metropSB: Metropolis-Szymura-Barton algorithm

Description

Stochastic global optimization using the Metropolis-Szymura-Barton algorithm. New parameters are chosen from a uniform candidate distribution with an adaptively tuned scale, and accepted or rejected according to a Metropolis rule.

Usage

metropSB(fn, start, deltap = NULL, scale = 1, rptfreq = -1, acceptscale
= 1.01, rejectscale = 0.99, nmax = 10000,
retvals = FALSE, retfreq = 100, verbose = FALSE, ...)

Arguments

Objective function, taking a vector of parameters as its first argument. The function is minimized, so it should be a negative log-likelihood or a negative log-posterior density.

start

Vector of starting values

deltap

Starting jump size; half-width of uniform distribution

scale

Scaling factor for acceptance

rptfreq

Frequency for reporting interim results (

acceptscale

Amount to inflate candidate distribution if last jump was accepted

rejectscale

Amount to shrink candidate distribution if last jump was rejected

nmax

Number of iterations

retvals

Return detailed statistics?

retfreq

Sampling frequency for detailed statistics

verbose

Print status?

...

Other arguments to fn

Value

minimumminimum value achieved
estimateparameters corresponding to minimum
funcallsnumber of function evaluations
If retvals=TRUE:
retvalsmatrix of periodic samples including parameters, jump scale, current value, and minimum achieved value

Details

Metropolis-Szymura-Barton algorithm: given function and starting value, try to find parameters that minimize the function Algorithm: at a given step, 1. pick a new set of parameters, each of which is uniformly distributed in (p[i]-deltap[i],p[i]+deltap[i]) 2. calculate function value at new parameter values 3. if f(new)f(old), accept with probability (exp(-scale*(f(new)-f(old))) 5. if accept, increase all deltap values by acceptscale; if reject, decrease by rejectscale 6. if better than min so far, save function and parameter values 7. if reject, restore old values

References