## How to choose among alternative narratives

The arithmetic of choosing among alternative narratives in the clinic and elsewhere, can be made rigorous by selecting a numerical scale for representing the extremes of falseness/impossibility all the way truthfulness/certainty. If the scale is selected as a probability one ranging from 0 to 1 and certain rules for the manipulation of probabilities as mathematical objects are employed, then one arrives at a formal inferential system. This system which allows for a logically consistent reasoning in the face of uncertainty is known as Bayesian probability theory and its modern development can be found in the texts by Keynes, Cox and Jaynes.Choosing among alternative narratives (or models of reality), is accomplished by means of a non-controversial mathematical rule known as Bayes theorem. For each narrative one forms the product of the a priori belief in the plausibility of the narrative and the compatibility of the data at hand with the narrative (“likelihood). In the medical diagnosis example we called these quantities $x_1,x_2, ... ,x_n$ and $y_1,y_2,...,y_n$) respectively, but for the sake of conformity we will use the notation $p(H_i)$ and $p(D|H_i)$ for $x_i$ and $latex$y_i\$ respectively. After forming these quantities, one calculates the a posteriori belief in each narrative by dividing each one of the $p(H_i) \times p(D|H_i)$ by the totality of the evidence  provided by the sum of all such products.  These a posteriori beliefs are also explored in a probability scale and thus too range between the extremes of falseness/impossibility to truthfulness/certainty represented by the numbers of 0 and 1 respectively.

In order to choose among alternative models of the world, it suffices to select the narrative with the highest posterior probability.

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### 2 Responses to “How to choose among alternative narratives”

1. Valentin Tihomirov Says:

That is interesting. It seems that you have to start with a uniformly plausible theories for initial prior and, by series of tests, correct the theory plausibility (probability). The posterior for the first test is a prior for the next test. Can you combine all tests so that you do not need the serial evaluation and you can simply do a single aggregate test? Won’t it solve your dispute with frequentialists? I am just a profane trying to figure out the basics of the scientific method and the subject of the dispute between Baesian/Frequentialist statistics.