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I have tried to figure out the difference between the two views of looking at the world: Bayesian and frequentist.

Can someone please let me know if I have it right? (Please do not refer me to some old thread or article that is pages long. Simply just confirm if the statement below is correct, and if not, what is wrong with it.)

I have got he impression that the frequentist conducts a measurement and believes the world to be exactly what his results state. Bayesian, on the other hand, has a prior/neutral view of the world, and he only uses the measurement data to update his views. I.e. he finds a balance between his prior view, and the view of the frequentist. Correct?

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    $\begingroup$ Here is related discussion previous thread: stats.stackexchange.com/questions/22/… D $\endgroup$
    – geo derek
    Nov 8, 2015 at 16:06
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    $\begingroup$ I have never met any statistician of any stripe who "believes the world to be exactly what his results state." I suspect most would feel insulted to have such a naive idea attributed to them, and so I also suspect this is not really how you intended to characterize any branch of statistics. You therefore might want to elaborate on what that phrase is supposed to mean. $\endgroup$
    – whuber ♦
    Nov 8, 2015 at 16:19
  • $\begingroup$ By that phrase I meant that if a person measures e.g. the outcome of 50 coin tosses and gets 30 heads, he would conclude that heads occur roughly 60% of the time in these conditions, and doesn't really careabout the fairness of the coin or the conditions of the surrounding world. $\endgroup$
    – kte80
    Nov 8, 2015 at 16:57

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I would not frame the difference in those terms. Frequentists and Bayesians both rely on probability models with unknown parameters for inference. Frequentists believe the parameters to be fixed constants, but unknown to the statistician. Inference involves making a probability statement about the relationship between the parameter estimate and the true value.

Bayesians, on the other hand, ascribe probability models to both the parameters and the data. Inference involves updating the distribution on the parameters (the prior), in light of the data.

Another difference is that frequentists take into consideration the sampling scheme used to get the data, whereas Bayesian inference follows the strong likelihood principle (all inference takes place through the likelihood function).

Both frequentists and Bayesians take the world as they find it, in the sense that they accept the data as data (facts). They differ in their interpretation of the parameters. If statisticians were philosophers, frequentists would be Platonists and Bayesians would be subjectivists.

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  • $\begingroup$ Maybe I can try again by formulating an example. Assume that we observe the gender of 100 people whose names we randomly pick from a phone book. 60 of persons we picked are male. Does a frequentist conclude that 60% of the phone book population is male? But a Bayesian combines this information with the prior that roughly 50% of all people are males, and comes up with a smaller percentage for the amount of men in the population? Does this summarize the difference between Bayesian and frequentist reasoning? $\endgroup$
    – kte80
    Nov 8, 2015 at 16:50
  • $\begingroup$ @kte80 you oversimplify things, see e.g. stats.stackexchange.com/questions/29835/frequentism-and-priors , you simply cannot make that sharp and definite statements. $\endgroup$
    – Tim ♦
    Nov 8, 2015 at 20:27
  • $\begingroup$ A frequentist would say that the sample average is approximately normally distributed with mean $p$ and variance $p(1-p)/100$. This statement allows one to build a confidence interval for the true parameter $p$, which would be centered at 0.6. $\endgroup$
    – Placidia
    Nov 8, 2015 at 21:59
  • $\begingroup$ Would this be correct: a frequentist views the world as a deterministic place, whereas a Bayesian views the world to be stochastic? $\endgroup$
    – kte80
    Nov 10, 2015 at 15:56
  • $\begingroup$ They understand probability differently. A frequentist looks at the probabilities that items from the population enter the sample. How weird could my sample be in comparison to the population? To a Bayesian, a probability is a "degree of belief". My PhD supervisor, a Bayesian, wrote a book called "Understanding Uncertainty" on basic statistics. Were I to write a basic stats book, I would call it "Understanding variation". I'm a frequentist. That's the difference. $\endgroup$
    – Placidia
    Nov 11, 2015 at 18:07

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