miércoles, 26 de noviembre de 2014

Evidence and Phylogenetic Inference

-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