Always in all life moment we place in the situation of choose between two or more options, maybe for social reasons in every area always tell us that we must take a decision, what religion we must believe, whether we are pro-yankees or not, what political party we belong, even in Biology we must choose. whether we are Botanist, Primatologist, Ornithologist, etc. In Compared Biologist class my professor asked me choose one philosophical current which I must use to make and approach my questions. I can choose between three different philosophical currents: Bayesianism, Likelihood Ism, Frequentist and Popperian Falsificationis
We're going to talk each of the three streams. Although the Bayesianism has a origin very old, until only a few years had a major resurgence in science. This stream applies the probability that some events occur given certain observations (priors), which are changing or being updated. The probability is denoted Pr(H|O), and is the probability of the hypothesis given the data, observations or evidence (Sober, 2008; Kruschke, 2011). On the other hand is the Likelihoodism, which lacks of priors and the logic is contrary to the Bayesianism, looks for the probability how well the hypothesis fits to the data Pr(O|H) (Sobber, 2008; Royal, 1998). Both branches are extremely powerful to make inferences and contrasting hypotheses, the only difference is the concept used for making comparisons (Sober 2008, Kruschke, 2011). The likelihoodism uses the concept of favoring to show that the evidence says regarding the comparison of two hypotheses, while the Bayesianism adopts the concept of confirmation to show that the evidence says regarding a hypotheses and it's negation (Sober, 2008. Pag 34). Finally, the frecuentism, which has dominated the last century, is based on the probability that an evidence or event occurs depending on a set of experiments and N (Johansson, 2011), that gives a ratio and the value P is calculated and compared with a null model or null hypotheses(Sober, 2008; Johansson, 2011; Wagenmakers, 2007). The main difference (i think) is it's philosophical perspective on the comparasion of hypotheses and the use of priors in Bayesianism (Sober, 2008), in other topics are very similar. As a first approach to this affirmation I put the following exercise: Suppose that we have our hypothesis (H) and data (T), now when we do the Bayesian analysis we seek the probability of H given T(Pr(T|H)), in contrast to Likelihood we want to look at how well H fits to our data T(Pr(H|T)), when we apply the Bayes theorem to our example we have: p(T|H)p(H) = p(H|T)p(T). Then = Pr(T|H)=[p(H|T)p(T)]/p(H). From a value of Likelihood we can get the posterior values, the example is somewhat crude and simplist but implies the idea. I don't pretend to fill this with formulas and derivations that even I can't explain but Branden Fitelson from page 7 of his article "Likelihoodism, Bayesianism, and Realtional Confirmation" shows us some examples of how some Bayesian measures are more Likelihoodians than Bayesians and vice versa, if someone wants deepen in the topic.
One of the main problems in Bayesianism and Frecuentism is little objectivity when the data are managed (Ayacaguer, 2000). On one side are the priors of the Bayesian analysis, and have more influence in the analysis and their value can be altered to benefit any particular hypothesis, this is one reason why many people argue the unreliability of this method when is used in daily life, in government agencies because anyone can manipulate priors to the own benefit. It has used 'flat-priors' as a solution to this problem, which causes that the entire analysis falls on the Likelihood, but the Frequentism is not far behind, because you can manipulate the P values or the values of positive or negative false (the famous alpha and beta), to favor some result in special, just as the criticism is the use of a null hypothesis (Ayacaguer, 2000; Johansson, 2011). Similarly the Frequentism present the N problem, because the P values are influenced by the sample that was used, so we can know beforehand what would be the result if we use a small N or a big N and the P value also can be influenced subjectively by the amount of N that is used (Ayacaguer, 2000; Wagenmakers, 2007; Johansson, 2011). So if it's subjectivity we have a winner ¡Likelihoodismo!. But we don't get excited because Likelihoodism also has crtitics and one of these is it's restriction to some cases (Sober, 2005).
