Help - Search - Members - Calendar
Full Version: Bigfoot as a Fermi problem
Bigfoot Forums > Bigfoot/Sasquatch Discussion > General Discussion
Judaculla
How can we know the weight of a sasquatch if we've never put one on a scale?
How can anyone estimate the population of sasquatch in North America?
How can we know anything about sasquatch at all?

These are questions that really don't bother me, because I think that we already know a lot about sasquatch, not a little. The reason is that any sasquatch question is almost automatically a Fermi question or problem.

Fermi was a famous physicist who would ask outlandish questions in class that were impossible to know the exact answer for. But, he required his students to answer them anyway. One perhaps apocryphal question from him was, "How many piano tuners are in Chicago?" Given the knowledge they currently had in their heads, students were told to devise a method to estimate the answer.

What's amazing is that for almost all Fermi problems, with some contemplation, you do have the power to generate an answer with a fair degree of confidence in the level of its precision.

I was given Fermi problems when I went to school at UT - Austin. There's a good discussion of them at this website, which happens to be from my former physics professor. Read it over and see how much you think is applicable to sasquatch questions.

Fermi problems
VernF
Well, in a very general sense, I think this is the right idea, Jud. Have you read Farenbach's book? There are biometric formulae which can provide some assistance in estimating body mass. I think population numbers are far more problematic, but there are some ideas floating around on minimum breeding population sizes, there are well known numerical relationships between prey and predator species, and since caloric requirements can be estimated from the estimate of body mass, one can at least make a semi-educated estimate of the maximum carrying capacity of available habitat. The latter two relationships very much depend upon ones assessment of dietary habits, though.
Judaculla
I did read Fahrenbach's Cryptozoology article avalaible on-line at BFRO. If I remember the weight example, he showed that there was a known and fairly tight relationship between primate chest circumfrence and weight, no matter what primate species we are talking about. So, after estimating Patty's chest circumfrence, the weight could be inferred.

Wildlife biology is not my specialty by any means. I'm in business forecasting. The point has to do more with how knowledge is generated when a precise number is unknown. Many things don't have to be directly measured to get a reasonably good estimate that is a great deal better than just a pure guess.

HM recently provided an estimation example in the measuring of deer population in a given area by examining number of droppings. Knowing what the on average rate is for deer generating droppings, you can estimate how many are in the area. If the area sampled is representative of a much larger habitat from which the observations were taken, then you can say the densities are approximately the same and multiply out your sample area to get the whole area. That provides your estimate. It's immensely more practical than trying to count every last deer.

I can imagine that estimating populations for a very thinly distributed population of sasquatch would be extremely difficult, with different methods generating different answers. What I would like to see are the quantified relationships that are used in any method to generate those estimates. That's more interesting to me than the answer itself-how the answer was arrived at. I also think that's what Fermi was more interested in regarding his questions.
VernF
I can tell you that in the real world wildlife censuses are typically done based on sample data gleaned from direct observation, which is then statistically manipulated to provide an estimate for the relevant geographic area. The problem is that the algorithms are highly species specific, and they are derived from known information about the species.

With some it is really quite easy. Kirtland's warbler, for example, is a species which is tailor made for direct census. Except for the occasional nesting season stray which shows up in Ontario, Wisconsin or the Upper Peninsula, the whole worldwide population of 2000-3000 gathers every spring in a compact Jack pine forest in East central Michigan. Females are almost impossible to spot, but males are territorial and for a few weeks they are quite vocal. Count the singing males, multiply by two, and you can estimate the population probably within plus 1 percent (to account for strays)/minus 3 percent (to account for unmated males).

The ubiquitous white tail, on the other hand, is typically censused by statistical methods. But even with a species so well known and intensively managed for such a long time, different (presumably appropriate) algorithms can yield results which vary by 200-300 percent.

The smaller the population, the larger the range, the more reclusive the species, the remoter its territory, and the less which is known the species, the more difficult it becomes to census, as you would conclude intuitively. Where all these factors come together, statistical methods just don't work very well, and it usually becomes more of an art form than a mathmatical exercise. Take the wolverine, for example, which I think shares all these characteristics. Though there have been intensive efforts to learn more about the species recently in light of its obviously diminishing range, I don't think anyone can offer a very confident estimate of its North American population. I think that sasquatch falls into the same category. I hope this doesn't sound evasive. I suppose it is just a long way of saying that while there may be some ingenious way to get a handle on the population, I don't know it, and I wouldn't have much confidence in it either.
RogerKni
Here's an item I posted in Oct. on scat-hunting dogs. They could be trained to hunt for BF scat using a sample of suspected BF poop. Then maybe BF population estimates could be made based on scat finds within demarcated areas, in the same way as deer populations are estimated, as described by HM. (I realize this may not work as well as it does for deer, because there are more unknowns with BF, but it would at least be a start.)

