The first casestudy is the fusion of Bayequentist from DailyDigest and ManageChain from MonthlyModel. Three Bayesian checks are applied to chained system where demand/supply and material/information are matched. This is the diagram:
Originally posted by **hyunjimoon** September 12, 2022
## Goal
to figure out the best way to tune the following hyper-parameters and its useful resource. I left the link for each discussion (#12, #7, #9, #11) as they need active development, so please leave comment in each link! If you think of any other **tunable parmameters**, please leave a comment so that I can allocate a new discussion thread for that.
### 1. Typify model into PA or PAD based on the research purpose in https://github.com/Data4DM/BayesSD/discussions/12
- [Some models are useful, but how do we know which ones?Towards a unified Bayesian model taxonomy](https://arxiv.org/pdf/2209.02439.pdf)
### 2. Typify parameters to assumed or assumed time-series or estimated for testing in https://github.com/Data4DM/BayesSD/discussions/7
- [this](https://statmodeling.stat.columbia.edu/2013/01/05/understanding-regression-models-and-regression-coefficients/#comment-125256) discussion on holding constant (clamping) between two leaders (Andrew Gelman and Judea Pearl)
It is recommended to make each commit unified so that communication could be like: "see commit 684dfb16e0055bee6ae36753c4f11c610192d5ce for the update" but will do better next time.
Only the second moment is incorrect in the first run (row), while both the first and second moment is biased (second row).
The plot below compares the prior draws (true) and estimated values:
In other words, using lookups as a container for data? I wouldn't normally do that, unless I wanted random access to the data, or was planning to export to some other tool that couldn't digest Vensim data variables.
One possible strategy is to create placeholder lookups with generic values, then populate them at runtime with a .cin file (perhaps generated in Excel) containing the real values. This won't work if the goal is to export the .mdl though. In that case, with a little finagling, you could just generate the lookups in mdl syntax and paste them into the equation listing.
This attempt to use lookup function for driving data input structure started from digging into how pysd is using external data via initializing the model with .initialize(data_file = .tab). https://github.com/SDXorg/pysd/discussions/371
To introduce vensim2stan translator, the following must be completed by 10/21.
Must to do
a. prove vensim and stan draws2data generate equal results (with blue variables as vdfx or csv)
b. data2draws2 debug
c. plot using xarray or arviz inferencedata (how many draws, default 1000)
d. analyze fit, increase the number of estimated variable from 2 to 6
Can do
e. data2draws2 loglik computation
f. loo computation and PIT
g. extend to hierarchical model
h. how to incorporate hierarchical modeling with testing framework to make the test result less path dependent? Should we start from no pooling or complete pooling? https://github.com/Data4DM/BayesSD/issues/34
e. implement hierarchical Bayes in vensim + Venpy
Pass generated (via draws2data) vectors (averaged across 1,000 different prior draws) to data2draws.
ran draws2data for inventory management after transforming two flow rates (production start rate, production rate) into stocks by adding process noise then generated
This will cause Capacity to be initialized at 100; then the first value of target capacity will be Capacity * adjust from utilization. In general, this will not be 100; the initial expression is used only to compute the initial conditions of State variables.
SM posterior samples representing parameter and data joint (theta, y)
a. S = 2, M = 100, N = 20 weeks
200 theta posterior samples from joint space (theta, y)
b. S = 4, M = 50, N = 20 weeks
200 theta posterior samples from joint space (theta, y)
prior and likelihood distribution for draws2data, data2draws
2. PD model enforce symmetry of `draws2data` and `data2draws` while PAD allows asymmetry; `data2draws` is blackboxed map of $P_\phi(.|Y)$. https://github.com/Data4DM/BayesSD/discussions/12#discussion-4388611
3. plotting prior distribution vs aggregated posterior samples
5. Have you seen any seasonality data from epidemics https://github.com/Data4DM/BayesSD/discussions/32#discussioncomment-3774020
B.
1. two different ways of random variable input:
theta ~ N(2,1)
G1: Y|theta = 1
G2: Y|theta = 2
Y = .5(P(Y1 |theta =1) + P(Y1 |theta =2))
Estimate theta from Y
2. approximate: symmetric
Discussion on the value of one random variable (prior) can change in one vensim run or fixed (if later, we run S numbers of vensim with different value of parameter then aggregate outcomes)
Because of the implementational restriction of stochasticity, we are enforcing time-varying concepts in vensim?
$\theta \sim N(3, .4)$
random variable
driving data: 2, 3, 2, 3,...
comparing the probability of our implemented / numerically computed result.
Y_0
Y_1, Y_2
Predictive distirbution, or the p of realized data from the assumed model is greater when we assume homogeneity across time and heterogeneity across space.
P(Y_0|M) < P(.5(Y_1 + Y_2)|M)
Filtering is before ergodic or stationary or where time hetereogenity is not settled yet
\thetat-1 =0.5
\theta{t} =? generates samples from prior (sampled from a prior distribution = N(\theta_t-1 , 1)
@tomfid I am following your comment on using reference throughput. Thanks. However, I faced the following active initial error and I am not sure about its cause. Especially I don't follow how Process noise std norm data can be initialized in two different ways (leading to unmatched initial and active).
The end goal of this model are three:
The first casestudy is the fusion of Bayequentist from DailyDigest and ManageChain from MonthlyModel. Three Bayesian checks are applied to chained system where demand/supply and material/information are matched. This is the diagram:
I aim to address first two topics from https://github.com/Data4DM/BayesSD/discussions/5,
@tomfid the following are analysis code and vensim file readied for the above goal. Ready to go!
