Phylosophy in phylogenetic analyses

 

Phylosophy In Phylogenetic Analysis

María Cristina Navas Serrano – 2170058.

In the present written, I going to expose why the Bayesian philosophy, according to my perspective, have a frame of beliefs more credible than the philosophy of likelihoodism.

First of all, bayesian philosophy, in general terms, use the Bayes theorem to support its beliefs, used for Richard Royall's itself to answer question about what we should believe from the evidence. But, why believe in Bayesian philosophy and not in likelihoodism? The line of thought proposed by Bayesian philosophy is firm, stating with certainty we should believe in a hypothesis or not the given evidence, with a mathematical foundation, that is different to the likelihoodish, which don’t have an answer for this question. They support instead a degree of belief for the evidence, and that’s a different approach^{1, 2}.

The basis used by Bayesianism does not focus only on the results based on the present observations we make (called posteriori probabilities), it takes into account the probabilities of the hypotheses before we have the observations (called a priori probabilities)¹. Likelihoodism may be similar to Bayesionism in some aspects of the probability, they differ by those characteristics. Likelihood don’t take into account the prior probabilities, focusing only on how the evidence may or may not support one hypothesis compared to another alternative hypothesis. The probabilities a priori influence the posteriori probabilities, this evidence of possible results, an initial expectation, what Sober (2008) calls an "anchor" of the results, is necessary ¹.

And by focusing more on this part of the mathematical basis of Bayesian philosophy, that as I said first, is based on the Bayes theorem to support its beliefs, giving it a mathematical basis that supports its ideas. However, likelihoodism is based on any theorem. Likelihoodism is a concept based on the Likelihood function proposed and defended by R. A. Fisher, who justified that likelihoodism is the measure of the fit to the evidence to the hypothesis^{1, 2}. It doesn't take care if the evidence make changes in the hypotheses probabilities, it just compare hypotheses with determinate probability. This is closer approach, and it could generate mistakes when we want to know what is the reason of the changes. That mean that this is not applicable, or that it doesn't work to support theories or support hypotheses, eventually, my project is based on this philosophy. I don’t have another option by the nature of my data and because it allows leaving out some positions that can be subjective when it comes to Bayesianism. By not having a priori probabilities ​​or subjectively assigning the probabilities of the hypotheses, my knowledge acquired empirically doesn't influence the analysis that I'm making.

However, Likelihoodism is more efficient, but it doesn’t make it more precise. Bayesianism in addition to what we should believe from evidence, permits us to know the reliability of a hypothesis if we know how possible a hypothesis is to be true given the observations, and also permits us to know how sensitive the observations and procedures are to changes for answer the hypothesis, while likelihoodism depends on the quantitative ratio of likelihoods (support measure of the observations to one hypothesis or another) to give a degree of credibility to the hypotheses.¹ Likelihood don’t measure the reliability or the sensitive in the observations, because it doesn’t measure posteriori probabilities, and it doesn’t analyze one single hypothesis, it always need an alternative hypothesis to compare.

In likelihoodism, any hypothesis can have a degree of credibility. With this, we return to the topic of ignoring probabilities a priori, and I will use the example proposed by Sober (2008) to explain this a bit¹:

Suppose we hear noises in our attic. Analyzing the situation, we might think that gremlins are bowling in our attic. Under a likelihoodism and Bayesian frame, the probability that the noise was generated by gremlins is high, because if the gremlins were playing bowling in the attic, they would make a lot of noise, that's a fact. The probability that the noise was due to gremlins would be taken into account, which is a hypothesis with a very, very low probability under the likelihoodism and Bayesian frame, but, Bayesianism take account the probability of have gremlins, that give us more information, and that affects our posteriori probability and give us a more precise result¹. Because of this, we could use the likelihood philosophical framework to state any hypothesis, even giving it a low probability, whether it is supported by observations, it can become more likely than other more realistic hypotheses. The fact that it is possible to build any hypothesis does not justify the correctness, and it gives a degree of subjectivity to this method, thus allowing very strange hypotheses to be very probable and that any hypothesis can be raised.

If we put together everything described here, using Bayesian philosophy we can have more precise answers that cover more information about the total probabilistic frame that the hypothesis has, in addition to having more possibility of analyzing the data, and taking into account the probabilities a priori, due to its solid mathematical base provides better analysis to the data, even though it cannot be very flexible in all its terms and have some subjective aspects that could affect our analysis.¹. Because my question is based on answering how much data and methods influence the result, it is possible to do it under a likelihoodism framework, focusing on the methods that I use and the difference between them, however, I still support my philosophical position on the side of the Bayesianism.

 

 

BIBLIOGRAPHY

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

2.           Royall, R. (1997). Statistical Evidence. A Likelihood Paradigm. Chapman and Hall.