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Frequentists vs. Bayesians (and a comment about the optimal alpha approach)

November 14, 2012

Frequentists vs. Bayesians

If the frequentist had used the optimal alpha approach and calculated an optimal alpha for a scenario of unequal prior probabilities of null and alternate hypotheses, he/she would have agreed with the Bayesian.

The optimal alpha approach using unequal relative costs of error would have also resulted in the frequentist agreeing with the Bayesian. The cost of error Type I error (falsely concluding the sun has gone nova) would be $50 because he/she would have lost the bet.  The cost of Type II error (falsely concluding the sun has not gone nova) is negligible because there’s really no advantage to knowing the sun has just exploded since we’d soon all be dead. If Type I errors are more serious than Type II errors, the resulting optimal alpha that minimizes costs of errors would be much smaller than 0.05, leading the frequentist to the conclusion that the sun hasn’t gone nova.

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5 Comments
  1. What does this comment say about the interaction between Optimal Alpha and frequentist statistics/bayesian statistics? Does optimal alpha think one theory of statistics is preferred over the other? Is optimal alpha better suited to one particular view? I’m on the edge of understanding; I just need a nudge.

    • Optimal alpha is a frequentist approach that can prevent some of the silly conclusions that frequentist statistics can reach under some circumstances. There’s probably also room for optimizing Bayesian statistical thresholds, but I’m just starting to explore this stuff…

  2. Please read Andrew Gelman’s opinion about this cartoon – in a nutshell, the cartoon is flawed and it misrepresents frequentists.
    http://andrewgelman.com/2012/11/16808/

    • I won’t attempt to defend the veracity of this comic. It is clearly an oversimplification intended to provoke both laughter and discussion. The lengthy comments section of the blog post you provided suggests that the cartoon has served its purpose well.
      The intention of my blog post was to highlight how careful consideration of what alpha level is most appropriate for a null hypothesis test can prevent disagreements between conclusions reached using frequentist and Bayesian statistics.
      Thank you for directing me to andrewgelman.com, it is a very interesting blog.

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  1. There is no Theorem but Bayes’ and Laplace is His Prophet | Alea Deum

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