Here’s an interesting story; apparently dogs can be trained to locate poop in the field, and to indicate by their posture what animal the poop came from. The people involved in this work should be alerted to keep an open mind about the possibility of their dogs encountering BF poop, since they're working in WA state.

"Scat Dogs" Sniff Out Endangered Species Feces Maryann Mott for National Geographic News October 1, 2003 at: http://news.nationalgeographic.com/news/20...1_scatdogs.html
Judaculla
Thanks for the reply, Vern! I'm guessing that you are a wildlife biologist. If not, you missed your calling!

The wolverine example is great. I wonder how those who have tried to estimate the wolverine population have gone about it.

I've read the BFRO FAQ on estimates for a sasquatch population in North America. Here it is for those who haven't seen it.

BFRO Sasquatch population estimates

The estimate is 2K to 6K. I have read the layman's version of the theory behind generating a sasquatch estimate. What I want to know is if there is a statistical model behind it. I work with multivariate regression analyses regularly, and would like to see if there are any quantifiable variables with any degree of predictive power (if you could ever measure actuals!). Lower and upper bounds suggest slightly different methods to me.

But, as you said, if the estimate is more art than science given the paucity of observations, then maybe there is nothing to provide any statistical rigor. If the models are highly species-specific, there wouldn't be an existing model that could be applied to sasquatch.
goldie
Vern your reply was just the point I was trying to make regarding the lack of credibilty that I put to census data regarding animal counts.

QUOTE
Take the wolverine, for example, which I think shares all these characteristics. Though there have been intensive efforts to learn more about the species recently in light of its obviously diminishing range, I don't think anyone can offer a very confident estimate of its North American population. I think that sasquatch falls into the same category. I hope this doesn't sound evasive. I suppose it is just a long way of saying that while there may be some ingenious way to get a handle on the population, I don't know it, and I wouldn't have much confidence in it either.


As for wolverines, that is an interesting animal indeed. My daughter and her cousin were attacked when they were playing out in their grandmothers backyard when they were younger. The wolverine came after them but the bright sun blinded him so they got away. We spent some time trying to figure out what the animal was and finally found a picture that both girls independently verified was the animal that chased them. Now my mom lives outside of Portland in a small town on the way to the coast. Wolverines are never supposed to be found anywhere west of the cascade mountain ranges. This is why no one believed that the girls could have been chased by a wolverine. I also found the scat of this animal in the back yard and it was further identified when my daughter went into a museum filled with thousands of stuffed animals and she picked out the wolverine as the one that chased her.

In my research of this animal it is said that trappers can go their entire lifetime in the woods trapping animals and never see a wolverine. That is how elusive they are. Very much like our bigfoot. Yet do you know how they know that they are around? By their footprints. Quite ironic isn't it.

It just seems to me that all the fancy math in the world will not help unless the animals behavior and ability to be found at all times is very constant. goldie
VernF
Jud, I am not a biologist at all. I just happen to have enough knowledge to be danderous about a few topics which fascinate me.

And Goldie, your statement does, indeed, fascinate me. Are you really confident in your identification? If so, that critter was WAY out of range, and these are very civilization averse creatures. It would be significant if a wolverine really was there, and I would suggest that you report it to state wildlife officials but for the fact that I'm afraid you wouldn't be taken seriously.
VernF
QUOTE(Judaculla @ Jan 9 2004, 05:58 PM)
  I work with multivariate regression analyses regularly, and would like to see if there are any quantifiable variables with any degree of predictive power (if you could ever measure actuals!).  Lower and upper bounds suggest slightly different methods to me.

QUOTE


Your mention of MR analyses reminds me that I have pondered from time to time whether anything useful could be ascertained from such a process. My conclusion (a hasty one, I grant you) has always been that the data reliability just isn't there for the most part. As you know, a MR analysis based on bad data won't tell you much--it is a classic GIGO kind of analysis.

As I see it, sasquatch data consists of (1) good data and; (2) mistaken subjective impressions and; (3) hoaxes and lies, all hopelessly comingled together. Absent any way to reliably separate out (2) and (3), no mathmatical manipulation will have much value unless the bad data is irrelevant to the conclusions. This is why I was so impressed with Farenbach's footprint length-distribution analysis. You will recall that the result was the bell curve one would expect in nature. Now, since footprint length is an objective measured quantity, item (2) above, the mistaken subjective impressions, is automatically eliminated from our database. And unless one is willing to conclude that hoaxers are working in concert to yield footprint lengths which conform to a normal distribution, one can infer that hoaxes are not a statistically significant proportion of the database. Very ingenious idea, I thought, and a result which helps boost the credibility of the footprint evidence. Perhaps a math guy like you could come up with a few similar ideas for analyses where the bad data would be irrelevant!
Judaculla
I liked Fahrenbach's approach to the footprint dimension data, but I'm not convinced by it. I thought he left out an easy to generate control.

