Term
| Which models (of the 4 we have covered in class)allow testing for Goodness of Fit in MARK? Why? |
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Definition
Cormack Jolly Seber Model
Dead Recovery Models
These models do not assume that the user knows with 100% certainty the fate of the marked individual. You test GOF to see if model assumptions have been violated by the data. You chat will tell you if there is over or underdispersion. |
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Term
| Which models (of the 4 we have covered in class) do not allow for GOF testing? Why? |
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Definition
Known Fate
Nest Survival
Both of these models are known fate models, meaning the user is not uncertain about tag return or detectability when marked (although these assumptions are often violated). The GOF is considered unnecessary under these conditions. |
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Term
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Definition
| "The numeric expression of the expectation that an event will occur." The sum of all related outcomes to a single event is 1. |
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Term
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Definition
| "A product of probabilities that takes into account and is conditional on the distribution of the data." |
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Term
| How are probability and likelihood related? |
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Definition
| Probabilities are used to find the likelihood of an event taking place. Probability is absolute and does not take into account past events, where likelihood is conditional (related to past events). |
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Term
| Define Induction and give an example. |
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Definition
Induction is the use of past events to predict future, broad scale events.
Ex: I like this apple pie, therefore all apple pies are good. |
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Term
| Define Deduction an give an example. |
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Definition
Deduction is using a general law or principle to make specific predictions (ie, null hypothesis testing).
Ex: All apple pies are good, I will like this apple pie |
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Term
| Define Retroduction and give an example. |
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Definition
AKA Abductive reasoning. Making an assumption that event a led to event b without considering all possible alternatives. Similar to induction and often mistaken for it.
Ex: The lawn is wet. It must have rained last night. |
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Term
| Compare and contrast induction, deduction, and retroduction. |
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Definition
| Deduction is inferences made from hypothesis testing. It starts with the big picture to make assumptions about a very specific situation. Induction and retroduction are similar in that something learned from a specific situation is applied to a larger scale. However, induction is often referred to as correlative association and retroduction refers to post-analysis explanations. |
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Term
| What are the assumptions of capture mark recapture? |
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Definition
- no births/deaths, imm/emigration between trapping
-Marks are permanent
-Tags have minimal impact on indiv
-Homogeneity of survival and capture prob
-Enough time has passed that animals distribute through the landscape, but sort enough that the first assumption is not violated |
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Term
| What is an important biological issue with CJS? |
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Definition
| Only apparent survival is estimated. You can't really differentiate between animals that died and those that emigrated. |
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Term
| What assumptions must be met to calculate probability and/or likelihood? |
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Definition
| Independent and identically distributed data |
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Term
| Why are binomial or log distributions used most often with likelihood? |
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Definition
| Log-likelihoods are the basis for profile likelihood functions – unbiased estimators |
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Term
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Definition
Homogeneity of capture and survival probability for marked indiv w/in ea sampling period
Sampling periods are instantaneous (in reality they are very short periods) and recaptured animals are released immediately.
All emigration from the sampled area is permanent. |
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Term
| List dead recovery assumptions |
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Definition
1. Marked indiv are representative of the pop
2. Tags not lost
3. Tags are ID'd correctly and reported by hunters
4. Indiv fates are independent
5. Probability of survival and tag recovery homogenous |
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Term
| List known fate assupmtions |
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Definition
1. No tags lost
2. No radio tag failure (hahahahahaha) |
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Term
| List nest survival assumptions |
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Definition
-Nests are correctly aged when they are found
-Nest fates are correctly determined
-Nest discovery and check do not influence nest survival
-Nest fates are independent (not always the case w social animals)
-Homogeneity of daily nest survival rates (as nests age, more likely to be depredated so this assumptions is bs) |
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Term
| What is P(data|null) and what is wrong with this? |
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Definition
-The definition of r^2
-Also, the probability of the data given the null
-It's fundamentally flawed, values are arbitrarily chosen for rejection thresholds
