetic factors and health outcomes. In particular, they try
to understand causal effects. So in the next few chapters, we will also try to understand causal
explanations more generally.
Not Quite Death, but, um. . . Rain?
Perhaps it is a good idea to warm up, before we face the grim reaper. What does it mean to say
there’s a 30% chance of rain tomorrow in New York? Does it mean that it will definitely rain in
30% of the city (say, Brooklyn), but not in the other 70%? Or that it will rain for 30% of the day
(say, from 8am-3pm). Here are some possibilities to consider:
will definitely rain in some parts of the city but not in all of them
will definitely rain for some part of the day in all of the city
will definitely rain for some part of the day in some of the city
may or may not rain anywhere in the city at any point in the day.
Read here for an explanation of what meteorologists probably mean
Stochastic vs Deterministic relationships
Sometimes when I say definitely, I mean probably. Like if I say, I’m definitely going to
do something about all of this clutter on my desk. But when I really mean business, I
say deterministically. It definitely sounds more serious.
Meteorologists—scientists who model the weather—cannot tell us deterministically about weather
events. Recall that we previously considered deterministic associations between two two-kinds-people
questions. We imagined a world where if you knew a person’s answer to one question (e.g., are
you right- or left-handed?) then you would know for sure their answer to another. Now some of
our examples were hypothetical and unrealistic, because, well, people are not in actuality very
deterministic. If we want realistic examples, we end up making use of tautologies like “Are you
single? Are you in a relationship?”
But some events in nature are, more or less, deterministically related. An example might be
something like, if I let go of the umbrella I am holding, then it will fall to the ground. If A then B.
No exceptions (and no strings). You can imagine that I asked two questions: (a) did I let go of
the umbrella (at a certain time T)? and (b) immediately after time T, did the umbrella fall to the
ground? If you know the answer to one question, then you know the answer to the other.
Weather events are stochastic. As we know all too well from experience, they have an element
of chance or randomness, like tossing a coin or rolling a die. So, just as we can say that a coin
has a 50% chance of coming up heads—assuming it is a fair coin—we can make statements like
there is a 30% chance that it will rain tomorrow. Stochastic is another word for random, but I
prefer it because the word “random” is often used casually to mean weird or unusual (as in, “that’s
random!”) Although we can’t speak with certainty about random, or stochastic, events, that doesn’t
mean we can’t speak usefully about them. We just need to learn to speak probabilistically.
Ways of thinking about probabilistic statements
One way to think about the 30% chance of rain is to imagine that our experience in the world is
one possibility in a multiplicity of possible worlds. See, I told you this idea of multiple alternate
universes was going to be important! Imagine that there are 10 possible worlds, indistinguishable
from ours in terms of the laws of physics, and that tomorrow it will in fact rain in 3 of them. To
the great being-who-knows-all-things, which 3 worlds will see rain may well be known. However, to
us mortals who merely live in the world that we know, we don’t know which one of these possible
worlds is the one we live in. Nevertheless we are capable of imagining these different potential
outcomes. As you just did.
It didn’t have to be 10 worlds, of course. That was arbitrary. If we imagined thirty worlds, it could
rain in 9 of them, as I’ve represented in Figure 8.1. I did this by making thirty circles and coloring
in 9 of them at random. Since I like to pull back the curtain every once in a while, I will even show
you the R code I use to generate this simple figure.
# start with a 10 x 3 grid of points

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