We study three fundamental data challenges in empirical asset pricing: missing observations, infrequent measurements, and inherent noise in financial information. These challenges make firm characteristics uncertain inputs rather than fixed conditioning variables. We develop a Bayesian tensor model that treats characteristics as latent, exploits cross-sectional, characteristic-level, and time-series dependence, and generates posterior panels for missing and stale values. In global equities, accounting for characteristic uncertainty leaves systematic factor portfolios nearly unchanged, but substantially reduces the number of statistically significant residual alphas and attenuates arbitrage-portfolio Sharpe ratios. Averaging arbitrage portfolio weights across imputations yields more stable performance, especially internationally.