Thank you.
Explain Bayesian vs Frequentist statistics to me like I'm 5
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You have a sample of the weight of a bunch of students at your university for this year. You want to estimate the average. You sum up all the weights and you divide by the number of observations. That's frequentist statistics.
A Bayesian walks in and says that we've been weighing the students like this every year for the past 3 years. Maybe past information can be used in order to get a better sense of the true average value. Using the past information (a "prior") along with the new information (the current sample) gives us a new estimate of the average (the "posterior"). That's Bayesian statistics.
If you have no information about the past, Bayesian and frequentist statistics give the same answer.
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Frequentists: what are you estimating is a real existent physically measurable objective parameter
Bayesian: that parameter does not really exist if not as a belief in your mind, and you want such belief to be as reliable as possiblePretty good, I would only add that:
Frequentists: frequency is measurable, not probability
Bayesians: probability as pure belief (de Finetti) vs. probability as system of logic (Jaynes) -
https://xkcd.com/1132/
https://www.explainxkcd.com/wiki/index.php/1132:_Frequentists_vs._BayesiansThis cartoon actually does a poor job at presenting the differences between Frequentists and Bayesians and has been criticized on several stats blogs.
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Frequentists: what are you estimating is a real existent physically measurable objective parameter
Bayesian: that parameter does not really exist if not as a belief in your mind, and you want such belief to be as reliable as possibleThe Bayesian part is not necessarily true. The true parameter can exist. The Bayesian prior is the probability of the parameter's value on different realisation of worlds. However, we live in one realisation but we don't know what exactly it's. And in each realisation, the parameter is a measurable value.
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too many people in this thread (especially 240e) have a knowledge of Bayesian inference that is based mainly on philosophy textbooks written in 1950, rather than based on actual modern statistical practice. Very few modern Bayesians give a crap about "the meaning of probability" or di finetti - people use Bayesian inference because it is a more practical approach to fitting complex models than frequentism is. There is a reason why the machine learning literature is around 50% heuristics and 50% Bayesian inference, and its because Bayesianism broadly works, while frequentistm broadly doesnt. Who gives a crap about philosophy or the meaning of probability? We are meant to be scientists, and this isnt 1950 anymore.
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what if I take the average of all 3 yr data ?
You have a sample of the weight of a bunch of students at your university for this year. You want to estimate the average. You sum up all the weights and you divide by the number of observations. That's frequentist statistics.
A Bayesian walks in and says that we've been weighing the students like this every year for the past 3 years. Maybe past information can be used in order to get a better sense of the true average value. Using the past information (a "prior") along with the new information (the current sample) gives us a new estimate of the average (the "posterior"). That's Bayesian statistics.
If you have no information about the past, Bayesian and frequentist statistics give the same answer.