The best replacement for bayes is frequentist.

The best alternatives to bayes are rated as following:
★★★★★  frequentist
★★★★  decision tree
★★★  naive bayes
★★  popper
★★  markov
★  logistic regression
★  svm
  knn
  neural network
  not to bayes

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Speaking about bayes, one probably shouldn't forget about bernoulli.

Other search terms related to bayes and their ratings are:
★★★★★ bernoulli
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