Applied Mathematics the foundational discipline that guides everyone to ensure the findings are indeed backed by reality. As scientists we're primarily interested in probability interpretations.
Probability has a few approaches that have been taken over time. The subjective approach is where humans intuition is met and where you typically enter a problem. We need to move to more data driven methodologies which started with Classical, then Frequentist and Propensity blend into the mix ref
Subjective |
Classical |
Frequentist |
Propensity |
|
Main hypothesis |
Degree of belief |
Principle of indifference |
Frequency of occurrence |
Degree of causal connection |
Conceptual basis |
Knowledge and intuition |
Hypothetical symmetry |
Past data and reference class |
Present state of system |
Conceptual approach |
Subjective |
Conjectural |
Empirical |
Metaphysical |
Single case possible |
Yes |
Yes |
No |
Yes |
Precise |
No |
Yes |
No |
Yes |
Problems |
Reference class problem |
Ambiguity in principle of indifference |
Circular definition |
Disputed concept |
Subjective Intuition is based on personal opinions, interpretations, points of view, emotions and judgment. It is often the genesis for human innovations and a healthy component of human logic that can form hypothesis’s that can be proven by more mature mathematical approaches. Note: considered ill-suited for scenarios like news reporting or decision making in business or politics.
Classical Probability was developed from studies of chance. It states that probability is shared equally between all the possible outcomes, provided these outcomes can be deemed equally likely.[1]
Frequency probability of an event to occur in future is related to frequency of occurrence in past if repeating a process a large number of times under similar conditions.
- Classical probability would say there's a 50:50 chance on every coin flip regardless of history
- Frequency probability would take into account the historical trends to predict the future
Predictive modeling is an area of study to help humans leverage advanced mathematical approaches to find patterns in the historical data upon which future predictions can occur.