- You can't compare models! |
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Term
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Definition
| The probability of the model given the data |
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Term
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Definition
| The top rated AICc/lower ranking AICc |
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Term
| What is another term for multimodel inferencing? |
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Definition
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Term
| What is unconditional variance? |
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Definition
-"Variance given model selection uncertainty"
- also "a measure of repeatability based on model uncertainty"
-Standard error for Beta
-Accounts for model selection uncertainty
-Used when AICc<.9 |
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Term
| What is conditional variance? |
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Definition
-variance given the top model (AICc >.9)
-Does not incorporate model selection uncertainty
- |
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Term
| what d you do if your Chat is 2.6? |
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Definition
Adjustments tabs -> chat -> enter 2.6 -> run
QAICc will adjust accordingly |
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Term
| What 3 parameters do you always report when estimating survival? |
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Definition
| survival, st error, confidence interval |
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Term
| How do you calculate AIC from RSS in an ANOVA table? |
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Definition
| -2log(L)+2K = AIC L = -1/2n*log(sigma^2) sigma^2 = RSS/n |
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Term
| What are the 3 most common approaches for general parameter estimation? |
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Definition
| LS (least squares), ML (max likelihood), and Bayesian methods |
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Term
| What is the domain of LS? |
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Definition
| General linear models (regression, ANOVA) |
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Term
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Definition
| Maximum likelihood estimate - the value of the parameter that is most likely, given the data and model |
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Term
| What are the advantages of using MLE? |
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Definition
| unbiased, minimum variance, and normally distributed |
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Term
| Name 4 ways you can check for fit of a model to the data |
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Definition
| GOF, adj R^2, residual analyses, and checking for overdispersion in count data |
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Term
| What is underfitting a model? |
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Definition
| Not enough parameters - Some model structure is erroneously included in the residuals, leading to high bias and the illusion of high precision. |
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Term
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Definition
| Too many parameters - high level of uncertainty. Some residual variation treated as structural variation. |
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Term
| What is a loose translation of Occam's razor? |
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Definition
| To shave away all that is not needed |
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Term
| What is a negative consequence of overfitting? |
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Definition
Spurious effects! Imprecision! Madness! CHAOS!!!!!!!!
I've been studying too long. |
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Term
| Describe Kullback-Leibler Information |
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Definition
| I(f,g) - Info lost in the distance between full reality (f) and the model (g). We can only estimate K-L information, because we will ever know full reality (far out). WE are striving to minimize inefficiency - the quantitative measure from f to g. |
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Term
| How are statistical principles link with information theory (specifically K-L information)? |
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Definition
| Akaike used a property of logarithms to rewrite K-L theory and use that to derive AIC. He got rid of the true zero inherent to K-L info. This means we can rate models for best fit without having to know full reality (true zero). |
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Term
| What three concepts did Akaike link? |
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Definition
Boltzmann's entropy, K-L info, and maximum likelihood
AKA
thermodynamics, info theory, and statistics |
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Term
| What is the the information criterion eqn used by Akaike to link thermodynamics, info theory, and statistics? |
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Definition
AIC = -2log(L(Ohat)|data) + 2K
(L(Ohat)|data) = likelihood of the parameter, given the data |
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Term
| Why multiply by -2 in the AIC eqn? |
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Definition
| deviance penalized by 2K to correct for asymptotic bias |
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Term
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Definition
| Problem solving the lazy way (not based on rejection of all possible hypotheses). Examples of this method include using a rule of thumb, an educated guess, an intuitive judgment, stereotyping, or common sense. |
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Term
| What is AICc and when do you use it? |
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Definition
AIC for small sample sizes; it's AIC with an additional bias correction term to deal with too many paramters in relation to sample size.
