ibn Harm

Category: Mathematics

  • Frequentists and bayes (3)

    I was revisiting the first articles on this topic and it was not really clear to me what I meant. Thus this entry is sort of a mental note for me.

    As I understand it researchers who prefer frequentists methodologies do not speculate on events which researchers choosing Bayes’ mathematics will state have “probabilities.”

    So before a soccer match is played frequentists can say things like: “based on the previous data, if we assume previous data can say something about future events, we expect team a to win the match.”

    Researchers using Bayes on the other hand might say things like: “based on the previous data we expect the score to become ‘3-1’ (yielding team a as matchwinner).”

    Frequentists should not be able to predict “net results” or “expected goals” I think.

  • Game Theory 2

    The form best embedded in the homo sapiens’ conscious is the prisoner dilemma which considers the problem that two actors have incentive to defect (confess in order to gain reduced sentence). Moral issues aside, game theory is a mathematical analysis that investigates how to reach an optimal outcome.

    Where calculus has as one primary application the finding of (local) maxima and minima Game Theory can be understood as another optimization problem but expressed commonly from a selfish point of view. To rephrase where calculus concerns abstract data that can but not necessarily reflects individual agents, Game Theory does emphasize rewards of individual actors.

    The nash equilibrium in this bounded universe expresses the state of outcomes in which none of the actors can improve without depression of one of the other actors.

    Another interesting configuration is the case where actors reach a suboptimal outcome (with regards to the interests of both actors) because of the absence of absolute information.