Recruit 40 or 50 people and have them each draw or construct a BF track. I don't mean a big group project. I mean get one person in a room by themselves, and do that 40 or 50 times. Give them artistic supplies, rulers, sizes of paper or foam that range from small sheets to very large butcher paper. Tell them they can use any of the materials available to them. Make sure there are no left over patterns or scraps when you get the next person.

If you did the same analysis on the constructed tracks as Fahrenbach did for the casts, I'll bet you wouldn't get a distribution with random peaks. I bet it would look normally distributed. But, then you could perform a t-test (an inferential statistical test to tell if two distributions are significantly different based on their means and variance) to see if you're "true" cast data holds up.

An analysis of variance was performed by colleagues of John Green with the data in AAU. He calls it "the computer study" in his book. But, he didn't have enough observations to really say anything.

There are lots of things you can do to clean up data. Factor analysis, reliability testing comparing subgroups of data, etc. But, if you throw too many variables in the mix, two things happen. One, you split up your observations so much that you begin to lose predictive power. Everything becomes insignificant. Two, you begin to erode the explanatory power of each independent variable as they are likely not independent of each other (i.e. multicolinearity). There are ways to get around that too (e.g. step-wise multiple regression), but it gets to be a pain in the butt to figure out what's driving what and to what magnitude.

As far as populations, I'm neither a demographer nor am I a wildlife biologist. Instead of me reinventing whatever methodological wheel someone has used for the BFRO population estimate, I'd just love to see their model (if there is one).

I have thrown my hat in the ring on the black bear project. It started as a back of the envelope exercise I did on Christmas Day. The more I delve into it, it's beginning to look like something that will take a while and would eventually be published as a journal article. As I am walking in uncharted territory for me(i.e. wildlife biology, environmental science), I've managed to find some folks to help me with it (or I help them!).

I won't be surprised if this project changes 50 times before all is said and done. That's just the nature of empirical research. But, I enjoy doing it. smile.gif
HarryHenderson
As fascinating as 'mutivariable regression analysis' is <<gag puke gag....actually it is kinda sorta fascinating...kinda>>, in regards to Bigfoot I'm with Vern in that 'how could you ever be sure ANY of the factors/variables being used are 'real' and 'true'. Not being a mathemetician, is there a sub-branch of say 'statistical analysis' that deals ONLY with hypotheticals using only hypothetical data for input? I guess in theory you can do that without a 'special discipline' but my thinking is more about the notion that the 'hypotheticals' would be KINDA-MAYBE based on POSSIBLY-WHO-KNOWS-FER-SURE real evidence that's out there. I think what I'm really asking is, can there be a 'Presumed-To-Be-Garbage-But-Maybe-Not-IN/Possible-Truth-OUT' scenario? new_whistle.gif

Back to reality. IMHO, anything short of an actual BODY or some other VERY similar HARD evidence, most everything else is always just gonna be anecdotal speculation and conjecture, never true scientific fact. icon_confused.gif

"Harry"
bipto
QUOTE(VernF @ Jan 9 2004, 08:47 PM)
I just happen to have enough knowledge to be danderous about a few topics which fascinate me.

You and me both, brother!

Um...biology ain't one of them, but I know what you're talking about...
VernF
QUOTE(Judaculla @ Jan 9 2004, 10:45 PM)
.


An analysis of variance was performed by colleagues of John Green with the data in AAU.  He calls it "the computer study" in his book.  But, he didn't have enough observations to really say anything.

QUOTE


You know, I don't recall the size of Farenbach's sample, but I do recall being concerned that it wasn't a little larger.

Your study sounds interesting. Fill us in on it a little more when you have the time.

-Vern
VernF
QUOTE(HarryHenderson @ Jan 9 2004, 11:11 PM)
Back to reality. IMHO, anything short of an actual BODY ...

QUOTE


It always comes back to that, doesn't it? No type specimen, no species.

-Vern
Judaculla
QUOTE
As fascinating as 'mutivariable regression analysis' is <<gag puke gag....actually it is kinda sorta fascinating...kinda>>, in regards to Bigfoot I'm with Vern in that 'how could you ever be sure ANY of the factors/variables being used are 'real' and 'true'. Not being a mathemetician, is there a sub-branch of say 'statistical analysis' that deals ONLY with hypotheticals using only hypothetical data for input? I guess in theory you can do that without a 'special discipline' but my thinking is more about the notion that the 'hypotheticals' would be KINDA-MAYBE based on POSSIBLY-WHO-KNOWS-FER-SURE real evidence that's out there. I think what I'm really asking is, can there be a 'Presumed-To-Be-Garbage-But-Maybe-Not-IN/Possible-Truth-OUT' scenario? 

Back to reality. IMHO, anything short of an actual BODY or some other VERY similar HARD evidence, most everything else is always just gonna be anecdotal speculation and conjecture, never true scientific fact. 

