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.