fssem1
commented
3 years ago Hi Sara,
In case you're curious, I have continued this conversation with Curry Cunningham (below)
Rich
From: Curry Cunningham cjcunningham@alaska.edu Sent: Tuesday, October 27, 2020 4:41 PM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov Subject: Re: lnalpha.c from Hamachan
That didn’t clarify anything for me either, if I’m being honest.
Also, in my opinion it should apply only to regression (liberalized Ricker) type approaches.
I use a correction even if my model is estimated in normal space and I specify my likelihood in log space.
Stan equivalent:
R_pred = Salphaexp(-BS);
ln(R_obs) ~ normal( ln(R_pred), sigma);
As we discussed on the porch, the other way is to pre-account for the bias correction in the likelihood:
ln(R_obs) ~ normal( ln(R_pred) - ((sigma^2)/2) , sigma);
Which has the effect of reducing the log predicted recruitment, and should, in theory, adjust alpha and beta accordingly.
This approach has been pretty common in marine fisheries stock assessments.
Why that is common practice in the marine assessment world, and not in the salmon world is beyond me.
Methot, R. D., and I. G. Taylor. 2011. Adjusting for bias due to variability of estimated recruitments in fishery assessment models. Canadian Journal of Fisheries and Aquatic Sciences 68:1744-1760.
Maunder, M. N., and R. B. Deriso. 2003. Estimation of recruitment in catch-at-age models. Canadian Journal of Fisheries and Aquatic Sciences 60:1204-1216.
Aldrin, M., S. Aanes, and S. Subbey. 2019. Comments on incongruous formulations in the SAM (state-space assessment model) model and consequences for fish stock assessment. Fisheries Research 210:224-227.
On Oct 27, 2020, at 1:40 PM, Brenner, Richard E (DFG) richard.brenner@alaska.gov wrote:
Again, I'm not entirely clear about his point on this discussion.
From: Hamazaki, Hamachan (DFG) toshihide.hamazaki@alaska.gov Sent: Wednesday, October 7, 2020 2:30 PM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov Cc: Munro, Andrew R (DFG) andrew.munro@alaska.gov Subject: RE: Whether to lnalpha.c
Yes, I read those, and it starts from an introduction of Regression analyses is the traditional approach to fit and estimate Ricker model parameters….. and goes on lognormal error and bias correction… Yes, lognormal bias correction is appropriated to get mean expectation of lognormal error model, GIVEN that parameters are estimated by regression method.
Toshihide "Hamachan" Hamazaki, 濱崎俊秀PhD Alaska Department of Fish and Game: アラスカ州漁業狩猟局 Division of Commercial Fisheries: 商業漁業部 333 Raspberry Rd. Anchorage, AK 99518 Phone: (907)267-2158 Cell: (907)440-9934
From: Brenner, Richard E (DFG) richard.brenner@alaska.gov Sent: Wednesday, October 7, 2020 12:42 PM To: Hamazaki, Hamachan (DFG) toshihide.hamazaki@alaska.gov Cc: Munro, Andrew R (DFG) andrew.munro@alaska.gov Subject: RE: Whether to lnalpha.c
Thanks for sending these, Hamachan.
I have been looking at Fleischman’s 2013 manuscript and his justification for using lnalpha.c and I keep re-reading the text surrounding equation 22, but I’m still not sure that I understand whether, in his opinion, one only needs to use the correction if using mean values for parameter estimates, or if the correction is also needed if we use the median values, which I believe that we have been (50%):
“Equations 14–19 and 21 are germane to “median” production R and “median” yield Y. Because we assume that production condi- tional on spawning abundance has a lognormal distribution, which is skewed, this differs from “mean”, or expected produc- tion. To obtain inference about expected production and yield, ␣= must be substituted for ␣ in eqs. 14–19 and 21, where
(22) ln(␣?) ⫽ ln(␣) ⫹ 2(1 ⫺ ?2)
corrects for the difference between the median and the mean of a lognormal error distribution from an AR(1) process (Pacific Salmon Commission 1999; Parken et al. 2006). The optimal yield plots in Figs. 6 and 7 describe expected yield, obtained using the correction in eq. 22. Because there is no equivalent correction for the random walk model, Fig. S5 in the online supplement1 is based on”
Rich
From: Hamazaki, Hamachan (DFG) toshihide.hamazaki@alaska.gov Sent: Wednesday, October 7, 2020 12:06 PM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov Cc: Munro, Andrew R (DFG) andrew.munro@alaska.gov Subject: Whether to lnalpha.c
Just reviewing several papers: Sue & Peterman (2007) used Bayesian SS and calculated Smsy with lnalpa Cowichan River Fall Chinook BEG (2005) used lnalpha Lassard et al (2007) used lnalpha (B-H model)
Actually, I am not finding any examples (possible Fleishman) of using lnalpha.c
Toshihide "Hamachan" Hamazaki, 濱崎俊秀PhD Alaska Department of Fish and Game: アラスカ州漁業狩猟局 Division of Commercial Fisheries: 商業漁業部 333 Raspberry Rd. Anchorage, AK 99518 Phone: (907)267-2158 Cell: (907)440-9934
Curry J. Cunningham Assistant Professor College of Fisheries and Ocean Sciences University of Alaska Fairbanks 17101 Point Lena Loop Road Juneau, AK 99801 Website: currycunningham.com/ Twitter: @CurryCunningham
OK – thanks for the clarification.