According everything written above, it appears that Likelihoodism is the best stream and therefore I'll choose it, but no. It can sound crazy but for me and after of all this timeexploring this trend I can conclude that one can't choose any stream in special, but I have to highlight that all have good and bad things and for that reason I consider they complement each other and all can be used in Bayesin analysis (obviously without declare Bayesianista). To understand this idea we must have the main components in mind of Bayesian analysis: the priors and the Likelihood. Already I denote the relationship between both Likelihood and Bayes using the theorem. On the other hand, in priors is where It would enter the Frequentism, we can consider the results from a Frequentist analys as priors in the Bayesin analysis, let me give you an example: Suppose you arrive to a new city and want to know if that month is rainy or not, throughout the month you take notes on what days is raining and is not raining, assuming that it rains 25 of 30 days. From that relationship and calculating the P value you will know that this month is rainy or not, but What could you say from this assertion on the following months?, really nothing, but from these observations you could infer how likely is that the next month it will rainy, because throughout that month we have noticed that in general before the rain come the sky is clouded, so if the next day we see the sky is clouded (O), we know that the probability of rain is going to be high (H), all thanks to the prior value we obtained from our frequentist observations. I would like to give an example that occurred to me while I played Xbox to better explain my idea. Suppose we are going to fight with the Final Boss, at the begining, we dont know anything, how are attacks, his moves and we have to spend one or more lives to defeat it, is in that moment where our Bayesian, Likelihoodism and Frequentism analysis arises !!. At first we do not know how to approach the enemy (flat priors) and defeat it (H) with our initial strategy (T) is very unlikely (low likeliihod, p (T | H)), which ultimately leaves a unlikely to pass the game (posterioris bayes, Pr (H | T)). As we move forward in the fight we noticed that the enemy has a particular frequency for certain attacks, then we will know what is the probability of making certain attack, these probabilities increase as you fight more and make more observations on the movements of the enemy, this, I believe, is a well frequentist analysis (we have an accumulation of knowledge and increase our priors), once we know these make a change in our strategy (T) and the probability of defeat given that our change strategy (Pr (T | H)), so that eventually the probability of passing the game increases (Pr (H | T)).
So, you will ask, ¿ where is the Popperian Falsificationism ?, well, I think that is the less critical among the 4 currents. Basically Popper says us: In science we must reject some theories and hypotheses to corroborate others ( but, It doesn't mean that these are true), something like Modus Tollens Tollens (If A is true, no mean that B are true too). So in this way the three currents use Popper's logic: The likelihood 'favoring' one hypotheses over another, Bayesianism 'confirms' one hypotheses respect its own negation, and Frequentism compare one hypotheses against the null hypotheses, but we never corroborate that are true hypotheses
I think choose between any of these three currents, is like choose just one phylogenetic search method is better, all three have good and bad things and often what really influences is the data, not the method. I consider more appropriate, for example what Morrone and Crisci do with the two methods of historical biogeography (Panbiogeography and Historical Cladistic), they show how each method is complementary each other, and that are necessary steps for a good biogeographic analysis (Morrone & Crisci, 1995; Morrone 2001). This (I think), allows us to look the problem at multiple ways and allows find multiples and well solutions, avoiding bias. Always tell me that extremes are not good, so, why we don't avoid the extremes, and find a intersection between them ? and take the better of each one, just imagine how world will change if religious zealots get find a middle point. At the end these are only methods and it seems to me more crucial and critical the objectivity with which the researcher will analyze the results.
- Branden Fitelson. Likelihoodism, Bayesianism, and Relational Confirmation. Syntheses (2007).
- Tobias Johansson. Hail the imposible: p-values, evidence and likelihood. Scandinavian Journal of Psychology (2011).
- L.C. Silva Ayacaguer & A. Muñoz Villegas. Debate sobre métodos frecuentistas vs bayesianos. Gac Sanit (2000).
- Eric-Jan Wagernmakers. A practical solution to the pervaise problems of p values. Psychonomic Bulletin & Review (2007).
- Silvio Pinto. El Bayesianismo y la Justificación de la inducción. Principia (2002).
- Royall, R. Statistical Evidence: A Likelihood Paradigm, Boca Raton, Fla.:Chapman and Hall.(1997).
- Elliot Sober. Evidence adn Evolution: The Logic Behind The Science. Cambridge University Press, United States of America. (2008).
- Kruschke, J.K.. Bayesian data analysis: A tutorial with R and BUGS. Amsterdam: Elsevier. 2011.
- Juan J. Morrone. Homology, biogeography and areas of endemism. Diversity and Distribution (2001).
- Sober, E.: 2005, ‘Is Drift a Serious Alternative to Natural Selection as an Explanation of Complex Adaptive Traits?’. In: A. O’Hear (ed.): Philosophy, Biology and Life. Cambridge: Cambridge University Press.