σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Skills›Bayesian Inference
B

Bayesian Inference Skill

LiveStart here

A back-test gives you one number, but how sure should you be of it? Bayesian inference answers with a whole range of plausible values instead of a single guess. This skill explains it in plain steps, with short checks (numbers you compute, steps you order, concepts you match) and finance examples: how a prior belief and a few days of results combine, why a strategy that won 7 days out of 10 is not yet proven, how to read a credible interval and make a decision from it, how a sampler explores a posterior that has no formula, why the average returns of many stocks should be pulled toward each other, and how to compare two models fairly. The capstone is a code lab where you write the sampler and the shrinkage yourself and use them on real stock returns.

3 modules10 graded labs~10 hoursIntermediate → Advanced
Start skill

Prerequisites

Probability is expected (conditional probability, common distributions) and basic statistics helps. No Bayesian background is needed.

  • PProbability
  • SStatistics

Syllabus

10 topics · open any topic, in any order
  1. 1Priors likelihoods and posteriorsNot started50 minStart
  2. 2Conjugate models: beta-binomial and normalNot started50 minStart
  3. 3Posterior intervals and decisionsNot started45 minStart
  4. 4Bayesian linear regressionNot started1 hrStart
  1. 5Metropolis-Hastings from scratchNot started1 hr 5 minStart
  2. 6Gibbs samplingNot started55 minStart
  1. 7Hierarchical models and shrinkageNot started1 hrStart
  2. 8Model comparison and Bayes factorsNot started50 minStart
  3. 9Bayesian updating of strategy performanceNot started55 minStart
  4. 10Capstone: Bayesian Sharpe ratio and shrinkage on real stocksNot started1 hr 30 minStart

Completion

Pass all 10 labs with a score of 70+ to complete the skill and earn the Bayesian inference badge on your profile.

0 / 100%

Prerequisites

Probability is expected (conditional probability, common distributions) and basic statistics helps. No Bayesian background is needed.

  • PProbability
  • SStatistics

Tools you'll use

PythonNumPypandaspytest

What you'll learn

  • Combine a prior with data to get a posterior, and say in plain words what each part means
  • Use conjugate models and Bayesian regression, read credible intervals and make decisions from them
  • Write Metropolis-Hastings and Gibbs samplers and check that a chain has explored the posterior
  • Shrink noisy estimates with a hierarchical model and compare models with Bayes factors
  • Put honest error bars on a Sharpe ratio and test on real returns whether shrinkage predicts better
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All roadmapsAll skillsPython skillC++ skillSoonOxCaml skillSoonMarket Structure skillCalculus skillLinear Algebra skillProbability skillStatistics skillMatrix Decompositions skillOptimization skillTime Series skillStochastic Calculus skillBayesian Inference skill
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