"Harry"


When we talk about the reliability of regression variables, we need to specify whether we are talking about left hand side variables (dependent) or right hand side variables (independent). The right hand side variables may have zero to do with how bigfoot field evidence is collected. Precipitation levels, habitat types, elevation, known wildlife densities, etc. can all be stated as possible drivers (that's what right hand side variables are) of bigfoot sightings. The reliability of those variables is independent of the idiosyncracies of collecting track casts and garnering reports.

In the case of use multiple regression analyses for bigfoot, it's the left hand side variables you have to worry about, for all the reasons that Vern stated. Again, there are ways to clean that up. Depending on how rigorous you want to be about it, you might end up excluding lots of perfectly valid tracks or sightings. But, it's not impossible to do to subject the data to "purification".

Back to reality? You start putting significant p-values in a rigorously controlled study, and journal editors start listening to you. Statistics is the language of science, and cuts through a lot of bullshit in a hurry. The suggestion I gave regarding Fahrenbach's distribution study is just one example.

What if I could show that the whole bear misidentification hypothesis for bigfoot sightings is full of it? You don't prove that to a scientist by showing them a diagram, saying "But, Sasquatch don't look like bears!"

One way to show that would be to take a state with no bears but with suitable black bear habitat. Check the rate of sasquatch sightings. Then, introduce a whole bunch of bears and check the rate of sightings again. If they aren't really significantly different, then black bears don't explain any significant amount of sasquatch sightings.

So, how the hell am I going to run an experiment and have a state without black bears but suitable black bear habitat import a few hundred bears? I don't have to. Arkansas and Ohio have already done it for me.

Black bears were extirpated from central and western Arkansas, Oklahoma, and Ohio by the early 20th century. In the 50s and 60s, Arkansas reintroduced black bears by importing a few hundred from northern Minnesota. They are now numbering about 3K in the state and have bled over into Oklahoma and Missouri starting in the 80s up to the present day.

Ohio also hadn't seen black bears come back into the state until the early 90s. There was suitable habitat, but the bears had been eliminated. Populations grew in West Virginia and eventually started moving back into Ohio.

So, for the states in question, compare sasquatch sightings prior to and after reintroduction of black bears. There has been minimal change to the habitat in question, so we aren't measuring that. If black bears are sometimes mistaken for sasquatch, the rates should jump upon reintroduction. If the rates aren't significantly different, the black bear hypothesis is a load of crap. That's what statistics can tell you.

Again, the only limiting factor here is the left hand side variable. I may have to wait a few years until there is enough data to really start subjecting it to something more rigorous, so that there will be something substantive left after weeding out garbage. That's OK. Sas will still be there.

And I'm all for going to get a body. Let me know when you get one, so I can drop the data collection!

I don't knock field researchers, so please don't knock the data nerds! cool.gif
peregrine
Vern,

You did some great research regarding the fundamentals of vertebrate censusing. I agree with Jud; you missed your calling.

Deriving population estimates of carnivores is a tricky business. Doug Peacock in his “Grizzly Years” talks about how often those responsible for managing grizzly bear populations are nearly clueless about their numbers. The standard response to questions regarding decreased sightings was often something to the effect that the animals had simply retreated into more remote areas. Peacock also states that the last few animals in an area are almost never seen; they don’t outlast the others of their species by being careless. I think the grizzly bear provides as good a model as anything else for comparing with the sasquatch. It’s an extremely large omnivore that takes down large prey, it inhabits secluded areas, and it is capable of changing its behavior in response to human pressures (becoming, for example, almost exclusively nocturnal as a way of avoiding contact).

A number of techniques are used to estimate carnivore populations; as with practically everything, information on the topic is available on the Internet via a Google search. Progress in analyzing DNA has enabled researchers to employ new, more efficient, census strategies for estimating grizzly populations using hair snares set along trails. Unfortunately, for a variety of reasons, this technique wouldn’t work for the sasquatch.

Ecological “laws” (or generalities) hold that large animals have larger home ranges than smaller animals. Meat eaters have larger ranges than hervivores. Highly mobile animals range farther than more sedentary animals. By virtue of the fact that the sasquatch appears to be three for three concerning these criteria, it stands to reason that the home range is very large. Add the animal’s apparent rarity into the mix and you have a situation that doesn’t lend itself to population counts or formulaic estimates based on coefficients of detectability and field data.

So that brings us back to Jud’s initial comments and his observations and experiences regarding the derivation of reasonable estimates. Resultant numbers (such as sasquatch population estimates) are not the product of a specific model but rather of a process based on (typically) self-correcting under- and over-estimates made in the course of establishing valid criteria and informed and/or intelligent parameters for those criteria. I think that’s all we’re left with, like it or not.
HarryHenderson
Trust me I wasn't being adversarial or confrontational...I was just being curious as I'm no statistician. smile.gif
QUOTE(Judaculla @ Jan 9 2004, 09:59 PM)
In the case of use multiple regression analyses for bigfoot, it's the left hand side variables you have to worry about, for all the reasons that Vern stated.  Again, there are ways to clean that up.  Depending on how rigorous you want to be about it, you might end up excluding lots of perfectly valid tracks or sightings.  But, it's not impossible to do to subject the data to "purification".

