- the editors invited 7 different commentaries on the article; I've posted links to those commentaries. After you've read the paper it might be interesting to read some of the commentaries (I don't know if we should try to do this for next week or for the week after?)
- I've written to Jay Ver Hoef to see if we can get the data from the original paper. (Update: he's agreed to send them, as soon as he gets back from the Vancouver Olympics and gets caught up ...)
- I have a hard time evaluating how useful the discussion of these techniques is because I'm already pretty familiar with them (so I tend to fill in any missing pieces for myself); I will be interested to hear others' reactions. As the authors say, they're not really presenting new methodology here, just trying to emphasize some points for a new(ish) audience.
Wednesday, February 24, 2010
Cressie et al paper
A few quick thoughts about the Cressie paper:
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I'm thinking a lot about how useful the concept of independence is now that quantitative methods for disregarding it are becoming widely available. In a lot of ecological scenarios I can think of, it seems like trying to achieve independence isn't really a worthwhile goal anymore. First of all, trying to achieve independence can be logistically costly. Second, all biological processes in the field are interrelated to some degree-wouldn't it be better to try and test hyperparameters first rather than just assuming independence?
ReplyDeleteInteresting point. However: independence still makes life easier (MCMC and other mixed-model techniques make estimation of dependence/correlation *easier*, but not necessarily easy), and *approximate* independence may not be that hard to achieve. So yes, I would say it's no longer as necessary to knock yourself out to make sure you have independence as you long as you think you can estimate the non-independence (a similar argument applies to balance in designs), but it still helps ...
ReplyDeletePS. "all biological processes in the field are [xxx] to some degree [so we should incorporate xxx in our models/test for xxx first]" is a very slippery slope when you consider the range of possible values of "xxx" -- spatially correlated or spatially varying, temporally correlated or temporally varying, nonlinear, density-dependent, non-normal, non-Poisson, phylogenetically correlated ...
ReplyDeleteI think this paper does a really great job of explaining what is meant by data model, process model and the ensuing ideas of sampling error versus process error, and I think there's some other good stuff here. However, I do have a few specific questions I'd like to have answered tomorrow: Firstly, there are situations where one form of statistical methodology seems quite obviously the/a "proper" thing to do. Given this idea, when is Empirical Bayes, which is related to standard Bayesian statistics, actually a preferred method, given that it seems as though it would underestimate uncertainty in a system? Also, a second question (overachiever) is what are the pros and cons of model-based versus design-based inference and can we put these into some context?
ReplyDeleteIt is an interesting paper and I look forward to discussing it tomorrow. That being said I did have two areas I was not clear on. First, I’m not sure I see the connection to how breaking up data, process, and parameters actually leads to accounting for uncertainty. It does make the various components of your model distinct, which could provide a chance to look at uncertainty in each part, but I was not clear from what we read how this is actually done. Second, is breaking a complex ecological process into a linear series of conditional probabilities realistic? How often do real world processes follow an “if A then B, if B then C” relationship? Again, this may just be due to my lack of familiarity with the topic but I would be interested in an example as their reference to seals seemed fairly vague.
ReplyDeleteI liked the approach, and I think the authors did a great job explaining it in more or less simple words. What I liked of this approach is that it confronts a philosophical question: what is the relationship between "reality" (process or E) and the data that we collect (Data or D) that we assume accurately represents the reality of the ecological process in question. To account explicitly for this potential error source is an interesting advance. I don't know if I understood Tim's concern on breaking a complex ecological process into "linear" series of conditional probabilities because I don't think that the hierarchical approach may necessarily be linear. I agree with Tommy's question on the pros and cons of design vs. model based approach, maybe we can discuss this in more depth.
ReplyDeleteI agree that the authors explained the difference between process error and measurement error, and how to break up the model into the different components (E, D, P_D and P_E), clearly. However, I am not sure I understand how/what the extended model (model B) adds to model A. Also, are there any disadvantages to incorporating all these uncertainties?
ReplyDeleteIn response to Olivia's post, I would think the biggest disadvantages to incorporating all these uncertainties lies in communicating your results to others, especially those outside your specific field. I have observed that when communicating uncertainties in science to policymakers and the public, the audience often gets preoccupied by the uncertainties and the true findings of the science can be lost. Do others agree with me or feel differently?
ReplyDeleteI don't understand the distinction between empirical-Bayesian and Bayesian.
