the Lotka-Volterra model in Stan

- Data: Lynx and Hare Pelts in Canada
- Mechanistic Model: The Lotka-Volterra Equations
- Statistical Model: Prior Knowledge and Unexplained Variation
- Coding the Model: Stan Program
- Solving the Inverse Problem: Bayesian Inference in Stan
- Conclusion: What are the Population Dynamics?
- Exercises and Extensions

Lotka (1925) and Volterra (1926) formulated parameteric differential equations that characterize the oscillating populations of predators and prey. A statistical model to account for measurement error and unexplained variation uses the deterministic solutions to the Lotka-Volterra equations as expected population sizes. Stan is used to encode the statistical model and perform full Bayesian inference to solve the inverse problem of inferring parameters from noisy data. The model is fit to Canadian lynx1 *Predator*: Canadian lynx