And that was kinda part of my question, how could you truly know if you're using OR eliminating something 'good' OR 'bad' when none of it can be assumed to be 'cosmic truth' due to 'the nature of the beast' (no pun intended)? To wit, can you (or anyone) do a worthwhile analysis using 'supposed facts' AS ABSOLUTE TRUTHS (for the sake of the analysis) but also knowing (but not accounting for it in your analysis) their dubious 'validity' and then come up with a legitimate REAL/TRUTH result? In essence 'Garbage In - Truth Out? I don't know if I'm getting across exactly what I mean. For instance, you can do a MVRA(?) of say 'industry comparable salaries' BUT I'm guessin' you can 'assume' the data you input to be, say, 99%(?) correct. Ergo the 'data in' is put into the equation as being 'correct' but more than that, it's basically KNOWN to be correct and thus the results SHOULD be REAL. Now, with anything 'Bigfoot' related, how could/would you ever KNOW any of the data/variables was indeed 'correct'. And thus would ANY kind of MVR analysis of ANY aspect of 'Bigfoot' be worthwhile KNOWING that it's all based on 'questionable' evidence/data of a 'questionable' entity?!? new_sleepysmileyanim.gif

Anyway, no worries, I was mostly just 'thinking outloud' about how we could go about trying to do what you all were talking about. And I was truly JUST ASKING cause I personally haven't a clue. smile.gif

QUOTE(Judaculla @ Jan 9 2004, 09:59 PM)
And I'm all for going to get a body.  Let me know when you get one, so I can drop the data collection!

You're on BAYBAY. smile.gif

QUOTE(Judaculla @ Jan 9 2004, 09:59 PM)
I don't knock field researchers, so please don't knock the data nerds!  cool.gif

I SWEAR I wasn't knockin' anyone...I swear. biggrin.gif Now, back to your regularly scheduled programming. wink.gif

"Harry"
RogerKni
Vern: Here's a link to an author-approved condensation of Fahrenbach's paper, on Bobbie's site. His sample included 706 prints.

Jud: Don't let me discourage you, but the problem is that the rate of sightings is really the rate of reported sightings, and that is dependent on how accepting the social environment is of such reports, as sociologist Ron Westrum has argued, and also of how many reports are thought fit to print by the local media. His "report release" effect describes how people come forward only when they read of other people's reports being treated credibly. He gave the example of physical abuse of children by parents being ignored by disbelieving doctors, until medical journals and the media began to publicize the phenomenon. A more recent example would be the pedophile scandal in the Catholic church--people wouldn't go public with their claims, and/or at least the media wouldn't report them, until a certain level of acceptance had been reached. This means that sighting levels are heavily "socially constructed," to coin a phrase.

EDIT: Sighting levels are also dramatically affected by the number and activity level of local-area researchers, as various BF buffs have pointed out. (E.g., the high level of Maryland sightings is explained by the intense level of activity of a group of researchers there in the eighties.)

Your suggestion that someone "Recruit 40 or 50 people and have them each draw or construct a BF track" is terrific, and would "firm up" Fahrenbach's footprint analysis. I may add it to my list of firm-up suggestions in an article I'm working on (crediting you, of course). I think firming-up is the way to go, to convince scientists to take a look at the BF situation. EDIT: But one problem with having people construct tracks is that one would have to allow them access to print models to copy, and moreover models similar to the models that hoaxers would have been aware of at the time. And that would be awfully hard to do in a convincing way.
Judaculla
Harry,

Thanks for the clarification! Sometimes in cyberspace, it's hard to tell if someone is just asking a question or picking a fight!

As far as whether having garbage in your data stream affects your findings, John Green mentions something about that in his summary statistics chapter near the end of AAU. He did his overall descriptive stats on the entire data set, and also on a dataset where he excluded dubious cases. He ending up getting essentially the same results either way, so he included everything. That's a decent layman's way to measure the reliability of a dataset, and not a bad way to go about doing things.

In my own work, I have to be good about finding "outliers", data points that don't fit the pattern and pull the central tendencies out into left field. When you build a best fit regression model, it allows you to detect residual data points that don't fit. You don't toss them immediately. I had a stats professor who said "Outliers are mostly data aberrancies, but occassionally they are the Nobel prize." Basically, as long as your outliers are a small portion of your data, you can ignore them and throw them out of your model. There are a few more "tricks of the trade" that are too complex (and boring!) to lay out in a forum. In short, it is a tough nut to crack, but I've got some really big hammers!

