-keeping the Popperian and Bayesian spirits alive
Most
of problems in phylogeny are not solved by simple hypotheses (i.e.,
Arthropoda and Onycophora as sister clades), they are rather assessed
by composed hypotheses that should not be addressed as it was just
one (let's make a reliable phylogenetic reconstruction of the group
you are most interested in). Therefore, sorting this out is a matter
of two components: Popperian vision of confirmation and Bayesian
analysis. It is possible that the aforesaid will always sound odd,
since Popper always expressed his disagreement about the Bayesian test.
Nonetheless, the purpose of this article is to give some attention on
the points that actually join these two approaches.
Evidence
and Popper
Searching
for evidence is an everyday task for the quizzical spirits who make
science as what it really is: a constant pursuit of the truth about
the processes that underlie the phenomena of life. However, there is
no absolute certain of anything, and what we call truth would rather
require a level of belief. This level of belief comes with the
evidence of the hypothesis, which is what we think is the possible
explanation of a particular event, or a statement that can not be
defeated by evidence per se.
Sober
(2009), states that the evidence we have do not render our theories
true, but if we follow an argument of deductive logic, “the
conclusion must be true if the premises are”. Hence, if the
premises are true, there is nothing wrong in believing
the conclusion. This concept is the antithesis of what Popper
has proposed in the past about the power of a hypothesis, which
relies on how improbable it is. The aforementioned, because in
contrast to a scientist who accepts the most highly probable
hypotheses, scientists according to the philosophy of Popper (1963)
seek for explanations that are not subjected to a limited number of
observations.
At
this point, it is very necessary to bring up some of the important
concepts of Sir. Karl Popper, which have contributed to this crucial
step of the scientific method. First, falsifiability is a necessary
criterion for scientific ideas, for it is the logical possibility
that a statement could be false because of a particular observation
or an experiment (Helfenbein and DeSalle R. 2005). Thereupon, a
common feature of every scientific hypothesis and theory is to be
“falsiable”, which not necessarily implies that they are false.
If there is no degree of falsifiability in the theory or hypothesis
you are formulating, it could possibly mean that it behaves as a
universal law or you are facing an artifact, which is undesirable in
scientific framework. Up to this point, I totally agree with Popper's
statement, because one good conclusion is derived from a good
hypothesis that could be contrasted with the evidence and other
researches could arrive at the very same conclusion using different
experiments.
The
only issue I take on Popper's proposal is because of the formulated concept of corroboration, which implies that hypotheses should
stand up to the most severe tests. In the cases where hypotheses were
not falsified under these tests, we call the concept of degree of
corroboration, which is the “appraisal of the worth of the
hypothesis” (Helfenbein and DeSalle R. 2005). So, if a hypothesis
has not been falsified, it has been corroborated.
To
put this into context, I am enormously fond on molluscs, whose
morphological and behavioral traits have defined them as a
monophyletic group. Among several features, the veliger larvae
constitutes the synapomorphy of this clade. Therefore the veliger
larvae is the evidence of this hypothesis of monophyly. Through
several analyses, we could be positive sure that it is a powerful
conclusion that suits the given evidence just fine. Thus, the
Popperian concept of a good hypothesis could really be in trouble
when testing, because there is not such unlimited number of available
observations.
Bayes
and Popper
“There
is not even anything irrational in relying for practical purposes
upon well-tested theories, for no more rational course of action is
open to us. (Popper, 1963)
First,
I agree with the point of Bernardo (1999): "we are able to embed
a Popperian take on the goal and methods of science into a genuine
Bayesian model of hypothesis testing(...)". This idea is
supported
mainly because Popper’s
judgement that an idea must be falsifiable could
interpreted as a manifestation of the Bayesian
conservation-of-probability rule (Yudowsky,
2014).
The
perks of Bayesian analysis
Then,
why is it preferable to use a Bayesian framework in phylogeny?
Because it
is flexible and allows you to use an evolution model. The prior
probability that is calculated is nothing else but the probability of
the model when you have not
take a look at the data. Thus, the posterior probability is the
probability of your model (hypothesis) given the data. These two
components are explicit, which allows further assessment. Moreover,
the Bayesian approach also takes account on the likelihood, which is
included on its theorem. The likelihood is the probability of the
data given the model, which gives us useful information, but not all
the information we need.
On
the other hand, due to the flexibility of the method, it allows using
complex models and large sets of data. This property always provides
the possibility of enlarge or enhance the method (Heaps et al.,
2014). And finally, you
can get a clearer grasp on the solution of your problem with the
posterior probability.
Thence,
the tests that are based on the calculus of probabilities, following
an evolution model seem to be a powerful way to evaluate a hypothesis
and determine how close we are to get a suitable likely answer. In
fact, contemporary science tends to accept robust hypotheses that
have been supported, rather than hypotheses of what can not possibly
be refuted for its highly degree of improbability. Therefore,
using a Bayesian approach would give very informative results and
could allow us to perform further analyses. As a matter of being
judgemental about an statement, Popper's philosophy
is strong and it is an important startpoint for the scientific
thinking: hypotheses must stand for severe tests. Nonetheless,
in any case, choosing the approach to work with is subjected to
personal criteria and to the aims of the study.
References
Bernardo
J M. (1999) “Nested Hypothesis Testing: The Bayesian Reference
Criterion”, in J. Bernardo et al. (eds.): Bayesian Statistics 6:
Proceedings of the Sixth Valencia Meeting, 101–130 (with
discussion), Oxford University Press, Oxford.
Helfenbein
KG, DeSalle R. (2005) Falsifications and corroborations: Karl
Popper’s influence on systematics. Molecular phylogenetics and
evolution, 35(1), 271-280.
Heaps
SE, Nye TM, Boys RJ, Williams TA, Embley TM. (2014) Bayesian
modelling of compositional heterogeneity in molecular phylogenetics.
Stat Appl Genet Mol Biol. 13, 589-609.
Popper
KR. (1963) Conjectures and Refutations: The Growth of Scientific
Knowledge. New York: Harper.
Sober
E. (2008) Evidence and Evolution: The Logic Behind the Science.
Cambridge University Press.
Addittional
references
How
Do Hypothesis Tests Provide Scientific Evidence? Reconciling Karl
Popper and Thomas Bayes Departmental Seminar, Philosophy Department
of Uppsala University, Uppsala.
Yudkowsky
E. An Intuitive Explanation of
Bayes'Theorem.http://yudkowsky.net/rational/bayes
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