Hypotheses and theories, how choose one in the light of the evidence

Viviana Lizeth Ayus Ortiz

Science is controlled by theories and hypotheses, but how to choose between hypotheses, how to decide which hypothesis is true or which is better?. The simplest approach is the parsimony principle, it states that simpler theories are better than the complex ones (Sober, 2015). Perhaps this principle can be tested easily. With this approach, it can be established which hypothesis is better due to its lack of complexity. On the other hand, from the logical-mathematical way, the big question is "How probable are different hypotheses given the current evidence?" (Sober, 2008). Including the word probability, it puts on the stage Frequentists, Likelihoodists and Bayesians, each one using in a differential way the available evidence, the previous knowledge, among other aspects.

Two of the questions presented by Royall (1999) can be solved under the approaches mentioned above. The first "What does the present evidence say?" Can be approached from Likelihoodism, P(E|H), following this law, probabilities can be assigned and it favoring a hypothesis due to differential support. The second question "What should you believe?" Is addressed by Bayesians following the Bayes theorem P(H|E), that uses the likelihood and takes into account the previous information (prior) to determine which hypothesis is probably true (confirms). Both approaches suggest that having the total evidence improves the hypothesis selection. However, the Frequentists affirm that a sample is sufficient to examine the expected frequencies of each result. The great problem of frequentists, whether viewed from the Fisherian or Neyman-Pearson scenario, is the sensitivity to sample size and error tolerated by analyzes even when Neyman-Pearson proposes a strategy to reduce type I and II errors.

Science is fallible and changes when new evidence emerges, that leads us to think about the falsifiability idea of Popper (1959). A hypothesis should be falsifiable according to empirical data that refute it and should avoid hypothesis ad hoc. Parsimony is consistent with Popper's ideas (Farris, 2008) while the Bayesian approach tends toward corroboration, and it should be avoided in hypothesis tests (Popper, 1959). Even so, from my perspective, the methodological approach under Bayesian inference is the most complete, since it integrates the law of likelihood and uses the probability of the prior to compute the posterior probability of the hypothesis. It is possible that phylogenetic results from likelihood will be similar and in some cases equal to those obtain by bayesian inference, this could be redundant at the moment of choosing the method of phylogenetic reconstruction.

Popper, K. (1959) Logic of Scientific Discovery, London: Hutchinson.

Royall, R. (1999) The Strength of Statistical Evidence. In The 52nd Session of the International Statistical Institute, Conference Proceedings.

Farris, J. S. (2008) Parsimony and explanatory power. Cladistics, 24(5), 825–847.

Sober, E. (2008) Evidence and evolution: The logic behind the science. Cambridge University Press.