This contains the codes used in the paper 'A randomized Multi-index sequential Monte Carlo method' (https://arxiv.org/abs/2210.15390) for implementation of the following examples: 1D analytical Elliptic PDE, 2D non-analytical Elliptic PDE, 2D log-Gaussian Cox process and 2D log-Gaussian process.
Please see the documentation.m file in each example/folder for instruction of implementing the tests.
All the MISMC codes are adapted from the codes used in the paper 'Multi-index sequential Monte Carlo ratio estimators for Bayesian inverse problems' (https://arxiv.org/abs/2203.05351), see the GitHub link for original codes (https://github.com/Shangda-Yang/MISMCRE.git).
MLSMC codes in 1D analytical Elliptic PDE are structured based on the MLMC work by Prof. Mike Giles (http://people.maths.ox.ac.uk/~gilesm/mlmc/#MATLAB).
The solver for 2D non-analytical Elliptic PDE 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).