Percentiles Bayes Plot for QMM

[greenTara]

Let's start with delta = 0 to verify we get the same as the MM plot.

We also need to add a plot underneath with the same horizontal scale showing the value of mu at the estimation time.

[alexlafleur]

Delta=0 Plot

Deciles_Bayes_QMM.pdf

Parameter and Intermediate Printouts

[greenTara]

Is this plot for a single model (numruns = 1)? Please print out all parameters and include in the comment with the plot, includling the additional parameters for the QMM model. I don't see any parameters in the attached text file.

[greenTara]

The QMM parameters include:

tauquasi edgewidth edgeshift gammamin gammamax delta gamma

[greenTara]

The decile plot itself looks like it is working ok for delta = 0.

[alexlafleur]

Deciles_Bayes_QMM.pdf

Parameter and Intermediate Printouts

[alexlafleur]

Deciles_Bayes_QMM_Mu.pdf

For a test, I executed the script with num_trajectories=5, numsims=1. Deciles_Bayes_QMM_Mu.pdf

[alexlafleur]

Edgeshift=1 Deciles_Bayes_QMM_Mu.pdf

evaluate_deciles_qmm_mu.txt

[alexlafleur]

Edgeshit=100 Deciles_Bayes_QMM_Mu.pdf

evaluate_deciles_qmm_mu.txt

[alexlafleur]

Tauquasi = 4 Deciles_Bayes_QMM_Mu.pdf

evaluate_deciles_qmm_mu.txt

[alexlafleur]

Edgeshift=8 Tauquasi=4 num_estimations_min=2 Deciles_Bayes_QMM_Mu.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Edgeshift=64 Tauquasi=4 num_estimations_min=5

Deciles_Bayes_QMM_Mu.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Deciles_Bayes_QMM_Mu.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

With random seed 1101 num_estimations_min=7 Deciles_Bayes_QMM_Mu_Delta_0.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

With random seed 1101 num_estimations_min=7 Deciles_Bayes_QMM_Mu_Delta_0_1.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Edgeshift=52 With random seed 1101 num_estimations_min=7 Deciles_Bayes_QMM_Mu_Delta_0.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Edgeshift=48 With random seed 1101 num_estimations_min=9 Deciles_Bayes_QMM_Mu_Delta_0.1.pdf evaluate_deciles_qmm_mu.txt

[greenTara]

Some plots to generate:

Delta: 0.2, 0.5, 1.0 with all other factors the same.

Also with these values of delta, Edgewidth = 8, 64, 256

[alexlafleur]

Delta=0.2 Edgewidth = 8 Deciles_Bayes_QMM_Mu_Delta_0.2.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Delta=0.5 Edgewidth = 64 Deciles_Bayes_QMM_Mu_Delta_0.5.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Delta=1 Edgewidth=256

Deciles_Bayes_QMM_Mu_Delta_1.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Delta = 1 Edgewidth=4 Num_trajs=8 Deciles_Bayes_QMM_Mu_Delta_1.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Delta=0.5 Edgewidth=4 Num_trajs=8 Deciles_Bayes_QMM_Mu_Delta_0.5.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Delta=0.2 Edgewidth=4 Num_trajs=8 Deciles_Bayes_QMM_Mu_Delta_0.2.pdf evaluate_deciles_qmm_mu.txt

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf

Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 96 Gammamin: 1 Gammamax: 1.01 Delta: 0.2 Gamma: 1.00837315683 Simulating data num_trajectories = 256 numsims = 32 num_trajs per simulation = 8 Parameter Overview: taumeta: 4 tauquasi: 4 eta: 16 scale_window : 16 shift: 64 window_size: 1024 num_estimations: 34 len_trajectory: 3201 num_trajectories: 8 num_trajectorieslen_trajectory: 25608 NAIVE window_size num_estimations 35840 BAYES window_size + num_estimations*shift 3200

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 128 Gammamin: 1 Gammamax: 1.01 Delta: 0.2 Gamma: 1.00837315683 Simulating data num_trajectories = 256 numsims = 32 num_trajs per simulation = 8 Parameter Overview: taumeta: 4 tauquasi: 4 eta: 16 scale_window : 16 shift: 64 window_size: 1024 num_estimations: 48 len_trajectory: 4097 num_trajectories: 8 num_trajectorieslen_trajectory: 32776 NAIVE window_size num_estimations 50176 BAYES window_size + num_estimations*shift 4096

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.pdf Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 128 Gammamin: 1 Gammamax: 1.01 Delta: 0 Gamma: 1.00713131633 Simulating data num_trajectories = 256 numsims = 32 num_trajs per simulation = 8 Parameter Overview: taumeta: 4 tauquasi: 4 eta: 16 scale_window : 16 shift: 64 window_size: 1024 num_estimations: 48 len_trajectory: 4097 num_trajectories: 8 num_trajectorieslen_trajectory: 32776 NAIVE window_size num_estimations 50176 BAYES window_size + num_estimations*shift 4096

[alexlafleur]

