The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations. Specifically, the asymmetric version of the problem is examined, where different requirements are placed on the two error probabilities. Accurate nonasymptotic expansions with explicit constants are obtained for the error probability, using tools from large deviations and Gaussian approximation. Examples are shown indicating that, in the asymmetric regime, the approximations suggested by the new bounds are significantly more accurate than the approximations provided by either of the two main earlier approaches -- normal approximation and error exponents.

翻译：考虑两个概率测度之间的二元假设检验问题。对于基于独立同分布观测的最优可达到错误概率，推导了新的紧界。具体而言，研究了该问题的非对称情形，其中对两种错误概率设定了不同的要求。利用大偏差理论和高斯逼近工具，获得了具有显式常数的精确非渐近展开式。示例表明，在非对称条件下，新界建议的近似值比两种主要早期方法——正态逼近和误差指数——所提供的近似值显著更精确。