Fisher scoring optimizer

Similar to Newton-Raphson but uses expected Fisher information (negative expected Hessian) instead of observed Hessian. More stable for some problems.

Usage

fisher_scoring(loglik_fn, params, max_iter = 100, tol = 1e-08, verbose = 0)

Arguments

loglik_fn

Log-likelihood function

params

List of value objects (initial parameter values)

max_iter

Maximum iterations, default 100

tol

Convergence tolerance, default 1e-8

verbose

Print progress every N iterations (0 for silent)

Value

Same structure as newton_raphson

Details

For regular exponential families, Fisher scoring is equivalent to Newton-Raphson since observed = expected information.

Fisher scoring: θ_n+1 = θ_n + I(θ_n)⁻¹ S(θ_n) where I = -EH (Fisher information) and S = gradient (score).

This implementation uses the observed Hessian as an approximation to the expected Hessian, making it identical to Newton-Raphson. For a true Fisher scoring implementation, one would need to compute EH analytically or via Monte Carlo.