Prior distribution in Bayesian efficient design

[Yuchenj]

Dear professor

I'm now making a Bayesian efficient design and want to ask some questions about defination of prior distribution. Like my code, I have set these variables to follow normal and uniform distributions. How should I implement them as log-normal distributions?

Code: Select all

Design
;alts=Car,PT,UAM
;rows=6
;eff=(mnl,d,mean)
;bdraws=gauss(2,3,3,3,3,2,2,3)
;alg=mfederov(stop=total(10000 iterations))
;con
;model:
U(Car)=ASC_car[(lognormal,0.4,0.764)]+TC[(n,-0.057,0.078)]*Cost_c[10,15,20]+ET_f[(n,-0.043,0.029)]*FFT_c[15,20,25]*PFFT_c[0.15,0.2,0.25]+ET_h[(n,-0.043,0.029)]*HCT_c[35,40,45]*PHCT_c[fcn(1-Car.PFFT_c)]+SL[(n,-0.058,0.029)]*Safety_c[0]/
U(PT)=ASC_PT[(n,0.6,0.973)]+TC*Cost_p[2,5,10]+ET_f*FFT_p[40,45,50]*PFFT_p[0.3,0.4,0.5]+ET_h*HCT_p[55,60,65]*PHCT_p[fcn(1-PT.PFFT_p)]+SL*Safety_p[-1,0,1]/
U(UAM)=TC*Cost_u[25,30,35]+ET_f*FFT_u[10,15,20]*PFFT_u[0.75,0.8,0.85]+ET_h*HCT_u[25,30,35]*PHCT_u[fcn(1-UAM.PFFT_u)]+SL*Safety_u[-1,0,1]+RG[(u,0.309,0.675)]*Guarantee[0,1]+SCP[(n,-0.05,0.5)]*Cancel[2,5,10]
$

Look forward to your reply!

Yuchen jin

[Michiel Bliemer]

Ngene currently only supports normal and uniform distributions for Bayesian priors. If you need a bounded distribution, please use a uniform distribution.

We have been testing lognormal priors and we found that lognormal distributions have heavy tails that may lead to extreme draws resulting in very large D-errors and hence skewed Bayesian D-errors. But we will consider implementing lognormal priors in the future, possibly with the recommendation to use only "median" instead of "mean".

Michiel