metropSB: Metropolis-Szymura-Barton algorithm

In emdbook: Support Functions and Data for "Ecological Models and Data"

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

fn	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 (<0 means no reporting)
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

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 4. 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

Value

minimum	minimum value achieved
estimate	parameters corresponding to minimum
funcalls	number of function evaluations

If retvals=TRUE:

retvals

matrix of periodic samples including parameters, jump scale, current value, and minimum achieved value

Note

If scale=1 the algorithm satisfies MCMC rules, provided that the other properties of the MC (irreducibility and aperiodicity) are satisfied.

Author(s)

Ben Bolker

References

Szymura and Barton (1986) Genetic analysis of a hybrid zone between the fire-bellied toads,Bombina bombina and B. variegata, near Cracow in southern Poland. Evolution 40(6):1141-1159.

See Also

optim, MCMCmetrop1R (MCMCpack package)

emdbook documentation built on July 9, 2023, 6:33 p.m.