Chapter 7 Data Integration
7.1 Sample splitter to count insects
Sample Splitter
Some of the designs that I first set up with some of the first things, but the Forest Service used — reverse sequential sampling to drop things out, but in a reverse — see the guy that was eventually, what was the guy, the other fellow that was the heavy hitter for the Forest Service? He eventually came on the department later on. I can’t think of his name.
*Who was at the Forest Service?
Yeah.
*Bill Bedard, CJ?
No.
*Fields Cobb? Carl Huffaker?
He ended up being the head of the department there for a while.
*Bill Waters?
Yeah, Bill Waters, yeah. So Bill Waters back in — was some of the first cuts out of putting a sequential sampling, see if you could reduce the amount of labor put into the sampling aspect actually, interestingly enough. So he was more than interested in reverse sequential sampling — at the time and then with the layout that was symmetric, that maybe analysis of the experiment ever so much easier.
14.1
I’m really curious about what you dug up in terms of bits and pieces of the work that was going on in the modeling effort, especially for Dave Wood and the group.
*Well, I haven’t been able to get too much. What I got, I got the sample splitter stuff so I’ve got all the papers related to the sample splitter, including a copy of Ken Lindahl’s thesis.
Let me ask a question at this point. Does the sample splitter include the stuff – statistics, and I also as I remember ran some tests on them to make sure that the sample splitter was working correctly, and even though the tests were not significant with the normal distribution test, they were with the – statistic. And this was something that happened a number of other times when we looked at fields called the data for a whole bunch of things, especially –. So is that data available, and is that what you found?
*Yeah, I’ve got all that data. It’s all on sheets so it’s all on paper.
Were the plots, did they still have the plots?
*Yes.
Wonderful.
*Yeah, so I’ve got all the plots and I’ve got all of Paul Tilden’s stuff, Fields Cobb, whatever the data analysis. Now there’s a lot of it to sort through. There’s huge, you know, a big format blue binders with the 11 x 17 paper, computer paper. It’s all dusty but I’ve got it. So the data is there and then the work that Ken Lindahl did on the sample and the bias and the sample splitter is all there in his thesis. That’s the main stuff that I’ve been able to pull together. Don Dahlsten allegedly has some other material and Bob Luck is supposed to contact him but I haven’t heard anything directly on that yet. So that’s still in limbo, and that may be where the Bayesian stuff is, in Don Dahlsten’s office.
Yeah, may very well be. Well that’s very encouraging.
*Yeah, Dave Wood sent me about 75 pounds of stuff.
Wonderful. So maybe his final statement at the end of that application and the data will be analyzed will finally come true.
*And he would like that, he would like that. So I’ll probably look at the sample splitter stuff this summer. I’ve got it all in one place.
Well then I really have to, two pieces of the, the sample splitter stuff, and part of that it seemed to me I was beginning to do the work that the first estimate said that the math likelihood estimator of the reverse sampling technique was just a simple ratio.
*Right.
But if you went to a traditional type of mean and variance type of estimator, the one – direct, it was a messy expression that I was in the first part of unraveling the plots on the APL work on the plotter. Did that ever show, did that stuff show up?
*Yeah. The plots, well I think that’s there. There are certainly plots that I did that, they’re sort of wavy lines that show that the bias is largest right near to the end. I recognize some plots that I did over 20 years ago.
Wonderful. Then my other question, it seemed that there were some pieces of Ken Lindall’s work that were used finishing up his dissertation. That work, Dave also sent me copies of that, but I had the impression that that piece had gone back to pure – theory with no number type of – relationship. Am I right on that?
*I think you’re right on that. I started to look through Ken’s thesis but it’s real hard to go through it because he’s got titles like Introduction, Methods, Theory. I mean it’s hard to tell what section is what, so I just sort of flipped through it.
As far as you could tell right off the top, it was – theory, – theory with no –. Even say a log normal which we were using – estimator. Now what am I trying to remember? The – and it’s a generalization that the — quotient is a multivariate. Is that right? Am I pulling that out of the – OK?
*That sounds right.
And with the multivariate, then it was basically sort of an exact counting function for numbers that would run between 0 and N, with N being a very finite number in mathematical things, and minus numbers being total garbage in terms of making sense in terms of that. So although the physical systems sometimes – make sense, in this particular case it made no sense at all, and also because of the number of pieces involved, they were being sampled by Don Dahlsten and you got some incredible number of zeroes. By far the most common value that you would get would be zero. Is that all – seem reasonable? – 20 years ago with the first –?
*Yeah, I mean it’s, you know, talking about counting processes where you have lots of zeroes, I mean it’s familiar to me in a general way. I’m not familiar with the specifics because I wasn’t involved specifically with the counts and with Don Dahlsten. I was involved more with the.
14.4
My question was that it seems when we were trying to design ways of gathering data, counting data across many, many different species, with highly variable numbers, both off traps and off of other equipment, it seemed like no matter if the samples were bored out of trees and reared, it was all over the map. – also. So no matter where I looked, a number of species highly variable and in some cases like the counting stuff or the traps, the numbers could be gigantic sometimes. Huge numbers in the traps because of the size and effectiveness and at other times they caught very little and it could be all over the map, say – hosts of the tree or related insects say that Don Dahlsten was studying.
