CarlWesolowski

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Please remember to sign your messages on talk pages by typing four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or , and a volunteer should respond shortly. Again, welcome! Barbara (WVS) ✐ ✉ 20:35, 8 February 2017 (UTC)

I put in the OLS criterion for AIC determinations. Open question; How does one apply AIC when the regression has to be weighted, for example, when the norm of the relative residual is the more proper regression criteron? That is, Min||(R-Y)/Y|| as opposed to OLS Min||R-Y||, where R is the residual vector Y the data, and ||.|| means norm. I must say, I find AIC is overused, and recommended by default in scenarios in which it should not be used at all. This mirrors the overuse of OLS, which should not be applied when X is randomly distributed as opposed to exact, where by "exact" I mean for example, X is 0,1,2,3,,,n. I find AIC annoying. How does AIC account for agreement to within the noise level of the data? Is AIC actually correct? For example, if I do a simulation of an exact model with two different injected noise levels, will the AIC be blind to the difference between them? Or, will it select the less noisy data set? Mind you, both models are perfect, and in that case so if the AIC result is not identically good, then AIC is meaningless. Which leads to the final question, what does AIC mean?

The standard reference for AIC is the volume by Burnham & Anderson; for details, see Akaike information criterion#History. A recent paper that discusses "the world view of AIC" is Aho et al., which is also cited in the article. AIC is not in any way specific to OLS; rather, as long as we know the likelihood function, AIC can almost always be applied.

AIC cannot be applied to different data sets. Rather, it is applied to different statistical models of the same data set. This is discussed in the article.

SolidPhase (talk) 09:01, 21 March 2015 (UTC)

The point was that the likelihood approach is often inappropriate as models often are ill-posed with respect to the data. For example, when one uses monotonically decreasing functions to fit peripheral venous samples of drug concentrations, AIC is often used with OLS regression. There is no transformation of a concentration curve fit of a monotonically decreasing function, where the initial concentration is zero that will transform the correspondence between model and data into a likelihood of any kind. The problem is ill-posed. Moreover, a technique that assigns noise a role in assessing information content is in teleological error. I strongly think this technique is fundamentally flawed on two counts. Count one: the non-existence of any likelihood function. Sure, a likelihood function can be assumed, and sometimes one might actually be assumed correctly. However, that is a long way from saying that that assumption is appropriate the way it is used in practice. Count two, information is context dependent, and one man's noise is an others information. The AIC technique lumps error from model misspecification and noise, and as such does not quantify information, or give any information about when its use is inappropriate.

I do not know the medical application to which you are referring. If people choose an OLS model where such a model is inappropriate, though, then the problem is that they choose OLS. The problem is not with AIC.

Your comment says that "a technique that assigns noise a role in assessing information content is in teleological error". That is not true: sometimes an appropriate way to model something is to assign noise to some portion—even when that portion is deterministic. In statistics, it is commonly said that "All models are wrong, but some are useful".

Choosing a set of candidate models is an art, and it is often difficult and error-prone. AIC, however, can really only come into play after a set of candidate models has been chosen. There is a Wikipedia article related to all this: Model selection. That article, unfortunately, is currently "start class", i.e. it needs a great deal of work.

SolidPhase (talk) 03:28, 22 March 2015 (UTC)

