閒聊概率论2

解释概率论

 

 

	Classical	Frequentist	Subjective	Propensity
Main hypothesis	Principle of indifference	Frequency of occurrence	Degree of belief	Degree of causal connection
Conceptual basis	Hypothetical symmetry	Past data and reference class	Knowledge and intuition	Present state of system
Conceptual approach	Conjectural	Empirical	Subjective	Metaphysical
Single case possible	Yes	No	Yes	Yes
Precise	Yes	No	No	Yes
Problems	Ambiguity in principle of indifference	Circular definition	Reference class problem	Disputed concept

 

Note:  frequentist: 常客，propensity: 趋向，propensity accounts 可用于量子力学。

Reference class problem: 引用类问题－－different may assign different prior prob.

Classical interpretation (Laplace) :  

Laplace’s principle of insufficient reason: if there is no reason to believe that outcomes are not equally likely, take them to be equally likely.  However, not believed to be unequally is one thing; known to be equal is another. 这里有逻辑上问题。有点像广义相对论中引力质量与惯性质量等价问题。

Evidential (证据) prob.  Baysian prob. :

Subjective interp.

Logical interp.  如，一个恐龙灭绝的假设可能是真。

Eplstemlc (认知) or inductive interp.