Method and system for utilizing Markov chain Monte Carlo simulations
Systems and methods for determining a probability of changing from one state to another in a stochastic entity, comprising: determining the compact component matrix utilizing characteristic information of the stochastic entity; determining the compact composite component matrix by taking a Kroneker product of the compact component matrix and an identity matrix; determining and placing all current states for the stochastic entity into a state space matrix; determining a Q matrix and/or a transition rate matrix using the compact composite component matrix and basic conditions or variables of the problem domain and/or a compact transition rate matrix; and performing Markov chain Monte Carlo (MCMC) simulation using information from the state space matrix and information from the transition rate matrix to determine the probability of changing from one state to another state in the stochastic entity.
1. A method for determining a probability of changing from one state to another in a stochastic entity, comprising;
performing processing associated with determining, using the processor, the compact component matrix utilizing characteristic information of the stochastic entity;
performing processing associated with determining, using the processor, the compact composite component matrix by taking a Kroneker product of the compact component matrix and an identity matrix;
performing processing associated with determining and placing, using the processor, all current states for the stochastic entity into a state space matrix;
performing processing associated with determining, using the processor, a Q matrix and/or a transition rate matrix using the compact composite component matrix and basic conditions or variables of the problem domain and/or a compact transition rate matrix; and
performing processing associated with performing, using the processor, Markov chain Monte Carlo (MCMC) simulation using information from the state space matrix and information from the transition rate matrix to determine the probability of changing from one state to another state in the stochastic entity.
2. The method of claim 1 , wherein the current states of the stochastic entity are determined by:
performing processing associated with determining a probability of transitioning out of a current state to another state; and
performing processing associated with utilizing the probability of transitioning information to determine the current states of the stochastic entity.
3. The method of claim 1 , wherein using indices of non zero entries of the state space matrix ensures that only possible current states are used in a compact state space matrix; and/or using non zero transition rates ensures that only possible current transitions are used in a compact transition rate matrix.
4. The method of claim 1 , wherein a transition from one state to another state does not need to be constant.
5. The method of claim 1 , wherein transition paths out of each current state are tracked rather than all possible transitions.
6. The method of claim 1 , wherein the MCMC simulation scales with increasing size and complexity of the stochastic entity.
7. The method of claim 1 , wherein the method performs MCMC simulations of multiple stochastic entities simultaneously.
8. The method of claim 6 , wherein the MCMC simulation scales by using memory and computational resources.
9. The method of claim 1 , wherein the stochastic entity is in the field of: social science, economics, chemistry, finance, physics, biology, computer science, or engineering, or any combination thereof.
10. The method of claim 1 , wherein the MCMC simulation is computed by: a GPGPU, a CPU, any other distributed and/or parallel processor, or any combination thereof.
11. The method of claim 1 , wherein the stochastic entity is a cluster of ion channels.
12. A system for determining the probability of changing from one state to another in a stochastic entity, comprising:
a processor configured for:
performing processing associated with determining, using the processor, the compact component matrix utilizing characteristic information of the stochastic entity;
performing processing associated with determining, using the processor, the compact composite component matrix by taking a Kroneker product of the compact component matrix and an identity matrix;
performing processing associated with determining and placing, using the processor, all current states for the stochastic entity into a state space matrix;
performing processing associated with determining, using the processor, a Q matrix and/or a transition rate matrix using the compact composite component matrix and basic conditions or variables of the problem domain and/or a compact transition rate matrix; and
performing processing associated with performing, using the processor, Markov chain Monte Carlo (MCMC) simulation using information from the state space matrix and information front the transition rate matrix to determine the probability of changing from one state to another state in the stochastic entity.
13. The system of claim 12 , wherein the current states of the stochastic entity can be determined by:
performing processing associated with determining a probability of transitioning out of a current state to another state; and
performing processing associated with utilizing the probability of transitioning information to determine the current states of the stochastic entity.
14. The system of claim 13 , wherein using a indices of non zero entries of the state space matrix ensures that only possible current states are used in a compact state space matrix; and/or using non zero transition rates ensures that only possible current transitions are used in a compact transition rate matrix.
15. The system of claim 12 , wherein a transition from one state to another state does not need to be constant.
16. The system of claim 12 , wherein transition paths out of each current state are tracked rather than all possible transitions.
17. The system of claim 12 , wherein the MCMC simulation scales with increasing size and complexity of the stochastic entity.
18. The system of claim 12 , wherein the method performs MCMC simulations of multiple stochastic entities simultaneously.
19. The system of claim 17 , wherein the MCMC simulation scales by using memory and computational resources.
20. The system of claim 12 , wherein the stochastic entity is in the field of: social science, economics, chemistry, finance, physics, biology, computer science, or engineering, or any combination thereof.
21. The system of claim 12 , wherein the MCMC simulation is computed by: a GPGPU, a CPU, any other distributed and/or parallel processor, or any combination thereof.
22. The system of claim 12 , wherein the stochastic entity is a cluster of ion channels.
23. The method of claim 1 , wherein the following are in compact form: state space matrix, transition rate matrix, or Q-matrix, or any combination thereof.
24. The method of claim 1 , wherein the transition rate matrix changes based on changing conditions and/or variables of the problem domain.
25. The system of claim 1 , wherein the following are in compact form: state space matrix, transition rate matrix, or Q-matrix, or any combination thereof.
26. The system of claim 1 , wherein the transition rate matrix changes based on changing conditions and/or variables of the problem domain.