PCR amplification plays a central role in the measurement of mixed microbial communities via high-throughput sequencing. Yet PCR is also known to be a common source of bias in microbiome data. Here we present a paired modeling and experimental approach to characterize and mitigate PCR bias in microbiome studies. We use experimental data from mock bacterial communities to validate our approach and human gut microbiota samples to characterize PCR bias under real-world conditions. Our results suggest that PCR can bias estimates of microbial relative abundances by a factor of 2-4 but that this bias can be mitigated using simple Bayesian multinomial logistic-normal linear models.