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Third example: A researcher has millions of datasets to analyze, with each dataset containing enough data points such that frequentist asymptotics are satisfied

Third example: A researcher has millions of datasets to analyze, with each dataset containing enough data points such that frequentist asymptotics are satisfied. You are tasked with finding summary statistics for all datasets. The maximum likelihood and maximum a posterior (MAP) estimators are equal within some tolerance for a subset of these datapoints. However, the marginal likelihood function is computationally intractable, so the Bayesian must use expensive methods to produce MAP estimates, e.g. using Markov chain Monte Carlo (MCMC). For complex posterior distributions, MCMC requires careful programming and verification procedures, which can be prohibitive in practice. There are very many real-world problems that have fast and accurate frequentist solutions, but slow and difficult Bayesian solutions. Despite my personal bias -- my research primarily relies on Bayesian inference -- I can't fathom how one can reasonably argue that frequentist approaches are always inferior, even in applied statistics.

loup-vaillant 13y ago
> I can't fathom how one can reasonably argue that frequentist approaches are always inferior, even in applied statistics. My original claim is broader than I wanted it to be. The fact is, a Frequentist approach will always be less accurate than the correct application of probability theory. But of course, > Bayesians know that using probability theory correctly is sometimes intractable (combinatorial explosion and all that). In those cases, they will use approximations. But at least, they will know it's an approximation. https://news.ycombinator.com/item?id=6793905 https://news.ycombinator.com/item?id=6793905 The key to the Bayesian outlook is to remember that no matter what, there is a correct answer, even if you can't afford to compute it. As Eliezer Yudkowsky put it, there are laws of thought. Want to use Frequentist tools? Sure, why not. Just remember that they often violate the laws of ideal though. Some inaccuracy inevitably ensues.

loup-vaillant 13y ago

> I can't fathom how one can reasonably argue that frequentist approaches are always inferior, even in applied statistics. My original claim is broader than I wanted it to be. The fact is, a Frequentist approach will always be less accurate than the correct application of probability theory. But of course, > Bayesians know that using probability theory correctly is sometimes intractable (combinatorial explosion and all that). In those cases, they will use approximations. But at least, they will know it's an approximation. https://news.ycombinator.com/item?id=6793905 https://news.ycombinator.com/item?id=6793905 The key to the Bayesian outlook is to remember that no matter what, there is a correct answer, even if you can't afford to compute it. As Eliezer Yudkowsky put it, there are laws of thought. Want to use Frequentist tools? Sure, why not. Just remember that they often violate the laws of ideal though. Some inaccuracy inevitably ensues.