We forecast 18 groups of individual components of the Consumer Price Index (CPI) using a large Bayesian vector autoregressive model (BVAR) and then aggregate those forecasts in order to obtain a headline inflation forecast (bottom-up approach). De Mol et al. (2006) and Banbura et al. (2010) show that BVAR's forecasts can be significantly improved by the appropriate selection of the shrinkage hyperparameter. We follow Banbura et al. (2010)'s strategy of "mixed priors," estimate the shrinkage parameter, and forecast inflation. Our findings suggest that this strategy for modeling outperform the benchmark random walk as well as other strategies for forecasting inflation.