Roger, with money, time and effort, almost any confounding variable can be quantified, controlled, and accounted for. I can imagine some survey data being collected that would examine willingness to report a BF sighting or other sociopsychological wrinkles. For all I know, somebody has already done that. Same thing with researcher availability. I've jumped over those kinds of hurdles before in other work. I've also hit brick walls before. This is going to be a long term endeavor, so I'm OK if I don't have everything ironed out before-hand. And I'm completely OK with going back to square one when something doesn't pan out. To quote Harry, it's just the nature of the beast.
goldie
Oh how I hate math. Can't stand math. Math hates me and I hate it. Whew.
Well I got that rant out of my system. So now that my idiot cards are on the table can one of you brainiacs help me out by pointing me to a good source that will explain how to go about the MVRA statistical analysis that you are trying to do that will give good explanations to all the terminology that you are using.

I'm in the formatting stages of doing some analysis of the area that I'm working right now. Since I'm home bound for the most part due to a shoulder problem I won't be able to get out into the field for a number of months probably so I'm currently working on setting it up.

You talk about right and left variable and outliers blink.gif
QUOTE
In my own work, I have to be good about finding "outliers", data points that don't fit the pattern and pull the central tendencies out into left field. When you build a best fit regression model, it allows you to detect residual data points that don't fit. You don't toss them immediately. I had a stats professor who said "Outliers are mostly data aberrancies, but occassionally they are the Nobel prize." Basically, as long as your outliers are a small portion of your data, you can ignore them and throw them out of your model. There are a few more "tricks of the trade" that are too complex (and boring!) to lay out in a forum. In short, it is a tough nut to crack, but I've got some really big hammers!


What I need is some kind of on line source that will help me get a good understanding of the statistics necessary so that I can reasonably determine the environmental changes to the habitat and the animals in that habitat when a group of bigfoot move through an area.

If I can get a good idea of what is needed for the statistics to be quatifiable then perhaps I can set it up and someone with a more advanced math background can then help me analyze the data. goldie
Judaculla
Goldie,

I didn't start really learning about regression analysis until I had already taken two semesters of undergraduate statistics classes and a graduate methods course. It's something that just takes time to absorb and figure out.

Beyond introductory probability and descriptive statistics, there is no way I could have self-taught with any available source or even with an enthusiastic and patient coach. I'm always struck by how much more there is to know. My boss has her masters in economics, is way smarter than me, and she gets stumped every now and then.

If anybody really wants to learn about statistics, I recommend starting with an introductory stats class at a local community college. If that doesn't turn you off completely, you can go from there.

I know it sounds like a complete cop-out, but this stuff is hard to learn, hard to teach, and hard to use. That's why top statisticians get paid the big bucks by research institutions (the bucks I get paid are only small to medium in size! laugh.gif ).
RogerKni
Goldie: Here's a link to a page on Amazon where you can buy the amusing How to Lie with Statistics for about $9, or for $20 also acquire Larry Gonick's Cartoon Guide to Statistics. (Or order 'em from the library.) These'll get you to first base, or at least give you a feel for the subject. But it's as Jud says, the data-dicing stuff he and others have been talking about is a whole 'nother topic, further down the road.
goldie
Thanks Judaculla and Roger,
After going out to the USGS site I pulled up this and have pretty much given up hope that I would be able to put together any meaningful statiistics.
However I'm not going to give up on my project and will just do what I can to note observations in my research area. Below is all greek to me and what is kind of ironic is that given all this technical stuff they still seem to be saying that it is hard to really get an accurate indication of the number of bears. Thanks goldie

Fitting the model

We used the pooled absence/presence data from all years to estimate parameters for a beta-binomial model. In this model, each trail has a constant probability of sign occurrence on all segments. These probabilities vary among trails and follow a beta distribution. Within each trail, the presence or absence of sign on each segment is an independent Bernoulli event; therefore, the total number of segments with sign on a trail is a binomial variable. The beta distribution is a highly flexible, two-parameter model that can create variously shaped probability densities over the interval (0, 1). It has been used to model a variety of data (e.g., Griffiths 1973, Paul 1979).

For a given year, let Yij be a 0-1 variable representing absence/presence of sign on segment j of trail i, i=1,...,k and j=1,...,ni, where ni is the number of segments in trail i. The beta-binomial model assumes the following:

1) The probability of sign on any segment of trail i is pi where p1,...,pk are independent beta random variates. That is, pi is a random variable with probability density function




where a>0 and b>0 are unknown parameters and G(×) is the gamma function.