AICc= AIC+(2K(K+1))/(n-K-1) |
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Term
| Why shouldn't R^2 be used for formal model selection? When can it be use for model selection? |
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Definition
| R^2 is a descriptive statistic and exaggerates the predictive ability of models fit to a given data set. In exploratory work, you may use R^2 to assess the worth of models (ranks mean nothing if all of the models suck) and direct future data collection. |
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Term
| What is the crucial initial starting point for advancement in the life sciences? |
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Definition
| A set of multiple working hypotheses defined a priori. Then using these you make a priori set of candidate models representing the hypotheses. |
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Term
| Is the value of AICc important? |
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Definition
| No, the differences between AICcs are more important - they can be related to information |
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Term
| What is exp(-1/2 deltai)? |
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Definition
| The L(Ohat|data, g) aka the likelihood of the parameter given the data and the model |
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Term
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Definition
| exp(-1/2 deltai)/(summed exp(-1/2 deltar)) |
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Term
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Definition
| The Prob(gi|data) - probabilty of the model given the data |
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Term
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Definition
Evidence Ratio
L(gi|x)/L(gj|x) = wi/wj
The likelihood of one event relative to another given the data |
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Term
| What are the 3 main types of evidence? |
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Definition
1) Model probabilities (the prob that model i is the K-L best model) wi and Bayesian posterior model probabilities
2) L(model|data)
3) Eij - provides empirical evidence of hypothesis i vs hypothesis j |
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Term
| Name the pitfalls of information-theoretic methods |
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Definition
1) Poor science question
2) Too many models
3) True model not in the set
4) Information-theoretic methods treated as a test
5) Poor modeling of hypotheses
6) Failure to consider aspects of model selection uncertainty
7) Failure to consider overdispersion in the data
8) Don't use post hoc data mining
9) GOF should be used with global model |
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Term
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Definition
| The relative likelihood of the model given the data |
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Term
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Definition
| a method of fitting a model to data by minimizing the squared differences between observed and predicted values |
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Term
| Define maximum likelihood |
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Definition
| A method of fitting a model to data by maximizing an explicit likelihood function. This function specifies the likelihood of unk parameters of the model given the model form and data. The parameter values are termed MLE (maximum likelihood estimators) |
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Term
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Definition
Naive occupancy = estimated number of sites occupied/ total sites
DOES NOT INLCUDE DETECTION PROB!!!! |
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Term
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Definition
| CJS time-dependent survival and recapture probs |
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Term
| What does dead recovery diagram look like? |
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Definition
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Term
| What do K-L and delta AIC diamgrams look like? |
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Definition
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Term
| What does a known fate diagram look like? |
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Definition
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Term
| What does a mark resight diagram look like? |
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Definition
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Term
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Definition
| Extent of occurrence and area of occupancy |
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Term
| What kinds of data types are use for occupancy analysis? |
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Definition
Museum/collection records
Anecdotal reports (Ex: ebird)
Biological surveys |
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Term
| What is a major issue that must be accounted for in occupancy modeling? |
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Definition
Probability of detection
(false absences or present, but not detected) |
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Term
| What is the difference between occupancy and use? |
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Definition
| Occupancy is binary, used is not (used can mean sometimes). Occupied means ALWAYS physically present. |
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Term
| Name the assumptions of occupancy modeling |
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Definition
1) closed populations
2) P(occupation) constant
3) Detection among sites independent (unless modeled differently) |
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Term
| What 2 parameters does PRESENCE calculate? |
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Definition
Psi - proportion of sites occupied
p - detection prob for a survey (dependent of occupancy model type)
A measure of variance is given for ea parameter |
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Term
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Definition
"present at a site and detected in at least one of k samples"
d= 1- (1-p)^k
d = probability of detecting the species
p = probability of detecting the species in a single survey
k = # of surveys |
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Term
| Why do you average models? |
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Definition
| To account for model selection uncertainty. Even the lower-ranked models have valuable information |
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Term
| What is Ybarhat (model averaged value for a parameter)? |
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Definition
| the sum of wi*Yhat for all models |
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Term
| The variance of beta is said to be _______ on the model. |
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Definition
conditional
Given this model, one can obtain a numerical value for var(Beta) using LS or ML theory. |
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Term
| Variance of a parameter is the sum of what? |
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Definition
| Sampling variance given a model and variation due to model selection uncertainty |
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Term
| What is an unconditional variance actually conditional on? |
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Definition
| Unconditional variance is condition on the set of models considered (a weaker assumption than using just one model) |
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Term
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Definition
UNCONDITIONAL VARIANCE
What's 20 feet long and has 5 teeth?
The line for funnel cake at the TX state fair. |
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Term
| CJS estimates 3 things. What are they? |
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Definition
| Abundance, survival, and capture probability |
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Term
| What is the main problem with CJS assumptions? |
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Definition
| Under normal circumstances, these assumptions are violated |
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Term
| Brownie model and Seber model are for what purposes? |
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Definition
| Harvest recovery and found dead recovery, respectively |
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Term
| What is the benefit of using information theory over null hypothesis testing? |
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Definition
Ho testing finds p(data|null)
You can't compare models; models are not penalized for having more parameters
Information theory finds p(model|data)
K-L gives you the ability to test multiple hypotheses, compare evidence across models, rank models, and average them |
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Term
| What is the importance of building a strong foundation for your science house? |
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Definition
| You'll never know full reality (remember I(f,g)?), but you can collect great data and design the study well. |
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Term
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Definition
The value of your B parameter that is most liekly to occur, given your data. MLE is the link between null hyp and information theory.
[image] |
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Term
| When can you use AIC and not AICc? |
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Definition
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Term
| What exactly does the (2K(K+1))/(n-K-1) do to AIC? |
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Definition
Applies this idea:
[image] |
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