Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

5 Modeling of the ExperimentRunning the procedure for a artificial observation trajectory, based upon the same parameters butwith the length 6000 delivered the same results.Now we took the estimated parameter set for the two sates HMM model⃗π gen =T gen =σ (1)gen =σ (2)gen =( ) 1.0,0.0( 0.91 0.090.86 0.14( 0.6 0.00.0 0.6( 162.1 0.00.0 159.1),)· 10 −35 ,)· 10 −35 ,and after generating artificial trajectory data, based on this parameter set and running estimationprocedure on the this trajectory data, we received the following re-estimated parameter set⃗π est =T est =σ (1)est =σ (2)est =( ) 1.0,0.0( 0.91 0.090.86 0.14( 0.6 0.00.0 0.6( 162.8 0.00.0 160.1),)· 10 −35 ,)· 10 −35 .Obviously the results for the two states HMM parameter set are even better than those for the threestates HMM parameter set.5.4 Separate Estimation on the Experimental Transducin X-and Y-ComponentsHere we present the results of the estimation procedure on the single x- and y-components of theexperimental transducin two-dimensional observation data, each regarded separately.We assume a two-states HMM-SDE model as basis of the estimation process and thus the resultsfor the diffusion coefficients are:x-component:D (1) = 3.1 µm2 ,sD (2) = 0.01 µm2 .s82