2) The segment responses Yij, j=1,...,ni, on trail i are independent. Therefore, conditional on the value of pi, the total number of segments with sign on trail i, say Zi, is a binomial random variable with parameters ni and pi; that is,




It follows from 1) and 2) that the marginal (unconditional) distribution of Zi is beta-binomial:



Given observations z1,...,zk of the number of segments with sign on trails of lengths n1,...,nk, respectively, maximum likelihood estimators of the unknown parameters a and b are obtained by maximizing the likelihood function,


with respect to a and b. We used a Newton-Raphson algorithm programmed in GAUSS (1988). We estimated a and b for both scat and grizzly tracks by pooling the data for all five years and considering them a sample of 96 separate trails (Table 2). The values of a and b reflect both the average rate of sign incidence on the trails and the variability of this rate across trails. The goodness-of-fit of each model was measured in the following manner. Equation (3) was used to compute the probability distribution under the fitted model of the number of sign for each trail in the sample (the distribution depends on the length of the trail). These probabilities were summed over all trails and multiplied by the number of trails to give expected counts for the number of segments with sign. We considered these fits satisfactory and used the beta-binomial distribution to model
VernF
QUOTE(peregrine @ Jan 10 2004, 12:08 AM)
Vern,

You did some great research regarding the fundamentals of vertebrate censusing.

QUOTE


No research, just an attempt to reconstruct conversations I've had over the years with wildlife managers and biologists. I hope it didn't sound more authoritative than I intended, because I'm certainly no expert.

-Vern
VernF
QUOTE(Judaculla @ Jan 9 2004, 11:59 PM)
One way to show that would be to take a state with no bears but with suitable black bear habitat. Check the rate of sasquatch sightings. Then, introduce a whole bunch of bears and check the rate of sightings again. If they aren't really significantly different, then black bears don't explain any significant amount of sasquatch sightings.

So, how the hell am I going to run an experiment and have a state without black bears but suitable black bear habitat import a few hundred bears? I don't have to. Arkansas and Ohio have already done it for me.

Black bears were extirpated from central and western Arkansas, Oklahoma, and Ohio by the early 20th century. In the 50s and 60s, Arkansas reintroduced black bears by importing a few hundred from northern Minnesota. They are now numbering about 3K in the state and have bled over into Oklahoma and Missouri starting in the 80s up to the present day.

Ohio also hadn't seen black bears come back into the state until the early 90s. There was suitable habitat, but the bears had been eliminated. Populations grew in West Virginia and eventually started moving back into Ohio.

QUOTE


Jud, I do think this is an interesting idea. I wonder how suitable Ohio really is for inclusion in this study? (I have lived there for a number of years.) As you state, a few are filtering in from W VA and, I suspect, PA too. But residents are still pretty low in numbers--most are probably transients. I'm pretty sure Ohio DNR is maintaining sighting reports, and you might want to analyze that data. Blackie sightings are concentrated in the Southeastern tier of counties, and Sasquatch reports are not entirely congruent with that area.

I suspect that RK is right that a whole lot of factors drive bogus/erroneous Sasq. reports, but I don't think that should deter you from giving this a whirl.

Man this board moves fast and it is massive. Don't think I can keep up with it--my job demands a major proportion of my meager intellectual resources. Clearly a whole lot of very bright folks posting here too, very stimulating to read some of their thoughts.
RobUstes
Wow .. took awhile to get caught up reading ! Great thread !

ok, take a nap while i ramble, please laugh.gif

Biologists, lacking "proof positive" make what they in fact call "Educated hypothesis" (good guess) on populations or other statistical data.

Given a known or suspected population in a given area, they can multiply that number by the amount of suitable habitat throughout the State to arrive at an educated hypothesis of population.

Using that method, i conclude that Maryland has a Sasquatch population of between 200 and 500 individual animals. Actually, rather a dense population, but given the amount of sightings in Md, it stands to reason. So a total population count in North America around 6k, may actually be underestimating unsure.gif (boy, i'm gonna catch hell for making THAT statement laugh.gif )
jimf
Not from me Rob..Well maybe not on the Maryland figures..but as a viable breeding population nationwide...I think we do estimate too conservatively.At the same time don't think they're as dense in certain areas as some seem to think...confusing I know. wink.gif
RogerKni
QUOTE(VernF @ Jan 10 2004, 11:29 PM)
I wonder how suitable Ohio really is for inclusion in this study?

You can order a fairly recent 75-page book on BF sightings in Eastern Ohio (mostly), The Sasquatch Triangle Revisited, by the director of the Eastern Ohio Bigfoot Info Center (EOBIC). They have a website. The book is $13.95 ppd. from:

Don Keating
P.O. Box 205
Newcomerstown OH
43832-0205
Judaculla
Vern,

Thanks for the encouragement! As part of my job, I'm often given problems that others consider impossible to solve, and I'm asked to solve them anyway. Fermi problems are just part of my everyday experience! If I let confounding variables stop me, I'd be out of a job. biggrin.gif

There is a lot of work I have to do before I even start approaching the black bear hypothesis and assessing how viable it would be to use data from various states. The baby steps and the grunt work that it takes to get there aren't nearly as glamorous as answering the final question, but are essential in this whole process. And, like all BF researchers, I can't afford to quit my day job! So, I'll do this catch-as-catch-can and approach it a hundred different ways before all is said and done.

