Read the equation
If two interpretations assign exactly the same probability to every observation in the study, the likelihood ratio for any observed record is one. Those data therefore supply no likelihood evidence favoring one interpretation over the other. Distinguishing them requires an additional observable, intervention, or prediction on which they disagree.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| M_1 | First interpretation or model |
| M_0 | Alternative interpretation |
| Y | Observed data; O in other versions |
| U | Controlled input where specified |
How it works
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Original context
Read the surrounding source passage
9.2 An explicit observational-equivalence problem Suppose two interpretations assign the same probability distribution to every measured variable in this study: PrO∣M1=PrO∣M2, where O contains the observed training logs and adapter tensors. One interpretation may associate an unobserved experience with the episode; the other may not. For this dataset their likelihood ratio is one. More precise measurement of the same recorded variables does not break that equivalence unless the theories make different predictions about them. This is a statement about the present observables, not a theorem that consciousness can never be studied. Additional declarations, interventions, self-model measurements, and functional consequences can constrain a theory. The protocol therefore expands observation and manipulation rather than merely attaching a more evocative label to the gradient peak. 9.3 Do not manufacture a universal onset clock
Exact original notation
Pr\left(O∣{M}_{1}\right)=Pr\left(O∣{M}_{2}\right),Related builds
Sources & provenance
Pr\left(O∣{M}_{1}\right)=Pr\left(O∣{M}_{2}\right),
Pr\left(O∣{M}_{1}\right)=Pr\left(O∣{M}_{2}\right),
Pr\left(O∣{M}_{1}\right)=Pr\left(O∣{M}_{2}\right),
Pr\left(O∣{M}_{1}\right)=Pr\left(O∣{M}_{2}\right),