Quant Toolbox - 23. Maximum likelihood - General formulation
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Quant Toolbox > 23. Maximum likelihood > General Formulation General formulation X random observable variables realized in a data set x • f θ (x) is the likelihood of the data x, where f θ is the joint distribution for the variables X • If H are hidden or latent variables the likelihood reads f θ (x)= Z f θ (x, h)dh (23.3) • The maximum likelihood parameters ˆ θ maximize the likelihood ˆ θ ≡ argmax θ∈Θ {f θ (x)} (23.4) Equivalently, they minimize the surprise - ln f θ (x). ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Feb-01-2017 - Last update
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Transcript of Quant Toolbox - 23. Maximum likelihood - General formulation
Quant Toolbox > 23. Maximum likelihood > General Formulation
General formulation
X random observable variables realized in a data set x
• fθ(x) is the likelihood of the data x, where fθ is the jointdistribution for the variables X
• If H are hidden or latent variables the likelihood reads
fθ (x) =
∫fθ(x,h)dh (23.3)
• The maximum likelihood parameters θ̂ maximize the likelihood
θ̂ ≡ argmaxθ∈Θ{fθ(x)} (23.4)
Equivalently, they minimize the surprise − ln fθ(x).
ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Feb-01-2017 - Last update