Current Time 1023 Mu at Current Time 7.16093850883e-15 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1087 Mu at Current Time 5.30686605771e-14 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1151 Mu at Current Time 3.92130772298e-13 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1215 Mu at Current Time 2.89762658312e-12 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1279 Mu at Current Time 2.14106510299e-11 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1343 Mu at Current Time 1.58204616074e-10 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1407 Mu at Current Time 1.1689825774e-09 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1471 Mu at Current Time 8.63767796178e-09 TM at Current Time [[ 0.93620659 0.02020545 0.03760997 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1535 Mu at Current Time 6.38242834139e-08 TM at Current Time [[ 0.93620659 0.02020545 0.03760997 0.00597798]

[alexlafleur]

Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 128 Gammamin: 1 Gammamax: 1.01 Delta: 0.2 Gamma: 1.00837315683 Simulating data num_trajectories = 256 numsims = 32 num_trajs per simulation = 8 Parameter Overview: taumeta: 4 tauquasi: 4 eta: 16 scale_window : 16 shift: 64 window_size: 1024 num_estimations: 48 len_trajectory: 4097 num_trajectories: 8 num_trajectorieslen_trajectory: 32776 NAIVE window_size num_estimations 50176 BAYES window_size + num_estimations*shift 4096

Current Time 1023 Mu at Current Time 7.16093850883e-15 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1087 Mu at Current Time 5.30686605771e-14 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1151 Mu at Current Time 3.92130772298e-13 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1215 Mu at Current Time 2.89762658312e-12 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1279 Mu at Current Time 2.14106510299e-11 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1343 Mu at Current Time 1.58204616074e-10 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1407 Mu at Current Time 1.1689825774e-09 TM at Current Time [[ 0.93620659 0.02020545 0.03760998 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1471 Mu at Current Time 8.63767796178e-09 TM at Current Time [[ 0.93620659 0.02020545 0.03760997 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]] Current Time 1535 Mu at Current Time 6.38242834139e-08 TM at Current Time [[ 0.93620659 0.02020545 0.03760997 0.00597798] [ 0.07053943 0.88780283 0.03583715 0.0058206 ] [ 0.05236292 0.0241041 0.91465715 0.00887582] [ 0.04702273 0.02403464 0.05817443 0.8707682 ]]

Mean Error Values: [0.026900390407634679, 0.026487959547234659, 0.026371743540016215, 0.026058675413958891, 0.026341695692404209, 0.026085129241899763, 0.026181652870564807, 0.026301357226336385, 0.026490314244742075, 0.027263698145661892, 0.026708046028690102, 0.027093521638468232, 0.026705168211816645, 0.026281696662821624, 0.026359483098434149, 0.026735609953965098, 0.026203569309121384, 0.026207115910270078, 0.026454542385539435, 0.026284778203748908, 0.026231035943473601, 0.025639438931464635, 0.025449511192637747, 0.026666827867684137, 0.027177702600081177, 0.027399698155350191, 0.027324393281464188, 0.027369350145145143, 0.027542970055314787, 0.027226917288331851, 0.025026575528892869, 0.019260776899486874, 0.017478008144701913, 0.018087178714074965, 0.017751302081677252, 0.017334221290740214, 0.017327483234945141, 0.017454255014777761, 0.016406343533274872, 0.016396225064162918, 0.016993315694030106, 0.016707418129165819, 0.016579936105311194, 0.015692355106793131, 0.016092772051300337, 0.016656757792221002, 0.016304742902234229, 0.016496414634735383, 0.015886500740220157]

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 256 Gammamin: 1 Gammamax: 1.01 Delta: 0.2 Gamma: 1.00837315683 Simulating data num_trajectories = 256 numsims = 32 num_trajs per simulation = 8 Parameter Overview: taumeta: 4 tauquasi: 4 eta: 16 scale_window : 16 shift: 64 window_size: 1024 num_estimations: 48 len_trajectory: 4097 num_trajectories: 8 num_trajectorieslen_trajectory: 32776 NAIVE window_size num_estimations 50176 BAYES window_size + num_estimations*shift 4096

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf evaluate_deciles_qmm_mu_0.2.txt

[alexlafleur]

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf

Deciles_Bayes_QMM_Mu_Delta_0.2.pdf evaluate_deciles_qmm_mu_0.2.txt

[greenTara]

I made some changes in parameter handling, but the main fix is to include the scaling by tauquasi when the data is simulated. Now the error behaves the way it is supposed to, that is it is close to the predicted formula except in a region around the non-stationary behavior that has a buffer of about window_size.

Deciles_Bayes_QMM_Mu_Delta_1.0.pdf

Numruns 1 Statconc: [ 1. 1. 1. 1.] Timescaledisp: 2 Edgewidth: 4 Edgeshift: 64 Gammamin: 1 Gammamax: 1.01 Delta: 1.0 Gamma: 1.00222097524 Simulating data num_trajectories = 512 numsims = 32 num_trajs per simulation = 16 Parameter Overview: taumeta: 4 lag: 1 tauquasi: 8 eta: 8 scale_window : 8 shift: 32 window_size: 256 num_estimations: 128 len_trajectory: 4353 num_trajectories: 16 num_trajectorieslen_trajectory: 69648 NAIVE window_size num_estimations 33024 BAYES window_size + num_estimations*shift 4352

Transition Matrix Error Calc: [[ 0.83971433 0.06173242 0.0596093 0.03894396] [ 0.01116055 0.92779761 0.04130821 0.01973363] [ 0.02699801 0.03281698 0.88764996 0.05253506] [ 0.02560979 0.05728527 0.07012157 0.84698338]]