if i understand your point correctly, you're saying that in the case of evolution all stochastic terms in any model really correspond to omitted variables.
You said the key word right there: "model". And one can't scrutinize it any further for 100% accurate description of the real-world phenomenon, because it will never be that. It will always be just a model.
Mmm... I wouldn't exactly say stochastic terms in a model correspond to omitted variables ..I would say in many cases the stochastic term would be a
composite variable, that
simulates the effects of a large number of complex or not-understood real-life variables. But this can ONLY be done, if the overall effects of these complex parts can be described statistically in a meaningful way. For instance, if you observe how often certain mutations occur in DNA in a population, with a large enough sample number you would get a statistically meaningful set of data. And you can
reliably use that information to anticipate the likelihood of occurrence of those mutations in the future. As an example, let's say you notice that whenever a strand of DNA makes a copy of itself, it screws up part of it. A few nucleic acids get their order swapped when it recombines. (Now you know, that this was a consequence of
something, this was NOT out-of-the-ass random, but watch how we don't really need to worry about what caused this)
Now the second time it replicates, the same group of a few nucleic acids are again swapped in some way. And imagine this goes on for thousands of replications. This has now become a large sample set of nucleic acids taking "steps" one or two places to one side or the other, relative to each other. You can describe it as having become a statistical drift. If you were now to make a "model" that describes this effect, you could take your clever formula and stick in there a term that may use a randomly-generated value to simulate the swapping step, of some small DNA piece at each single replication. And you would indeed find that this simulation would
also generate a
drift of the same magnitude that the real-life natural phenomenon would create.
Again, the important part is, in nature everything happens as an effect of a cause. It's in
the simulation that you can speak of "randomness", a shortcut to extensively simplify these complex factors and generate roughly (or accurately) the same
statistical effect as the real-life process.
*
hyena said:
now, i don't know enough about evolution to say whether this is true or false, but i want to draw your attention to the fact that if these unobserved factors are somewhat correlated to the ones you include you are going to get
omitted variable bias, meaning that in the end your estimates are not going to be centered.
Exactly. And in many areas (and many examples do come to mind as I type this) this is the goal of mathematicians and scientists: to come up with better and better models. To include more and more of the most subtle factors that have an influence, or to have their corresponding mathematical term describe the real-life situation better and better.
The point, again, is that these are all just "models".
In engineering, for instance "gas constants", I was made to learn about Joe Schmoe's model, Jack Floggardy's model, QRV's girlfriend's model, as well as Dick's and Harry's. They were all mathematically different, each one more complicated and longer than the last, and they all had their arguments for support. If doing a specific calculation of the gas constant, and plugging in all the givens into their models, one would get say: 8.31789 vs. 8.29932 vs. 8.3259734 vs. 8.36778 ..you get the idea.
hyena said:
of course this is a very stupid example, in the sense that i certainly don't think that one can explain evolution with linear models
Certainly, certainly, not
hyena said:
but the same rule applies to other methods as well. if you leave out something that is correlated to what you put in, then what you get on the observed variables is flawed. of course if you are positive that the phenomenon is driven by something you can't observe you're going to use latent variable modeling - say, latent markov chains, or what have you. but then again you need hypotheses on what your latent factor is, and would this be true in the case you mention?
Exactly. You obviously understand that sometimes you simply cannot make certain measurements directly or there is just no way to separate out the magnitudes of the effects of an ocean of complexities and causes. In the case I mentioned, if you mean Random Walk modeling of diffusion, a supercomputer would never be able to accurately process the position, speed, and orientation, of every single molecule at all times, as there are trillions and trillions of them; let alone would a man be able to understand exactly every single factor that goes into determining the precise angle of rebound after a collision between two molecules (you have a speed, orientation, shape!, atomic forces of all sorts, it's insane). You
have to reduce the whole thing to having a random number generator give you each angle of rebound, if you want to model the process.
hyena said:
note that in this case i am not trying to say anything at all about religion, just methodological curiosity re stochastic processes that are actually deterministic
[size=-2]What? God doesn't exist? Yeah, I know.[/size]
* [size=-1]If you remember, hyena, in my simple dot system I said that every time each dot made a copy of itself it wasn't necessarily the exact same shade. If the zapper were removed, and it was only the dots continuing to copy themselves and exist undisturbed, it would be analogous to a simple drift, like the one I discussed. Over time, you would see a drift of color shades because of this copying imperfection. If you give it a little thought, you'll realize that after a long period of time there would be a
broadening of the color spectrum represented by the population of dots, and with a mathematical model AND the use of a stochastic term, you would be able to predict the
extent of the drift pretty accurately[/size]
___________________________________________________________________
To everyone else out there who finds all this boring (very understandable) here's the take-home idea: If ever you see it written, or hear it said, that evolution, or any part of it, involves randomness ..know that it's not true! It is only human thinking and modeling that render certain things as random. The randomness is a tool for mathematicians and people who know what they're doing. It is a misconception to assume it
is that way in real-life. And it is simply a shame to think that our world is
that simple, and it is therefore an oxymoron to attribute randomness and chance as evidence of complexity and God.
[size=-2]Yes, I snuck in yet another Atheist attack, what![/size]
