ABC Tolerance Posterior

Approximate Bayesian Computation (ABC) is a class of methods used in Bayesian statistics when the likelihood function is difficult or impossible to evaluate, but simulating from the model is feasible. In this toy benchmark, we examine how a simulator acceptance tolerance affects the approximate posterior distribution.

Interactive Experiment

You can interact with these parameters in the ABC Tolerance Posterior module to see how they impact the approximate posterior.

1. Set Prior to "Uniform". Note how the prior distribution is flat across all probabilities.
2. Set Trials to 4 and Observed count to 2. This simulates observing exactly half successes.
3. Change Tolerance from 0 to 1. Notice how the acceptance probability curve widens, making it easier for parameter values farther from the observed proportion to be accepted. This flattens the ABC posterior compared to the exact posterior.
4. Change the Probe probability to 0.5 to see the specific numerical values of acceptance and posterior at the center of the grid.
5. Set Prior to "Center". Observe how a peaked prior influences the exact and ABC posteriors, pulling them towards the center (p=0.5).