Hoeffding's inequality, Chebyshev's inequality, and Chernoff's inequality are broadly applicable, and are therefore less likely to be misused. They also don't require philosophical assumptions about subjective probabilities.
In the theory of Multi-Armed Bandit algorithms, compare the Bayesian approach (Thompson sampling) with the Concentration Inequality approach (the UCB algorithm). The former assumes that payoffs are in the 2-element set {0,1}, while the latter allows payoffs to be in the interval [0,1].
I think Bayesian is cool, but it imposes a big burden with choosing sensible priors.
Hoeffding's inequality, Chebyshev's inequality, and Chernoff's inequality are broadly applicable, and are therefore less likely to be misused. They also don't require philosophical assumptions about subjective probabilities.
In the theory of Multi-Armed Bandit algorithms, compare the Bayesian approach (Thompson sampling) with the Concentration Inequality approach (the UCB algorithm). The former assumes that payoffs are in the 2-element set {0,1}, while the latter allows payoffs to be in the interval [0,1].
I think Bayesian is cool, but it imposes a big burden with choosing sensible priors.