  Reliable uncertainty estimation for time series prediction is critical in
many fields, including physics, biology, and manufacturing. At Uber,
probabilistic time series forecasting is used for robust prediction of number
of trips during special events, driver incentive allocation, as well as
real-time anomaly detection across millions of metrics. Classical time series
models are often used in conjunction with a probabilistic formulation for
uncertainty estimation. However, such models are hard to tune, scale, and add
exogenous variables to. Motivated by the recent resurgence of Long Short Term
Memory networks, we propose a novel end-to-end Bayesian deep model that
provides time series prediction along with uncertainty estimation. We provide
detailed experiments of the proposed solution on completed trips data, and
successfully apply it to large-scale time series anomaly detection at Uber.
