Field studies that measure vital rates in context over extended time periods are a cornerstone of our understanding of population processes. These studies inform us about the relationship between biological process and environmental noise in an irreplaceable way. These data sets bring ``big data'' and ``big model'' challenges, which limit the application of standard software (e.g., \textbf{BUGS}). The environmental sensitivity of vital rates is also expected to exhibit interactions and non-linearity, which typically result in difficult model selection questions in large data sets. Finally, long-term ecological data sets often contain complex temporal structure. In commonly applied discrete-time models complex temporal structure forces the analyst to make many competing decisions about discretizing time, which add complexity to any analysis and confuse the interpretation of parameters. I tackle these problems in three ways: 1) I apply and improve current state of the art statistical algorithms and software (Hamiltonian Monte Carlo with the NUTS sampler implemented in \textbf{Stan}) to implement the estimation of vital rates from mark-recapture data in a large Atlantic salmon data set; 2) I extend continuous-time time-to-event models with continuous estimated rate functions to mark-recapture and emigration data; and 3) I apply simple local regression to the estimation of vital rates to turn the model-selection problem resulting from interactions and non-linearity into an estimation problem, which is solved by the estimation algorithm. For each model I present methods for visualizing the results in biologically meaningful terms and use these for model criticism.