At the time we looked at just some sort of – for sequential sampling technique to cut back on the work. It turned out it was far easier to subdivide things until everything had gone to zero or some arbitrary number of times. It was a higher power that would assure that the remaining – would be –. With the two underlying assumptions, and then it would –.
At that time, I think I – one professor and a few of his students were doing reverse sequential sampling 20 years ago. That was what I was going to try to see if I could get any help from him to get things up and going but pretty much, and yet at that time who was the person that was, the name won’t pop into my head right now. He was the head of the whole program there at the Forest Service and then he moved over to the college of natural resources later as a department head, Waters.
*Yeah, Bill Waters.
Bill Waters, thank you, Bill Waters. Some days I have a very hard time pulling these back. As I remember Bill Waters, oddly enough his specialty was sequential sampling and its application to forest service problems. So here was this reverse sequential sampling technique, so my other question is where has that gone? Has anybody picked up on reverse sequential sampling? Is it a big deal, a huge deal, or what kind of thing?
*I haven’t checked the literature. I know that.
Or is that stuff that he did pretty much unique? And it still hasn’t followed up?
*Yeah, the one thing that I can think that’s related that I know of is a dilution plating where people are looking for bacteria and they’ll take 10-fold dilutions and then draw up plates and they’ll have a series of different series on a 10-fold dilution. It’s related but it’s not the same thing.
Yeah, and I could imagine that, looking under a stereo microscope or a – microscope, to estimate the area of growth of different things. The area estimation problem and mechanic problem underneath it. Thank you very much for picking that one up, but I’m quite curious.
*Yeah, they now have Petri dishes that have covers which have etched into them grids and the grids have different scales. There will be a large grid and then a part of it will be made as a small grid so you can count depending on the kind of problem. So that’s used in certain fields. I haven’t actually looked at that literature yet but I know people who can help me find that out.
OK, so that’s why I wanted to throw some things out that way because the follow-up on this is that the basically the thing for Dave’s stuff was all based on reverse sequential sampling techniques in terms of gathering the data and then setting up for data analysis. And we also read into some problems right at the first, with the sample not being ideally distributed and we were pretty fortunate that we ran a lot of test samples initially courtesy of, who’s the fellow there that did so much of the mechanical design? Can you think of his name?
*At the forest service?
No, he worked pretty much directly for Dave and Don Dahlsten designing equipment?
*Not Paul Tilden?
No, somebody else. He was not a help person, no he was a person involved in mechanical stuff. He was the one that did all the drawing of the decreasing stuff after my suggestion of using decreasing technique that was used industrial decreasing parts of stuff. It turned out that it did solve the problem and after that it didn’t tear things apart like blowing, high temperature, high pressure kerosene on the stuff to clean it which really shredded stuff. You came out the other side without being able to tell which piece was what.
*Count the number of legs.
Yeah. I can just see you trying to pair up the right head with the thorax with the right abdomen, huh? It was incredible. So there had to be some way of doing that that was a lot gentler and yet would get at the incredible design into stickiness and stick-to-it-tiveness of that, what do they call that – you did today? Making these trails of stuff that – because it was so sticky and so insoluble.
*Stick-em? I don’t remember.
Any way, at any rate, so we ended up with kind of a bear of a problem to solve there. It took a lot of testing. They had to go on also to resolve techniques that would really work correctly. There was a lot of other testing that was done on natural subsampling and other things by hand-picking area and then going back. Those were the ones that Don Dahlsten worked with because that area, he was interested in – species – samples that weren’t good enough. Actually put them into – collection of that stuff. So that was a little more tidbit of history. The math was interacting with experimental design. I guess that those are the big hanging ones that I was curious about. It also – 20 years ago.
18.1
It’s neat to see you and it’s neat to go on to this stuff again and am really intrigued about a number of things that I’ve been thinking about. First of all, did you ever – at Ken Lindahl’s work which I thought was just pure linear theory with no use of easier quad summation to – like the – normal or gamma function.
*I have the material but I have not had a chance to look at it yet.
But this is a really quick cursory glance, you didn’t, it looked like just classic normal.
*Yeah.
And no simplifying or computer simplifying assumptions that would make it easier to computer, a real life computer.
*No.
20.11
Ok, another question. Did you ever go back in Ken Lindahl’s paper, and is it straight linear theory with no gamma function or – normal in it?
*I haven’t gone back to that. I have it but I haven’t gone back to it.
In the word process these days, couldn’t you just reverse it? Isn’t that in a hardware form? I mean word processing form you could get from Dave?
*Oh, I have a copy of it.
Yeah, but I mean as an electronic copy.
*No, just paper.
Whoa. Get an electronic copy. Do you realize how fast you could do the job with an electronic copy?
*Yeah.
And you’re still not sure? What you need is an electronic copy. It would just save you all kinds of time.
