Approximate Bayesian Computation
Bayesian inference with Monte Carlo Method when the Likelihood is intractable
Approximating posterior probability distribution by generating data through simulation and comparing it with real data
First, we sample parameter values from the prior distribution. Then, we simulate a dataset using the statistical model specified by . If the simulated dataset Db differs too much from the observed data , we discard the sampled parameter .
In practice, we accept Db if it falls within a tolerance , meaning the distance where is a distance measure that quantifies the difference between both datasets (for example, using Euclidean distance).
The ABC rejection algorithm produces a set of parameter values that approximately follow the desired posterior distribution without requiring likelihood evaluation.