The first thing I've been tackling (with help from others) are the current black bear estimates by state. In the indepedent research forum, I have a whole thread devoted to that called "Correlating black bears to sasquatch". Rather than repeat a bunch of stuff here, please take a look at it.

Just to quickly speak to the black bears in Ohio question, I do have estimates from the Ohio DNR as well as a state habitat map available to me. I also have Ohio resident black bear estimates in a time series (i.e. year by year) starting with 1993. So, I can track population growth as well.

Most people equate research with field work. As important as that is, what I was trying to show is that there is important and compelling work that can be done with data that is already available in some form or another. Statistics is the tool to do that.

Even after a body is obtained, BF research will need scientists who are well versed in statistical modeling to speak to many questions: prey/predator relationships, habitat needs, population densities, and a host of other things that I can only begin to imagine. I'm brand new to this stuff, ya know! biggrin.gif
RogerKni
Jud, if you're "game," more power to you. But when I read the sentences below a month or so ago, I felt daunted by the difficulties of statistical analysis. (The last words quoted are the last words in the book; a very unusual book-ending!)
QUOTE(Barbara Wasson @ "Sasquatch Apparitions," pp. 161-62)
In order to establish a baseline for human activity in the woods I used forest service statistics from two Ranger Districts .... 

I had intended to present [at the UBC 1978 conference] the extensive data I have, which indicated sighting reports [are] more dependent on the rise of temperature and drop in humidity than on people being in the woods.  ...  For example, I took the Willamette National Forest, and in that I eliminated some numbers of people who are downhill skiers on one slope, to make a realistic ratio.  However, they did use cars to get to the area and so were more likely to see a Sasquatch by road than on a downhill slope, although less likely to see one than away from a crowded highway.  So you see how complicated statistics become to give at all a realistic picture.  Then one has to combine the witness validity rating in the sighting reports that you have.  I went into detail for each area on other points as to the number of road builders in the area. [?]  I recognized that the number of sightings that I had as the other part of the ratio was over a 103-year period, and there would have to be account taken of that in the final analysis.  For example, for the Oakridge Ranger District the ratio was 55,230 people to one report, over 103 years.  There were only two reports in the entire designated area.  Now what, I ask you, can you do with that?  Taken on a larger scale, perhaps you would get a little more sensible data.  I do not know.  So what.
HarryHenderson
QUOTE(RobUstes @ Jan 11 2004, 05:16 AM)
....So a total population count in North America around 6k, may actually be underestimating unsure.gif (boy, i'm gonna catch hell for making THAT statement laugh.gif )

HELL HELL HELL!!!!!!!!
JanV
This is a facinating thread. I am going to be brave and add my 2 cents worth...
The idea of using black bear to estimate BF population is risky. We know how black bear live. We don't know how BF lives (family structure). But I suspect that whatever form of social organization it would have would be found studying primates rather than black bears, elk, or cougars.
Does BF spend some or part of its life in a restricted home range? Do females and males live and travel differently? Where are the females and young? By this I mean that the majority of BF sightings seem to be of single male? animals. We don't know if the animal lives in the area or not or is alone or not ...or if it is following some pattern of travel (known only to itself) that could allow a single animal to be seen or reported over a very large area.
Sanderson (and Keegan) postulated specific vegetational/climatic territory for BF. Would it be possible to begin with that type of map using that data and overlay BF reporting information? (This is what I think Keegan did). Then using the frequency of reports in those areas and human population density data try to establish the boundries of BF ranges within? Or identify routes of travel?
We have got to get more information on BF before the correlation with black bear sightings could be used as a model.
Obviously, I am over my head here....
Jan
Judaculla
Jan,

Thank you for your enthusiasm! I don't want to seem like I'm putting you off, but I'm afraid this thread is turning into a replica of the black bear thread in independent research. Probably as much my fault as anyone else's!

If you haven't seen that thread yet, please read it. I'll be happy to answer any additional questions regarding that project over there.

Thanks again everyone!
JanV
QUOTE(Judaculla @ Jan 11 2004, 06:50 PM)
Jan,

Thank you for your enthusiasm! I don't want to seem like I'm putting you off, but I'm afraid this thread is turning into a replica of the black bear thread in independent research. Probably as much my fault as anyone else's!

If you haven't seen that thread yet, please read it. I'll be happy to answer any additional questions regarding that project over there.

Thanks again everyone!

Thanks Jud. I have read the thread over in the independent research forum too. I will ask one of the mods to move my post over to that thread.
Jan
This is a "lo-fi" version of our main content. To view the full version with more information, formatting and images, please click here.
Invision Power Board © 2001-2010 Invision Power Services, Inc.