Epistemic_uncertainty_subjective_probabi (1)

Introduction to Epistemic Uncertainty

• Epistemic Uncertainty: A major challenge in ancient history, especially with limited data.

• Quantitative Estimates: Often based on sparse and disparate information; for instance, lack of census data for Roman Empire population.

• Methodological Dilemma: Historians debate point estimates (e.g., 54 million vs. 45 million) without acknowledging margins of error or uncertainty.

Importance of Reporting Uncertainty

• Point Estimates: Hard to interpret due to lack of accompanying error margins.

• Use of Ranges: Often arbitrary and do not reflect true confidence levels.

• Estimating Multiple Quantities: Combining estimates increases uncertainty; knowledge from known quantities affects estimates for less-known quantities.

A Probabilistic Framework

• Alternative Framework: Proposes a rigorous accounting of uncertainty using probability to measure degree of belief.

• Historical Analysis Tool: Probability enables better handling of uncertainties.

• Application in Other Fields: Similar techniques used in forecasting, risk assessment; ancient historians can benefit from these methodologies.

Challenges of Estimating Roman Population

• Limited Data: Most Roman population data lost; the 48 C.E. census figures for Roman citizens only partial.

• Ambiguities: Confusion over whether census figures represent all persons or just adult males.

• Key Estimates:

  • Beloch's 1886 estimate: 54 million, later revised to 70 million.

  • McEvedy and Jones: proposed peak population of 46 million.

  • Frier & Scheidel: suggest ranges for populations in light of historical events.

Issues of Overlooked Uncertainty

• Debate Characteristics: Primarily focused on point estimates without discussing error margins, leading to obscured understanding of uncertainties.

• Formal Probabilities: Advanced representation and management of these uncertainties.

Understanding Types of Uncertainty

• Aleatory vs. Epistemic: Uncertainty can be due to randomness (aleatory) or limits of knowledge (epistemic).

• Philosophical Considerations: Different interpretations of probability (frequentist vs. subjective); emphasis on subjective probability as a degree of belief.

Approach to Historical Analysis

• Subjectivity of Probability: Historians' beliefs must be expressed probabilistically to clarify differences and enhance discussions.

• Integration of Knowledge: Probabilities reflect an individual historian’s state of knowledge and are influenced by the evidence available.

From Beliefs to Probability Distributions

• Using Distributions in Estimates: Probability distributions express historians' degrees of belief about uncertain quantities.

• Identifying Ranges: Establishing minimum and maximum population estimates to provide broader context.

• Types of Distributions: Various distributions (triangle, PERT) help represent uncertainty more accurately.

Monte Carlo Simulation in Historical Context

• Technique Overview: Aggregates uncertainties by mathematically combining input probabilities to assess output variables.

• Practical Utility: Enables historians to manage multiple uncertainties and derive distributions for complex estimates.

Sensitivity Analysis and Iteration

• Importance of Sensitivity Analysis: Determines which variables significantly impact uncertainty estimates, leading to more refined probability assessments.

• Iterative Process: Continuous review and refinement of probability distributions as new data emerges are critical.

Conclusion: Emphasizing Subjective Probability

• Value of Subjective Probability: A tool for addressing epistemic uncertainties in historical analysis.

• Clarity in Historical Discourse: Use of formal probabilities encourages clearer communication among historians and advances understanding of ancient demographics.