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📐 '''Prior distribution''' is a probability distribution that encodes an analyst's beliefs or available information about a parameter before new data is observed, forming a foundational component of [[Definition:Bayesian inference | Bayesian statistical methods]] widely used in insurance [[Definition:Actuarial science | actuarial science]], [[Definition:Catastrophe model | catastrophe modeling]], and [[Definition:Reserving | reserving]]. Unlike frequentist approaches that rely solely on sample data, Bayesian methods begin with a prior and update it with observed evidence to produce a posterior distribution, and the choice of prior can materially influence results — particularly when data is sparse, as is common with low-frequency, high-severity insurance events.

⚙️ In practice, actuaries and modelers select prior distributions based on expert judgment, historical market data, or regulatory guidance. When estimating the [[Definition:Loss development factor (LDF) | loss development]] pattern for a new [[Definition:Line of business | line of business]] — say, a recently launched [[Definition:Cyber insurance | cyber]] product — an insurer may lack sufficient proprietary [[Definition:Claims experience | claims experience]] to calibrate a model from scratch. A prior distribution informed by industry benchmarks, [[Definition:Reinsurance | reinsurer]] studies, or analogous lines allows the model to produce meaningful estimates even with limited data, and these estimates are progressively refined as the insurer's own experience accumulates. Similarly, [[Definition:Catastrophe model | catastrophe modelers]] use priors when incorporating expert seismological or meteorological opinion about tail-event frequencies that have few or no historical precedents. The selection between informative priors (which carry strong initial beliefs) and weakly informative or diffuse priors (which let the data dominate) is a modeling judgment that must be documented and justified, particularly under reporting standards like [[Definition:IFRS 17 | IFRS 17]], which require transparency in the assumptions underlying [[Definition:Actuarial reserve | reserve]] calculations.

💡 Regulators and auditors pay close attention to the role of priors in actuarial work because they introduce subjectivity into otherwise quantitative processes. Under [[Definition:Solvency II | Solvency II]]'s internal model approval standards, European supervisors evaluate whether the priors embedded in an insurer's [[Definition:Internal model | internal capital model]] are reasonable, well-documented, and subject to sensitivity testing. In the United States, the [[Definition:National Association of Insurance Commissioners (NAIC) | NAIC]]'s actuarial standards of practice address the use of professional judgment in setting assumptions — a process closely related to prior selection. For [[Definition:Insurtech | insurtech]] firms leveraging Bayesian machine learning in [[Definition:Underwriting | underwriting]] or [[Definition:Fraud detection | fraud detection]], the prior distribution is not merely an academic concept but a design choice that shapes model behavior from the first policy written, making its calibration a matter of both commercial performance and regulatory defensibility.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Bayesian inference]]
* [[Definition:Actuarial model]]
* [[Definition:Catastrophe model]]
* [[Definition:IFRS 17]]
* [[Definition:Partial identification]]
* [[Definition:Predictive modeling]]
{{Div col end}}

Definition:Prior distribution - Revision history

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