How does science work, really? You can read all
about it in plenty of texts in philosophy of science,
but if you have ever experienced the making of
science on an everyday basis, chances are you
will feel dissatisfied with the airtight account
given by philosophers. Too neat, not enough mess.
To be sure, I am not denying the existence of
the scientific method(s), as radical philosopher
Paul Feyerabend is infamously known for having
done. But I know from personal experience that
scientists don’t spend their time trying
to falsify hypotheses, as Karl Popper wished they
did. By the same token, while occasionally particular
scientific fields do undergo periods of upheaval,
Thomas Kuhn’s distinction between “normal
science” and scientific “revolutions”
is too simple. Was the neoDarwinian synthesis
of the 1930s and 40s in evolutionary biology a
revolution or just a significant adjustment? Was
Eldredge and Gould’s theory of “punctuated
equilibria” to explain certain features of
the fossil record a blip on the screen or, at
least, a minor revolution?
But, perhaps, the least convincing feature of
the scientific method is not something theorized
by philosophers, but something actually practiced
by almost every scientist, especially those involved
in heavily statistical disciplines such as organismal
biology and the social sciences. Whenever we run
an experiment, we analyze the data in a way to
verify if the socalled “null hypothesis”
has been successfully rejected. If so, we open
a bottle of champagne and proceed to write up
the results to place a new small brick in the
edifice of knowledge.
Let me explain. A null hypothesis is what would
happen if nothing happened. Suppose you are testing
the effect of a new drug on the remission of breast
cancer. Your null hypothesis is that the drug
has no effect: within a properly controlled experimental
population, the subjects receiving the drug do
not show a statistically significant difference
in their remission rate when compared to those
who did not receive the drug. If you can reject
the null, this is great news: the drug is working,
and you have made a potentially important contribution
toward bettering humanity’s welfare. Or have
you?
The problem is that the whole idea of a null
hypothesis, introduced in statistics by none other
than Sir Ronald Fisher (the father of much modern
statistical analyses), constraints our questions
to ‘yes’ and ‘no’ answers.
Nature is much too subtle for that. We probably
had a pretty good idea, before we even started
the experiment, that the null hypothesis was going
to be rejected. After all, surely we don’t
embark in costly (both in terms of material resources
and of human potential) experiments just on the
whim of the moment. We don’t randomly test
all possible chemical substances for their role
as potential anticarcinogens. What we really
want to know is if the new drug performed better
than other, already known, ones—and by how
much. That is, every time we run an experiment
we have two factors that Fisherian (also known
as “frequentist,” see below) statistics
does not take into account: first, we have a priori
expectations about the outcome of the experiments,
i.e., we don’t enter the trial as a blank
slate (contrary to what is assumed by most statistical
tests); second, we normally compare more than
two hypotheses (often several), and the least
interesting of them is the null one.
An increasing number of statisticians and scientists
are beginning to realize this, and are ironically
turning to a solution that was devises, and widely
used, well before Fisher. That solution was contained
in an obscure paper that one Reverend Thomas Bayes
published back in 1763, and is revolutionizing
how scientists do their work, as well as how philosophers
think about science.
Bayesian statistics simply acknowledges that
what we are really after is an estimate of the
probability of a certain hypothesis to be true,
given what we know before running an experiment,
as well as what we learn from the experiment itself.
Indeed, a simple formula known as Bayes theorem
says that the probability that a hypothesis (among
many) is correct, given the available data, depends
on the probability that the data would be observed
if that hypothesis were true, multiplied by the
a priori probability (i.e., based on previous
experience) that the hypothesis is true.
In Fisherian terms, the probability of an event
is the frequency with which that event would occur
given certain circumstances (hence the term “frequentist”
to identify this classical approach). For example,
the probability of rolling a three with one (unloaded)
die is 1/6, because there are six possible, equiprobable
outcomes, and on average (i.e., on long enough
runs) you will get a three one time every six.
In Bayesian terms, however, a probability is
really an estimate of the degree of belief (as
in confidence, not blind faith) that a researcher
can put into a particular hypothesis, given all
she knows about the problem at hand. Your degree
of belief that threes come out once every six
rolls of the die comes from both a priori considerations
about fair dice, and the empirical fact that you
have observed this sort of events in the past.
However, should you witness a repeated specified
outcome over and over, your degree of belief in
the hypothesis of a fair die would keep going
down until you strongly suspect foul play. It
makes intuitive sense that the degree of confidence
in a hypothesis changes with the available evidence,
and one can think of different scientific hypotheses
as competing for the highest degree of Bayesian
probability. New experiments will lower our confidence
in some hypotheses, and increase the one in others.
Importantly, we might never be able to settle
on one final hypothesis, because the data may
be roughly equally compatible with several alternatives
(a frustrating situation very familiar to any
scientist and known in philosophy as the underdetermination
of hypotheses by the data).
You can see why a Bayesian description of the
scientific enterprise—while not devoid of
problems and critics—is revealing itself
to be a tantalizing tool for both scientists,
in their everyday practice, and for philosophers,
as a more realistic way of thinking about science
as a process.
Perhaps more importantly, Bayesian analyses are
allowing researchers to save money and human lives
during clinical trials because they permit the
researcher to constantly reevaluate the likelihood
of different hypotheses during the experiment.
If we don’t have to wait for a long and costly
clinical trial to be over before realizing that,
say, two of the six drugs being tested are, in
fact, significantly better than the others, Reverend
Bayes might turn out to be a much more important
figure in science than anybody has imagined over
the last two centuries.
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