There is no likelihood function I know of that would transform a physical concentration of zero at time zero to be the infinite concentration predicted by a gamma variate fit function's magnitude for an appropriately parametered gamma variate model of concentration. It should be clear that you are missing the point. AIC is not appropriate for use in circumstances where the proper regression target is not a goodness of curve fit measure. An example of that is the Tikhonov Gamma Variate technique which I referenced in the article and which was removed because of a limited understanding of how limited AIC is. Read . Then tell me how you would apply AIC without making bad assumptions. I see no response to the last paragraph. The problem with AIC as a measure of goodness of fit is that goodness of fit is not the most general criterion for model selection. The regression problem is in general an inverse problem. If we accept the task of performing a regression, as a first, and almost universally ignored task, we should state in precise form what the problem is that we are attempting to invert. For example, suppose that we have data consisting of concentrations measured at n times from t1 to tn. A very common problem, for example for almost all pharmacokinetic models, requires finding the area under the curve (AUC) from t=0 to t=∞, even though the data is only defined at t1,t2,t3,,,tn. In that case, we wish to find the least error AUC from fitting a continuous model, which is an ill-posed integral the error for which can be regressed by fitting our available concentrations to minimize the error of AUC from error propagation. Suppose we do that by applying an inverse method, what form does our answer take? First of all, the concept of a good fit relates to AUC-values, and not to concentration values or residuals between the model and data. Indeed, the residuals will be biased in order to find an appropriate AUC. Second, the concept of a likelihood would have to somehow relate to finding the correct AUC, which frankly seems far fetched. Last but not least, in the scenario above, R-squared would be a lot more accessible and meaningful than AIC, because to find the proper AUC, our inverse solution we would in effect be maximizing covariance, as opposed to examining residuals. I see very little in this article about R-squared or indeed any other measure that has a better chance of applying to the more general inverse problem approach to regression, and by the authors own admissions, AIC is most useful for comparing method A with method B, only when the regression methods are the same for both A and B, which, in effect, makes it not clear how one compares regression method A with regression method B, especially when neither A nor B are related to goodness of curve fitting. The AIC method appears to be a solution awaiting a problem to which it properly applies as opposed a general-treatment absolute-value assessment of the effects of what should more generally be understood to be an inverse problem, i.e., regression. The popularity of AIC appears to arise from making simplifying assumptions that occur because the characteristics of the problem that is being inverted have not, in general, even been considered. AIC applies, as far as I can tell, to a subset of a subset of regression problems, and a lot fewer of them, than appear to be generally understood. I would request of the authors of this article, that they state what the limitations of AIC are, and reference some of the better methods available for doing much the same, or even better job as they are quantitative, like R-squared, orthogonal projection of variables, and probability treatments that apply to single regression problems, and not like AIC, which just applies to "controlled" experiments, which allow us only to say that A is better than B in generally unreproducible circumstances because the actual experimental variables are not tested for, understood, or even thought about, and where the parameters of interest are only sometimes the regression targets. The problem with controlled experiments, which AIC requires, is that they are done because the circumstances in which they are performed are unknown. It takes an infinite number of controlled experiments to define the space that they are performed in.

I still see no reply to my comments above. Let me put it another way, I disagree with the first sentence of this article, which reads "The Akaike information criterion (AIC) is a measure of the relative quality of statistical models for a given set of data." I have evidence to the contrary. In specific, a best statistical model is not constrained by any goodness-of-fit criterion. Just because the authors of this article have a "fit-O-centrist" view of numerical methods does not change the fact that information content is always defined in terms of the information that is being extracted, and that is from propagation of error of the target information, not "curve fitting." Can one define an AIC in terms more general than curve fitting? Perhaps, but this article lacks any acknowledgement of the Bayesian-ism in which it is steeped. In specific, there is a burning need to examine residual structure before any assumptions of the AIC type are made. The use of AIC out of proper context is likely more common than its proper usage. Finally, one should demonstrate that the AIC assumptions are met in every case in which it is used and that before using it, and, trust me on this, they rarely are. This situation closely mirrors the use of OLS regression when Theil regression would be more appropriate and many similar misuses of statistics. OLS is a biased technique, bias for AIC has not been explored that I know and its popularity does not justify its use without quality assurance, and as a measure its units are essentially non-quantitative, so that there is little possibility of assurance that its use is meaningful. It is much preferred to use Chi-squared, t-testing, residual plotting, standard deviations or bootstrap for non-normal conditions than AIC as those techniques are at least established statistical measures, and comparable to each other for cross-validation, and AIC, frankly, is not, yields unverifiable information without post-hoc quality assurance, and as mentioned is usually not even examined with respect to its assumptions. In sum, AIC is a made up index looking for a problem to which it applies.