Steve
From: Miller, Sara E (DFG) sara.miller@alaska.gov Sent: Monday, May 24, 2021 11:50 AM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov; Heinl, Steve (DFG) steve.heinl@alaska.gov Subject: RE: transformation and bias
I am in agreement. With the frequentist, you still need to use the bias correction. With the Bayesian, you don’t.
From: Brenner, Richard E (DFG) richard.brenner@alaska.gov Sent: Monday, May 24, 2021 11:38 AM To: Heinl, Steve (DFG) steve.heinl@alaska.gov; Miller, Sara E (DFG) sara.miller@alaska.gov Subject: RE: transformation and bias
Hi Steve,
At one point I knew the answer about the direction that using/not using pushed an estimate of e.g., Smsy but it’s not coming to me at the moment. But, when conducing an analysis in a spreadsheet, I believe that you SHOULD use the lnalpha.c correction.
I suspect that this topic is going to be discussed a good bit more in the future as we re-examine our previous escapement goals with the Board cycle.
Rich
From: Heinl, Steve (DFG) steve.heinl@alaska.gov Sent: Monday, May 24, 2021 11:09 AM To: Miller, Sara E (DFG) sara.miller@alaska.gov; Brenner, Richard E (DFG) richard.brenner@alaska.gov Subject: RE: transformation and bias
Thanks for this heads up, Sara. I read the attached paper and get the essence (though it’s quite technical for me). If I’m understanding this, the bias correction would have a slight positive bias – and – the retransformation bias is better handled by conducting the stock-recruit analysis in a Bayesian framework (in which the bias correction would not be applied). It will be interesting to know the effect that not using the bias correction would have had on previous EG analyses. Dumb question: if one is conducting simple linear regression in a spreadsheet (the “frequentist” approach, like the Ricker Estimation Lab spreadsheets we’ve been given at escapement goal workshops), is it also incorrect to apply the bias correction? That’s what I’m getting from Xinxian’s email.
Steve
P.S. – gotta love Xinxian’s email! P.P.S. – I was also going to ask about Hamachan’s app, but Rich just answered that question.
From: Miller, Sara E (DFG) sara.miller@alaska.gov Sent: Monday, May 24, 2021 9:41 AM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov Cc: Heinl, Steve (DFG) steve.heinl@alaska.gov Subject: RE: transformation and bias
Rich- Thanks for getting to the bottom of this. Moving forward, we will not use the bias correction. We will have to figure out how to word the next EGs to explain the change in equations. I think we can use some of the references from our email exchanges to explain the change. I’m not sure this would have changed the Taku analysis as Bob Clark was on the Fleischman paper and the ‘sport fish’ side of opinion. I guess we will never know.
Steve- All the state space EGs that I have co-authored with you have used the bias correction based on work by Fleischman et al. (specifically his main CJFAS paper that we referenced). Moving forward, we will not use the bias correction and we (or I) will have to explain that some of the change in the EGs could be because of not using the bias correction. We can deal with the wording then. Rich and I (mainly Rich) have been talking to biometricians across the state to find the answer. As we have support now from Xinxian and Hamachan, I think it is a needed change.
Sara
From: Brenner, Richard E (DFG) richard.brenner@alaska.gov Sent: Monday, May 24, 2021 8:08 AM To: Miller, Sara E (DFG) sara.miller@alaska.gov Subject: FW: transformation and bias
FYI, Xinxian and Hamachan say that the bias correction parameter (lnalpha.c) that we have used in our spawner-recruitment analyses (code borrowed from Steve Fleischman) is unnecessary/wrong. Xinxian’s explanation is below. I asked Jane Sullivan about this and she is of the same opinion.
Rich
From: Zhang, Xinxian (DFG) xinxian.zhang@alaska.gov Sent: Sunday, May 23, 2021 3:56 PM To: Brenner, Richard E (DFG) richard.brenner@alaska.gov Subject: RE: transformation and bias
Hi Rich,
The simple answer to your question is NO. In the Bayesian approach the bias-correction factor should not be used.
There is a log re-transformation bias, which in the frequentist (no-Bayesian) approach can be adjusted by lnalpha.c = lnalpha + 0.5 sigma^2. Note here lnalpha is the mean. But it is wrong to use it to adjust the entire posterior of lnalpha, rather than its mean. That is exactly what “our Bayesian spawner-recruit analyses” have been done.
The re-transformation bias problem is resolved naturally in the Bayesian framework. It is done by exponentiating the entire posterior distribution, not just the mean. For example, we have a set of x, and log-transformation: y=ln(x); re-transformation: z=exp(y) = x. exp(mean of y) is a biased estimate for the mean of x; but mean of z is not. After re-transformation of the entire data set y, we have z=x.
Using that kind of correction in ADFG Bayesian spawner-recruit analyses was originally from Sport Fish. I made argument with them almost a decade ago when I worked for Region II. I also asked Region II not to do so at that time. Well, I am glad you are aware of the issue now (like a “cold case” ^_^).
Xinxian
From: Brenner, Richard E (DFG) richard.brenner@alaska.gov Sent: Friday, May 21, 2021 10:40 AM To: Zhang, Xinxian (DFG) xinxian.zhang@alaska.gov Subject: transformation and bias
Hi Xinxian,
I don’t remember if I have already sent this article to you, but this pertains to the lnapha.c correction that is applied to our Bayesian spawner-recruit analyses. Given the statements in this manuscript, my big question is whether or not the lnalpha.c correction is necessary?
Take care, Rich
Rich Brenner, PhD
Salmon Stock Assessment Biologist Alaska Department of Fish and Game Division of Commercial Fisheries PO BOX 115526 Juneau, AK 99811-5526 office: 907-465-6154 e-mail: richard.brenner@alaska.gov