stepsize bug in MCMC

[odunbar]

CalibrateEmulateSample.jl/src/MarkovChainMonteCarlo.jl

Lines 526 to 536 in cb3a97e

	if doubled && halved
	stepsize = 0.75 * stepsize
	doubled = false
	halved = false
	elseif acc_ratio < 0.15
	stepsize = 0.5 * stepsize
	halved = true
	elseif acc_ratio > 0.35
	stepsize = 2.0 * stepsize
	doubled = true
	else

Just noticed that the order of doubled and halved matters here. i.e. if you have a situation where a good step is value 1.5*init_step then the search will do

init_step =>  acc_ratio = 36% => doubled = true
2*init_step => acc_ratio= 13% => halved = true

then the next step is 0.75*(2*init_step) = 1.5*init_step which makes sense.

But if a good step is value is 0.75*init_step then the search will do

init_step =>  acc_ratio = 13% => halved = true
0.5*init_step => acc_ratio= 36% => doubled = true

then the next step will do 0.75*(0.5*init_step) = 0.375*init_step which does not make sense.

likely my fault from previous iteration. Didn't catch it earlier, because as 0.375*step is too small the next iteration will double it to 0.75*init_step so it will usually still find a good value but it's not efficient.

We should include the order dependence.