Estimating likelihood from simulations in bayesian inference of ecological models with historical contingency

AbstractEcological patterns result from historical contingency and deterministic processes. Taking apart these processes to extract probabilistic models of ecological dynamics is of major importance for ecological forecasting. Due to the high dimensionality of historical contingency it is usually difficult to sample history from observed patterns. In environmental population genetics, the number of possible genealogies linking genetic data and environemental data through demographic and niche models is almost infinite. In ecosystem dynamics time series, the patterns are determined as much by probabilitic model parameters, as by historical variables contingency. Aproximate bayesian computation allows to use simulations to aproximate this inference process. The rationale is to simulate data, extract summary statistics and retain in the posterior, the parameters values that produced simulations with summary statistic close to observed summary statistics. The major drawbacks of this approach is that summary statistics distance is not exhaustive regarding model likelihood and may biais the results. In the present work, I show that if we can simulate the historical contingency from observed data and probabilistic model in a backward approach, we can to use the simulations to estimate a pseudo likelihood that can be used in bayesian inference. I apply to genealogy sampling in environmental demogenetics and ecosystem dynamics modelling.