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