Monitoring population trends is pivotal to effective wildlife conservation and management. However, wildlife managers often face many challenges when analyzing time series of census data due to heterogeneities in sampling methodology, strategy, or frequency. We present a three‐step method for modeling trends from time series of count data obtained through multiple census methods (aerial or ground census and expert estimates). First, we design a heuristic for constructing credible intervals for all types of animal counts including those which come with no precision measure. Then, we define conversion factors for rendering aerial and ground counts comparable and provide values for broad classes of animals from an extant series of parallel aerial and ground censuses. Lastly, we construct a Bayesian model that takes the reconciled counts as input and estimates the relative growth rates between successive dates while accounting for their precisions. Importantly, we bound the rate of increase to account for the demographic potential of a species. We propose a flow chart for constructing credible intervals for various types of animal counts. We provide estimates of conversion factors for 5 broad classes of species. We describe the Bayesian model for calculating trends, annual rates of population increase, and the associated credible intervals. We develop a bespoke R CRAN package, popbayes, for implementing all the calculations that take the raw counts as input. It produces consistent and reliable estimates of population trends and annual rates of increase. Several examples from real populations of large African mammals illustrate the different features of our method. The approach is well‐suited for analyzing population trends for heterogeneous time series and allows a principled use of all the available historical census data. The method is general and flexible and applicable to various other animal species besides African large mammals. It can readily be adapted to test predictions of various hypotheses about drivers of rates of population increase.