It is recommended to make each commit unified so that communication could be like: "see commit 684dfb16e0055bee6ae36753c4f11c610192d5ce for the update" but will do better next time.
First fit success with this model!
Only the second moment is incorrect in the first run (row), while both the first and second moment is biased (second row). The plot below compares the prior draws (true) and estimated values:
true dist:
Digging into dimension of
prior_pred,post_drawsin https://github.com/Data4DM/BayesSD/discussions/23#discussion-4429295I need help in using driving data using vensim's lookup function structure.
In other words, using lookups as a container for data? I wouldn't normally do that, unless I wanted random access to the data, or was planning to export to some other tool that couldn't digest Vensim data variables.
One possible strategy is to create placeholder lookups with generic values, then populate them at runtime with a .cin file (perhaps generated in Excel) containing the real values. This won't work if the goal is to export the .mdl though. In that case, with a little finagling, you could just generate the lookups in mdl syntax and paste them into the equation listing.
There are two forms in mdl syntax:
https://www.vensim.com/documentation/lookups.html
LOOKUP NAME([(Xmin, Ymin)-(Xmax, Ymax),(Xref1, Yref1),(Xref2,Yref2),...(Xrefn,Yrefn)]
(X1, Y1), (X2,Y2), . . .(Xn, Yn) ) ~ Units ~ Description |
The stuff in [ ] can be omitted.
or:
LOOKUP NAME( X1, X2, X3,....Xn, Y1, Y2, Y3,....Yn) ~ Units ~ Description |
.cin syntax is the same - just make sure it's all on one line, and omit the ~ and stuff after.
This attempt to use lookup function for driving data input structure started from digging into how pysd is using external data via initializing the model with
.initialize(data_file = .tab). https://github.com/SDXorg/pysd/discussions/371To introduce vensim2stan translator, the following must be completed by 10/21.
Must to do
a. prove vensim and stan
draws2datagenerate equal results (with blue variables as vdfx or csv) b.data2draws2debug c. plot using xarray or arviz inferencedata (how many draws, default 1000) d. analyze fit, increase the number of estimated variable from 2 to 6Can do
e.
data2draws2loglik computation f.loocomputation and PIT g. extend to hierarchical model h. how to incorporate hierarchical modeling with testing framework to make the test result less path dependent? Should we start from no pooling or complete pooling? https://github.com/Data4DM/BayesSD/issues/34 e. implement hierarchical Bayes in vensim + VenpyDone
Pass generated (via
draws2data) vectors (averaged across 1,000 different prior draws) todata2draws.ran
draws2datafor inventory management after transforming two flow rates (production start rate,production rate) into stocks by adding process noise then generatedFirst estimation success with realistic values:
realvalues in vensim (no int)set_priorcommandDiscussion with Hazhir
Recommend
loglikas reliable diagnosticsThis will cause Capacity to be initialized at 100; then the first value of target capacity will be Capacity * adjust from utilization. In general, this will not be 100; the initial expression is used only to compute the initial conditions of State variables.
a. S = 2, M = 100, N = 20 weeks 200 theta posterior samples from joint space (theta, y)
b. S = 4, M = 50, N = 20 weeks 200 theta posterior samples from joint space (theta, y)
prior and likelihood distribution for
draws2data,data2drawsnumeric data (using values in vensim; cannot specify)
numeric_assumption = { "n_t": n_t, "customer_order_rate": pd.read_csv('data/example_retail_sales.csv').iloc[:n_t, 1].values, "process_noise_std_norm_data": np.random.normal(0,1, size=n_t), "production_start_rate_m_noise_trun_norm_data": truncnorm.rvs(0, 2, size=n_t), "production_rate_m_noise_trun_norm_data": truncnorm.rvs(0, 2, size=n_t), "production_start_rate_stocked_obs": truncnorm.rvs(0, 2, size=n_t), "production_rate_stocked_obs": truncnorm.rvs(0, 2, size=n_t), }
model = StanVensimModel(structural_assumption, setting_dict = setting_assumption, numeric_assump_dict = numeric_assumption)
model.set_prior("inventory_adjustment_time", "normal", 2, 0.4, lower=0) model.set_prior("minimum_order_processing_time", "normal", 0.05, 0.01, lower=0) model.set_prior("m_noise_scale", "normal", 0.1, 0.02, lower = 0)
Discussion on the value of one random variable (prior) can change in one vensim run or fixed (if later, we run S numbers of vensim with different value of parameter then aggregate outcomes)
Because of the implementational restriction of stochasticity, we are enforcing time-varying concepts in vensim?
Y_0 Y_1, Y_2 Predictive distirbution, or the p of realized data from the assumed model is greater when we assume homogeneity across time and heterogeneity across space. P(Y_0|M) < P(.5(Y_1 + Y_2)|M)
Filtering is before ergodic or stationary or where time hetereogenity is not settled yet \thetat-1 =0.5 \theta{t} =? generates samples from prior (sampled from a prior distribution = N(\theta_t-1 , 1)
p(D|\theta_t1) + p(D|\theta_t2) + p(D|\theta_t3) + p(D|\theta_t4)
@tomfid I am following your comment on using reference throughput. Thanks. However, I faced the following active initial error and I am not sure about its cause. Especially I don't follow how
Process noise std norm datacan be initialized in two different ways (leading to unmatched initial and active).shadow structure success
reference initial stock