Why recent large earthquakes caused shaking stronger than shown on earthquake hazard maps for common return periods is under debate. Explanations include: (1) Current probabilistic seismic hazard analysis (PSHA) is deficient. (2) PSHA is fine but some map parameters are wrong. (3) Low-probability events consistent with a map sometimes occur. This issue has two parts. Verification involves how well maps implement PSHA ("have we built the map right?"). Validation asks how well maps forecast shaking ("have we built the right map?"). We explore how well a map can ideally perform by simulating an area's shaking history and comparing "observed" shaking to that predicted by a map generated for the same parameters. The simulations yield shaking distributions whose mean is consistent with the map, but individual shaking histories show large scatter. Infrequent large earthquakes cause shaking much stronger than mapped, as observed. Hence, PSHA seems internally consistent and can be regarded as verified. Validation is harder because an earthquake history can yield shaking higher or lower than the hazard map without being inconsistent. As reality gives only one history, it is hard to assess whether misfit between a map and actual shaking reflects chance or a map biased by inappropriate parameters.