This contains the implementation for the examples in the paper Jasra, A., Law, K.J.H., Walton, N. and Yang, S.. Multi-index Sequential Monte Carlo Ratio Estimators for Bayesian Inverse problems. Found Comput Math (2023). https://doi.org/10.1007/s10208-023-09612-z.
Examples include 1D Elliptic PDE with random force, 2D Elliptic PDE with random diffusion coefficient, log-Gaussian Cox process and log-Gaussian process.
Before carrying on the test, please take a look in the documentation.m files for each example.
For 1D example, MLSMC codes are structured based on the MLMC work by Prof. Mike Giles (http://people.maths.ox.ac.uk/~gilesm/mlmc/#MATLAB).
The 2D PDE solver is modified based on the T-IFISS toolbox by Prof. David Silvester, Prof. Howard Elman and Dr. Alison Ramage (https://personalpages.manchester.ac.uk/staff/david.silvester/ifiss/default.htm).