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.
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.