An overview of reconstructability analysis <s> Exhaustive analysis <s> 1: Introduction.- 1.1. Systems Science.- 1.2. Systems Problem Solving.- 1.3. Hierarchy of Epistemological Levels of Systems.- 1.4. The Role of Mathematics.- 1.5. The Role of Computer Technology.- 1.6. Architecture of Systems Problem Solving.- Notes.- 2: Source and Data Systems.- 2.1. Objects and Object Systems.- 2.2. Variables and Supports.- 2.3. Methodological Distinctions.- 2.4. Discrete Versus Continuous.- 2.5. Image Systems and Source Systems.- 2.6. Data Systems.- Notes.- Exercises.- 3: Generative Systems.- 3.1. Empirical Investigation.- 3.2. Behavior Systems.- 3.3. Methodological Distinctions.- 3.4. From Data Systems to Behavior Systems.- 3.5. Measures of Uncertainty.- 3.6. Search for Admissible Behavior Systems.- 3.7. State-Transition Systems.- 3.8. Generative Systems.- 3.9. Simplification of Generative Systems.- 3.10. Systems Inquiry and Systems Design.- Notes.- Exercises.- 4: Structure Systems.- 4.1. Wholes and Parts.- 4.2. Systems, Subsystems, Supersystems.- 4.3. Structure Source Systems and Structure Data Systems.- 4.4. Structure Behavior Systems.- 4.5. Problems of Systems Design.- 4.6. Identification Problem.- 4.7. Reconstruction Problem.- 4.8. Reconstructability Analysis.- 4.9. Simulation Experiments.- 4.10. Inductive Reasoning.- 4.11. Inconsistent Structure Systems.- Notes.- Exercises.- 5: Metasystems.- 5.1. Change versus Invariance.- 5.2. Primary and Secondary Systems Traits.- 5.3. Metasystems.- 5.4. Metasystems versus Structure Systems.- 5.5. Multilevel Metasystems.- 5.6. Identification of Change.- Notes.- Exercises.- 6: Complexity.- 6.1. Complexity in Systems Problem Solving.- 6.2. Three Ranges of Complexity.- 6.3. Measures of Systems Complexity.- 6.4. Bremermann's Limit.- 6.5. Computational Complexity.- 6.6. Complexity Within GSPS.- Notes.- Exercises.- 7: Goal-Oriented Systems.- 7.1. Primitive, Basic, and Supplementary Concepts.- 7.2. Goal and Performance.- 7.3. Goal-Oriented Systems.- 7.4. Structure Systems as Paradigms of Goal-Oriented Behavior Systems.- 7.5. Design of Goal-Oriented Systems.- 7.6. Adaptive Systems.- 7.7. Autopoietic Systems.- Notes.- Exercises.- 8: Systems Similarity.- 8.1. Similarity.- 8.2. Similarity and Models of Systems.- 8.3. Models of Source Systems.- 8.4. Models of Data Systems.- 8.5. Models of Generative Systems.- 8.6. Models of Structure Systems.- 8.7. Models of Metasystems.- Notes.- Exercises.- 9: GSPS: Architecture, USE, Evolution.- 9.1. Epistemological Hierarchy of Systems: Formal Definition.- 9.2. Methodological Distinctions: A Summary.- 9.3. Problem Requirements.- 9.4. Systems Problems.- 9.5. GSPS Conceptual Framework: Formal Definition.- 9.6. Overview of GSPS Architecture.- 9.7. GSPS Use: Some Case Studies.- 9.8. GSPS Evolution.- Notes.- Exercises.- Appendices.- A: List of Symbols.- B: Glossary of Relevant Mathematical Terms.- C: Some Relevant Theorems.- D: Refinement Lattices.- E: Classes of Structures Relevant to Reconstructability Analysis.- References.- Author Index. <s> BIB001 </s> An overview of reconstructability analysis <s> Exhaustive analysis <s> It is proposed that probability intervals be used in reconstructability analysis. A probability interval is a subinterval of the real interval [0,1]. Regarded as “interval-valued probabilities”, these intervals generalize real-valued probabilities and arise naturally in many situations. They may represent confidence intervals resulting from sampling; imprecisely stated subjective probabilities; known linear equality or inequality constraints; etc. Thus, probability intervals are sometimes a more realistic characterization of uncertainty than are real-valued probabilities. Furthermore, the problem of inconsistency can often be avoided by their use Although the utility of interval-valued probability distributions for the identification problem is emphasized, a reconstruction technique is also developed. This reconstruction method employs a metric distance for interval distributions that is monotonic with respect to model refinement. <s> BIB002 </s> An overview of reconstructability analysis <s> Exhaustive analysis <s> Abstract When the reconstructability analysis of a directed system yields a structure in which a generated variable appears in more than one subsystem, information from all of the subsystems can be used in modeling the relationship between generating and generated variables. The conceptualization and procedure proposed here is discussed in relation to Klir's concept of control uniqueness <s> BIB003
If the Table 2 data were for a directed system, with output C and inputs A and B, only the shaded models in Table 4 need be considered. For directed systems it is useful to state results in terms of reductions in the output uncertainty, knowing the inputs, rather than in terms of information. If the uncertainty reduction, ∆U(C|B) ≡ U(C)-U(C|B) = T(B:C) = U(C)-U(B,C)+U(B) is positive and statistically significant, model AB:BC is acceptable, i.e., B is a predictor of C. Because Shannon entropy involves a log term, even small ∆U may indicate high predictability. For example, if the odds of rain vs. no rain is 2:1 in winter and 1:2 in summer and 1:1 over the year (for equal seasons), then knowing the season makes a big change in the odds, but reduces U(rain vs. no-rain) by only 8%. For the Table 2 data, the results are shown in Table 5 . For this data, A and B reduce the uncertainty of C by only very small amounts, less than 1%. The last column of the table also shows that quantitative RA measures (such as U or T) can be thought of equivalently as assessing models. Note that there are two ways that A and B can both predict C. In AB:AC:BC they do so separately, but in ABC there is an interaction effect BIB003 . Here α is computed relative to the independence model, not the saturated (top) model; it is small if results are statistically significant. The table shows that A is a better predictor of C than is B; and that ∆U(C) using both inputs, either in ABC or in AB:AC:BC, is very small but still statistically significant at the 0.05 level. BIB001 .   , BIB002 and  have shown how inconsistencies among distributed data sets may be resolved. Anderson also showed how "nuisance" variables can be exploited in the composition of disparate data sets. To find a relation between A and C from inconsistent AB and BC distributions, the inconsistencies are first resolved, after which the adjusted AB′ and BC′ distributions are composed into ABC and projected onto AC.