Inference of the Potts model is always problematic due to the intractable normalizing constant in its likelihood function. This project proposed a novel method to solve the normalizing constant.

Below introduces the functionality of different files.

1. generatedata.m : generate data set for simulation study

2. decomnc.m : This is the main file. Given the simulated data, MCMC is implemented. In this file, posterior samples are drawn using MCMC.

3. composedecom.m : Find out pixels which belong to each split. Because for each split, the spatial correlation is different.

4. showneibou.m : This is used in composedecom.m. It is used to find out the neighbourhood of each pixel.

5. ncintegnew.m : This is used to calculated normalizing constant according to method proposed by Peter J Green. This method is referred as TDI in our paper.

6. potts_prop.m and prop_new_potts.m are used to generate Potts model.

7. RCoDAlike.m. This is used to calculate the likelihood of Potts model according to our method. The method is referred as RCoDA.

8. smalldecomcover_array.m : calculate the coverage probability.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% below is instruction for folder "Secondorder"

1. generatedata.m : generate data set for simulation study

2. decomncsecond.m : This is the main file. Given the simulated data, MCMC is implemented. In this file, posterior samples are drawn using MCMC.

3. composedecom.m : Find out pixels which belong to each split. Because for each split, the spatial correlation is different. This corresponds to RCoDA_M in our paper.

4. composedecom_newversion.m : Find out pixels which belong to each split. Because for each split, the spatial correlation is different. This corresponds to RCoDA_C in our paper.

5. showneibfirst.m : This is used in composedecom.m. It is used to find out the first order neighbourhood of each pixel.

6. showneibsecond.m : This is used in composedecom.m. It is used to find out the second order neighbourhood of each pixel.

7. ncintegnew.m : This is used to calculated normalizing constant according to method proposed by Peter J Green. This method is referred as TDI in our paper.

8. potts_prop.m and prop_new_potts.m are used to generate Potts model.

9. RCoDAlike.m. This is used to calculate the likelihood of Potts model according to our method. The method is referred as RCoDA.

10. smalldecomsecondcover_array.m : calculate the coverage probability.

11. conschess.m : divide the Potts model into several blocks according to coding method.

Zhu, W., & Fan, Y. (2018). A Novel Approach for Markov Random Field With Intractable Normalizing Constant on Large Lattices. Journal of Computational and Graphical Statistics, 27(1), 59-70.