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
9.3 Observational non-identifiability Let O be all observed data in an experiment: prompts, rewards, generated tokens, classifications, and recorded behavior. Suppose two candidate descriptions have the same observational distribution, P1O∣U=P0O∣U, but differ in whether they label the internal process conscious. For any observed dataset, their likelihood ratio is one. Repeating the experiment can sharpen the estimated behavioral effect while leaving this particular difference between descriptions unidentified. This is an illustrative identifiability argument, not a Bayes factor computed for Joseph’s theory. The present theory has not supplied a full likelihood, priors, or a competing quantitative observation model. No empirical posterior probability of consciousness is calculated here. The constructive implication is to add measurable constraints. A theory can make useful predictions about recurrent memory, reference accuracy, causal roles of self-representation, persistence, or intervention response. Those predictions can be evaluated even while the interpretation in terms of experience remains a separate question.
Exact original notation
{P}_{1}\left(O∣U\right)={P}_{0}\left(O∣U\right),Sources & provenance
{P}_{1}\left(O∣U\right)={P}_{0}\left(O∣U\right),
{P}_{1}\left(O∣U\right)={P}_{0}\left(O∣U\right),