Table of Contents
Public units
| Unit | Title | Use |
|---|---|---|
| Readme | Mathematical Modeling - Readme | Follow worked connections between modeling methods. |
| Preface | Mathematical Modeling - Preface | Understand the connected methods, their rationale, sources and limits. |
A. Formulate the subject question
| § | ID & Title | Status | Keywords & Search Queries | Dependencies |
|---|---|---|---|---|
| 1 | MMP.10 - Construct and Revise a Mathematical Constraint Formulation | Usable, evolving | objects; representation; domains; constraints; recovery; multiplicity; optimization. How can the objects and conditions of a working question be expressed so that mathematical answers still refer to the intended possibilities? | B.5.FM for initial formulation; MATH.1/.5 for construction and representation; C.29.1 for transferring results; MMP.11 for unknown relations. |
| 2 | MMP.11 - Construct a Mathematical Model Family from Known Relations | Usable, evolving | unknown relation; family; grounded structure; parameterization; completeness; identifiability. How can an unknown contribution vary without losing known relations, and which remaining ambiguity changes the requested consequence? | MMP.10 for admissible representation; A.3.3.TR for state; C.16.IR for observation-based inference; C.28.MR for intervention; MMP.9 for reduction. |
| 3 | MMP.8 - Formulate Information-Dependent Choices Mathematically | Usable, evolving | available information; action; policy; decision timing; objective; conditional requirement; average performance. What can be chosen with information available in time, and which conditions must that choice satisfy? | MMP.7 for reports; A.3.3.TR for change; MMP.10 for constraints; ME for changing the corresponding way of working. |
| 4 | MMP.8.SD - Construct a Sequential Decision Model from Information and Consequences | Usable, evolving | sequential decision; sufficient state; belief; policy; transition; accumulated consequence; continuation. What information must a continuing instruction retain, and how do present choices affect later possibilities and results? | MMP.8 for available choices; A.3.3.PI for predictive state and belief; MMP.7 for records; CMP.3/.5/.9 for policy computation. |
B. Infer, distinguish and revise
| § | ID & Title | Status | Keywords & Search Queries | Dependencies |
|---|---|---|---|---|
| 1 | MMP.7 - Construct a Probability Model of the Recorded Data | Usable, evolving | observation; recorded data; selection; missing records; censoring; noise; probability law. What distribution does the recording procedure produce from the modeled possibilities? | C.16.IR for interpretation and inference; MMP.11 for unknown relations; MMP.8 when the record informs a choice. |
| 2 | MMP.12 - Formulate an Inverse Problem and Choose Whether and How to Use Regularization | Usable, evolving | inverse problem; identifiability; conditioning; regularization; restriction; penalty; target. Which unknowns can the records resolve, and what improvement and loss does a stable reconstruction introduce? | C.16.IR for compatible cases; MMP.11/.7 for the forward and recording relations; MMP.13 for inferential uncertainty; CMP for solving the formulated problem. |
| 3 | MMP.13 - Infer Unknowns Statistically under a Stated Observation Model | Usable, evolving | estimator; confidence coverage; prior; posterior; predictive uncertainty; dependence; target propagation. Which inferential construction supports the statement the receiver needs? | MMP.7 for the record law; MMP.12/C.16.IR for ambiguity; CMP.8/.9 for numerical computation; MMP.14/.8 for prediction checks and decisions. |
| 4 | MMP.14 - Find and Repair a Mathematical Model’s Failed Predictions | Usable, evolving | model criticism; predictive comparison; residual; conditional response; selection; repair; held-out prediction. Which discrepancy changes the use, what assumption can repair it, and what consequence must be recalculated? | MMP.7/.11/.13 for comparable predictions; B.5.RR for affected revision; CMP.8/.9 for numerical error; C.11.DUA for worthwhile further checking. |
| 5 | MMP.15 - Identify an Intervention Effect from Available Data | Usable, evolving | causal identification; intervention; adjustment; mediation; population transfer; support; partial identification. Which intervention consequence follows from the available laws and causal assumptions? | C.28.MR for intervention meaning; MMP.7/.13 for recording and estimation; C.16.IR for compatible possibilities; MMP.16 for worthwhile distinguishing observations. |
| 6 | MMP.19 - Construct and Bound a Mathematical Counterfactual Comparison under a Causal Model | Stable | counterfactual; same case; factual inference; common input; joint response; pathway; bounds. What would happen to the same case under another action, and what does the available information determine? | C.28.MR for changed mechanisms; MMP.7/.13 for factual records and inference; MMP.15 for identification; MMP.10/.16 for bounds and useful observations. |
| 7 | MMP.16 - Design Observations to Separate Mathematical Model Alternatives | Usable, evolving | observation design; discrimination; nuisance; recording law; value of information; feasible design. Which obtainable observation separates a consequential ambiguity, and can its benefit repay its burden? | MMP.7/.11/.12/.13 for predicted record laws; MMP.8/.8.SD for decisions; C.11.DUA for worthwhile further work; subject methods for realization. |
C. Change the model while retaining its use
| § | ID & Title | Status | Keywords & Search Queries | Dependencies |
|---|---|---|---|---|
| 1 | MMP.9 - Derive a Reduced Mathematical Model of State Evolution | Usable, evolving | reduction; hidden state; closure; memory; approximation; error; sufficient bound. What contribution is left by eliminated detail, and which replacement preserves the consequence needed? | A.3.3.TR for evolution; C.29.1 for preserved structure; MMP.11 for a replacement family; B.5.RR for affected revision. |
| 2 | MMP.17 - Construct a Surrogate for Selected Model Responses | Usable, evolving | surrogate; selected response; input region; approximation; correction; tail; refinement. Which cheaper construction can supply the model response the next operation actually needs? | MMP.11 for retained structure; CMP.7/.6 for learning and updates; MMP.14 for consequential mismatch; MMP.18 for coupled use. |
| 3 | MMP.18 - Couple Models with Compatible Exchanges and Scales | Usable, evolving | coupling; interface; scale; conservation; closure; shared uncertainty; double counting. How can component models exchange quantities and information without changing the required joint answer? | A.3.3.TR and MMP.10 for joint conditions; MATH.18 for retained consequences; MMP.9/.17 for missing contributions; CMP.8/.14 for interacting computation. |