*Well, I’ll see if I can get that.
So why don’t you get an electronic copy of Ken Lindahl’s dissertation? It’s interesting I like to file things in the –. Use that as your basis to do all further work. And that way you can use a word processor the whole damn thing in a few moments –. How many hits do you get per normal distribution? How many hits do you get – and so on. And you get – at all for – normal, you’re going to have to allow for gamma functions. I’d be very curious.
But don’t do a thing until you got an electronic copy. Also this would be another illustration of – chance to use it, society’s going to go to electronic eventually. So that’s another matter.
– what he thought should be done and where he should go and I basically said that, I remembered this – what I just described to you and as a result also – the data and the data because the maximum in most of these levels were small, very small or zero. Lots of zero over all the – sample on the things, on the different traps and stuff – traps and all that junk. Lots of zeroes – small so the maximum – probably is the most reasonable estimator and that was just a part from the thing as I remember for the reverse sampling system that we were using.
So as I remember, for that reverse sequential sampling system that oddly enough – always picked up on easier it looks like, weirdly enough. Not to any degree, because a certain –, whole lot easier than to just do, force the other direction. And the thing is that – as I remember, maximum likelihood estimator just dropped way off of the simple proportions. Is that right?
*Yeah. But then it’s biased and then it’s a biased direction.
If you want the first and second moment.
*Yeah, then you could do some biased direction.
And that’s what I was trying to calculate there with – with the biased – for that. That was the last program I was working on in APL too.
*Yeah, the biased correction is in Ken’s thesis.
Oh, good.
*So he did that.
*When we first started using that.
20.13
And the thing is that Dave should have scanned anyway. If it hasn’t been done, have him scan it. It’s become trivial now. Have him scan it. Also the whole statistic society is going to have to face a little bit of this too very soon. You – on the problem of this sort of thing on the internet –. But you might very well ask Dave to, if you don’t have an electronic one. Please ask him if he has an electronic form of Ken Lindahl’s thesis. And if he doesn’t, please to have it scanned because he always has the resources to do that because that thesis work was his own direction now. But it should be electronically scanned and that costs zip money these days. The only one niche, it will cost you about $50 for any – version of things to make your computer to be able to listen to you and transcribe stuff by just having you talk. So it’s only – for not having – in the other direction –. But again, please contact Dave.
*I’ll do that.
About that Ken Lindahl thesis. Have him send you the electronic copy of it before you do anything.
*Yeah.
And if he doesn’t have one available – you need to be in that form anyway. How’s he going to manipulate it – publish – paper, there’s no way that he can’t have an electronic form. You don’t type things from scratch.
*I’m sure Ken has an electronic copy somewhere so I can go back to Ken on that.
So that’s what I would. So find an electronic copy from Ken or Dave Wood.
*So other stuff bubbling up here on that modeling.
Well, it really struck me that – the other core pieces of this thing – method that we were going to use was unbiased and wouldn’t skew results in way or another, and to the – I dug into, it seemed – is we had valid number generators and everything like that that would –. The transformations that were bearing on the mathematics weren’t screwed up because we did find some bug in the thing. Then we had to go back and refix only to find that Los – has a serious bug in their random number generators they have never fixed to this day. – remember that graphic program?
*Yeah.
So that’s the impression of the, that’s the amount of politicking you need to – idea because the whole system, you don’t need much – and the Monte Carlo converts it incredibly fast initially – doesn’t diverge for shit, if you want 5 positions, ok? But boy, does it convert fast at first, so the very kind of place that we need fast convergence, it’s ideal for imprecise systems. So it seemed to me that that turned out to also be on bias – which he hadn’t – and all this type of – describing like – random number generated out for underpinning it and that was how you’d biased it.
You’re going to assume that certain mathematics –, mathematics is indeed –, you can’t put in bad – and somehow have it –. And so of course that’s the one we kept having to go back and look –. Gee, will this work, will that work? I’d – because it’s, but on the other hand it seems that it’s a rapidly conversion, estimator, but boy if you – two decimals, but if you need three positions, position, third place for your –, you’re also doing heavy duty computation. And if you need 6 or 7 places, whoa. You’re going to have a super computer going all through the –. So it seems to me also that – was absolutely ideally suited for our purpose, our system was inherently imprecise. Ok, that was another thing I wanted to throw out.
*Yeah, I don’t think we had talked about that before.
But also, I also want to throw out some examples of places that we had looked a long time ago and in turn there were some real problems and they had never corrected them. – that problem still is on the random number generator, what 25 years later?
*At least. Yeah, it was almost exactly 25 years ago.
Quarter of a century ago.
*Yeah, right.
Quarter of a century – point it out to them? Nope. It’s still on after a quarter of a century. So that is another issue –.
21.2
Again, please – for electronic version on Ken Lindahl’s thesis. It doesn’t exactly – today.
*Well, that can be arranged. That can be arranged.
But at any rate, please, please, please do that first before you even think of – out. Otherwise it’s a waste of your time.
*Oh yeah, I’m not going to just type it in.
You’ve already taken the first couple of –.