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TL;DR

The initial probability assigned to a hypothesis before observing data, representing prior beliefs or knowledge. In Bayesian analysis, the prior is updated via Bayes' theorem to produce the posterior.

By Valenke Exam Prep Team·Last updated 2026-06-03

Prior Probability

The initial probability assigned to a hypothesis before observing data, representing prior beliefs or knowledge. In Bayesian analysis, the prior is updated via Bayes' theorem to produce the posterior.

Why it matters for interviews

Bayesian reasoning is fundamental to signal processing, portfolio allocation, and market regime detection. Interviewers test whether candidates can correctly specify and update priors.

Definition and Mathematical Foundation

The initial probability assigned to a hypothesis before observing data, representing prior beliefs or knowledge. In Bayesian analysis, the prior is updated via Bayes' theorem to produce the posterior.

Application in Quantitative Finance

Bayesian reasoning is fundamental to signal processing, portfolio allocation, and market regime detection. Interviewers test whether candidates can correctly specify and update priors.

Related Concepts

Bayes' Theorem

Related Terms

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Frequently Asked Questions

How do you choose a prior in practice?▼
Common approaches include: uninformative priors (uniform, Jeffreys), conjugate priors (mathematically convenient), and empirical priors (estimated from historical data). The choice depends on domain knowledge and computational constraints.
What is a conjugate prior?▼
A prior distribution that, when combined with a particular likelihood, produces a posterior in the same distributional family. For example, a Beta prior is conjugate to the Binomial likelihood, yielding a Beta posterior.
Does the choice of prior matter in the long run?▼
With sufficient data, the posterior converges to the truth regardless of the prior (under regularity conditions). This is Bayesian consistency. However, for small samples, the prior can strongly influence results.