📦 [Inven model] effect of # of estimated parameter + procession noise

[hyunjimoon]

Let alone the potential error in state value, six parameter estimation is very bad compare to two param. est.
Data4DM/stanify#11 (comment)

[tomfid]

What happens if you turn off process noise? Seems like this should be an easy problem for Stan.

[hyunjimoon]

Decreasing is not so different. Increasing process noise introduced two major difference:

1. posterior of manufacturing_cycle_time, wip_adjustment_time became unimodal (right) (from bimodal left)

2. divergence increased (if my memory is correct, it wasn't this severe with 0, .1 process noise scale)

	Chain 1 had 48 divergent transitions (96.0%)
	Chain 2 had 47 divergent transitions (94.0%)

In general what would be the effect of process noise on posterior geometry? My prior is it makes posterior space smoother and continuous. So increasing process noise may increase the quality of estimation (as it removes ruggedness and multimodality). I don't know the cause of divergence yet. Do you agree so far? @tomfid

(I am experimenting with increased process noise, so scale 0, .1 (baseline), .5. for both 2 and 6 parameters)

[hyunjimoon]

Re 2: recording the scream of Stan HMC sampler

Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.37) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.37) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.37) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.37) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.52) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.52) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.52) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45: ode parameters and data is inf, but must be finite! (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
	Exception: ode_rk45:  Failed to integrate to next output time (0.52) in less than max_num_steps steps (in '/Users/hyunjimoon/Dropbox/stanify/stan_files/Inven_6est_dot5_pnoise/Inven_6est_dot5_pnoise_data2draws.stan', line 51, column 4 to column 286)
Consider re-running with show_console=True if the above output is unclear!
02:49:23 - cmdstanpy - WARNING - Some chains may have failed to converge.
	Chain 1 had 48 divergent transitions (96.0%)
	Chain 2 had 47 divergent transitions (94.0%)
	Use function "diagnose()" to see further information.

[tomfid]

ode parameters and data is inf, but must be finite!
Not sure what this means. Is it an integration failure or a likelihood failure?

If it's integration, as the "failed to integrate" error hints, the cause could be the /TIME STEP time constants on the "stocky" measurements. Those are fine with Euler, but could be nonconvergent in RK45 auto because the flows grow as DT shrinks.

[tomfid]

In general what would be the effect of process noise on posterior geometry? My prior is it makes posterior space smoother and continuous. So increasing process noise may increase the quality of estimation (as it removes ruggedness and multimodality). I don't know the cause of divergence yet. Do you agree so far? @tomfid

I agree that the likelihood surface should get smoother with added noise. I'm not sure I'd say this improves "quality" - it makes the estimation easier and more likely to converge. But at the same time the unmodeled process noise makes your confidence bounds wrong and could introduce some biases. In a nearly-linear inventory model, that might not be much of a problem.

[tomfid]

See my suggestion at #94 (reply in thread)

[hyunjimoon]

Effect of S, P, HR

S

#43, S =1 is not enough as can be seen from the large variation:

P = 2,3,4 with HR