ReplyDeleteMollie, I would like to learn more about that as well. I think it has to do with how the prior probability distribution is constructed. I'm having a hard time grasping the concept of the prior distribution in general... if there are data from many previous experiments, they could be used to estimate the prior, but if one is making assumptions to estimate the prior, what makes that method better than simply stating a null hypothesis and testing it at a given significance level?
ReplyDeleteempirical bayes: I'm not tremendously familiar with EB either, but I can imagine that this will be helpful: Casella, G. 1985. An Introduction to Empirical Bayes Data Analysis. The American Statistician 39:83-87. http://www.jstor.org/stable/2682801.
ReplyDeletere: downsides of hierarchical models. One rarely hears hierarchical-Bayesian-type folks talk about this, but the bias-variance tradeoff is real -- there's only so much one can get out of a model. I think part of the issue is cultural/types of problems people work on -- many of the hierarchical modelers work on BIG (remote-sensed, survey, etc.) data sets ..
Caroline, Joe, Mollie
ReplyDeleteSampling design:
Pick a time of year when they're easily detectible and disease has been observed previously.
Assume Google Earth is sufficient to characterize vegetation and distance from agriculture. Choose a subset of ponds that stratifies vegetation and agriculture. Depth will be random in subset of ponds.
Sample the same ponds at the same time every year. In each sample, get depth, agriculture distance. Net a 4 square meter area of the pond and count all frogs (infected and uninfected), amphibians and vegetation.
i= pond
j=time
I_ij is sample # infected
A_ij is sample frog abundance
I*_ij is true # infected
A*_ij is true frog abundance
[I_ij|veg_ij,depth_ij,I*_ij]~Binom(p=f(veg_ij,depth_ij), n=I*_ij)
[A_ij|veg_ij,depth_ij,A*_ij]~Binom(p=f(veg_ij,depth_ij), n=A*_ij)
[I*_ij|ag_ij, density_ij, I*_ij-1,A*_ij-1]
~N(mu=f(ag_ij, density_ij, I*_ij-1,A*_ij-1), sigma)
[A*_ij|ag_ij, density_ij, I*_ij-1,A*_ij-1]
~N(mu=f(ag_ij, density_ij, I*_ij-1,A*_ij-1), sigma)
f is used to represent various linear and dynamical models
Here's what we were able to accomplish in class with respect to the acitivity to design a hierarchical model analyzing patterns of frog disease:
ReplyDelete- pilot study
- whats the size of the region
- what's the scale of interactions between the ponds
- determine where there is low, med, high frog abundance
- determine proximity to agriculture
- stratified random sampling of 200 ponds in the tropics (stratified by frog abundance, proximity to agriculture)
- look at 1 species of frog
- 10 years; sample multiple times per year
- net the frogs
- swab the frogs; do pathological test for detection of disease that is not visible; note visual evidence of disease; non-destructive sampling
- measure pond depth, vegetation
- covariates - precipitation, temperature
- define variables, probability distributions, levels
- process: incidence of fungal disease due to agricultural activity and amphibian abundance
- data: expected count of infected ij ~ Neg. Binomial (mu ij, k)
- mu ij = mu i (land use ij + density ij + date ij + precipitation ij + temperature ij)
Kristen, Miguel, Maja, Andrea, Olivia
Sampling strategy:
ReplyDeletePick ponds such that there is increasing distance from agriculture in multiple directions.
Visit each pond one week per year, picking similar times of year based on the climate signal.
--trap frogs (get xij, nij)
--collect pond data (coordinates, depth, veg)
In GIS, calculate pond area and distance to agriculture
Using model, calcuate Qij
Analyze to answer questions
___________________________________________
Nij= "true" # of frogs in pond i in year j
nij= how many "detected"
Xij= "true" # sick
xij= detected sick frogs
theta_ij= distance to agriculture, density
psi_ij= veg cover, pond depth
Qij= xij/nij= proportion of observed sick frogs in pond i to total observed frogs in pond i at time j
[nij|Nij, psi_ij(pond veg, pond depth)]
[xij|Xij, k]
[Xij|theta_ij(density, dist to ag), error]
[D1|E1,PD1]: [xij|Xij, k]
[E1|E, PE1]: [Xij|theta_ij, error]
[D2|E2,PD2]: [nij|Nij,psi_ij(veg, depth),error]
[E2|PE2]: unknown
D=proportion of detected frogs in pond with disease
E=disease spread
PE="environmental" characteristics
PD=data collection characteristics
Tim, Jessica, (Mary, Cherie)