Efficiency is a pretty loaded term, which many people aren't aware of.
Now, another breakdown due to my second field (statistics).
What type of probability, subjective, epistemic, empirical? Are we talking about : frequentist, bayesian or logical probability?
I guess you and I should just stop communicating with one another, lol.
This is an issue for me. Philosophy and logic are secondary in my education. I must uses all forms of analysis available as no one method results in a factually true conclusions in my field, I can not merely reject one on a whim. Archaeology is a science and history. So what may work for science does not always work for history. Models in archaeology are not complete nor reliable as examples you have posted. Models use both frequentist and bayesian probability. Both are used in conjunction as models as the two do not always include shared methodology in all models. Probability may only exclude a conclusion but not provide one. Subjective is prior believe as part of frequentist models. Empirical is divided rather than a singular model. Epistemic becomes part of a conclusion and the models used. History makes all models used have a degree of "fuzziness" due to incomplete data sets.
Objective: Identify a site's origins
Event: I find pottery samples in the strata of the site.
Frequentist-Model: Based on prior knowledge of identification markers, history of the area and it's people we can identify products of a people as a subset. Hebrew subset, Canaanite subset, Greek subset, etc. This prior knowledge is in the form of a belief as history is not as reliable as science. The sample could be found in an area associated with the Greeks thus probability of a Greek subset is greater than a subset foreign to the area by location or time.
Investigation: Visual analysis of samples share common identification markers of a subset which is relevant to the area. The sample can be placed within a subset which is relevant per the above. Samples could bear markers of Greek manufacturing technique, style, etc. Let say a major identification mark of the Greek subset is three handles which is not present in other relevant cultures. This marker is found on the samples.
(FC)Conclusion: Samples are Greek with a high probability.
Bayesian Objective: Analysis of samples based on the sample itself in order to confirm FC above.
Investigation: Carbon dating. I use this example to highlight the key differences in investigation between the two. Frequentist views in archaeology is based on prior knowledge as per above with Bayesian is based on knowledge we can gain of the item itself outside of prior knowledge. If carbon dating places the samples outside of the established frequentist priori subset then FC is wrong. Further more the sample contradicts the subset since it shares identification markers of the Greeks. So not only is FC wrong but the subset is now questionable. So the Greek subset could merely be assimilated.
Conclusion: Samples are not Greek, site is unknown.
So even using both methods we may not identify anything of value.
Topic: Why is there something rather than nothing?