Having received no discussion concerning the above, I put in some of the iff's for AIC, and a link to alternative goodness-of-fit measurements. AIC is a limited technique with lots of assumptions, some of which I listed. The elephant in the room is that goodness-of-fit is a criterion that solves all problems. If that were the case ridge regression, Tikhonov regularization, Pixon image reconstruction etc., would be used by no-one. Further, it should be intuitively obvious that goodness-of-fit is not a general assumption. For example, for fitting ill-posed integrals one should choose the regularization that minimizes the integral error, not the goodness-of-fit. Thus, the objective for modelling need not have anything to do with fitting the data with a handsome curve that is aesthetically appealing, it all depends on what the objective for regression is, and very often the objective in not to fit the local data, but to extrapolate and predict something else that is either outside the data range or is some optimal geometric combination of fitting parameters. Moreover, just using ordinary least squares (OLS) for everything and then expecting that to be meaningful is not a general enough approach to be generally useful, and AIC is in that category. Often Theil regression is better than OLS, especially for heteroscedastic residual data fitting or for x-axis data that is not uniformly distributed. Why then the inordinate attention paid to AIC? I claim that this is because it is a default value in researchers' minds more frequently than it is applicable in fact to the problems to which it is applied. The penalty accrued for this is severe, rather than try to solve problems in general terms, we are satisfied that our regression methods are sacrosanct when they have not even been investigated as to appropriateness. Thus, AIC is used thoughtlessly without considering that the appropriateness of the regression methods themselves are what we should be paying attention to as equally much as the models, not goodness-of-fit, which is not a central consideration for predictive modelling. For example, for extrapolation we also need goodness-of-fit of derivatives of the fitting function, and good luck finding two words glued together about that in the literature. Thus, the attention paid to AIC detracts from more general modelling considerations than it adds to them, and, in my personal work, I cannot imagine that I would ever use ACI in favor of Chi-squared, t-testing, or r-values, and those measures as well are of only limited utility for inverse problem characterization. Ask first why the regression is being performed, then use numerical methods of regression that address the purpose of doing the regression, then measure the goodness of outcome with respect to the stated purpose of regression. If one does that, the frequency of using AIC will decrease markedly, but more appropriate results will abound as the principal is as follows; if one does not ask for the type of answer one wants to obtain, one will not obtain it, so ask only for what you want rather than imagine that you are asking for it without thinking about how to pose the question.

You have repeatedly made inappropriate edits: every one of your edits has had to be undone. You have also left long messages on my Talk page, on your Talk page, and on the AIC Talk page. Each time, you again demonstrate that you do not know what you are talking about.

The Wikipedia article gives major references. There are thousands more references that can be found via Google Scholar—as noted in the article. You have not studied those references. Instead you come here with nonsense statements like this. The only way that you could make a statement like that is if you had not read any of the references.

I have tried to be patient with you for over a year. Stop wasting the time of other people with your gross ignorance. Read the major references before attempting to make further edits.

SolidPhase (talk) 14:29, 15 July 2016 (UTC)

I checked and Mathematica appears to use the negative of the AIC index , and edited my comment appropriately, which edited comment you apparently did not read. Every one of my edits has indeed been reversed, especially and almost always by yourself, including comments that other editors supported, for example, one of my comments about BIC. The article is, as it stands, misleading. I listed a reference of an article that is better written, in specific, . No, I am not perfect, but your efforts are not either. Fighting with me about personification in formal writing is not helpful. And, I stayed away from the site for a year and have done a lot of work to understand AIC. AIC is arguably useful in a limited context for some types of model selection. A comparison with BIC would be useful. Currently, there is no comparison, just a commercial for AIC that is unbalanced. It reads like "Use _____ toothpaste, not brand X." AIC implementation in statistical source code can be faulty , and misleading as well. The assumptions for ACI preclude general usage. The assumptions are perhaps listed in references but do not come across in the Wikipedia article. It is not appropriate to call me ignorant just because my opinion is different from yours, the article as it stands is poor quality, and I do have a practical problem with it. Reviewers sometime suggest that I apply AIC in contexts in which you yourself would understand are inappropriate. The article needs to say when AIC use is inappropriate, and as it stands, that does not come across. If you want to fix this, go ahead. Advocates for AIC have claimed, in print, that it is underutilized. However, I have experienced the opposite, requests for inappropriate usage by people who do not know what they are asking for. I have no need to be known as an author on an AIC Wikipedia article, but, I do have a need for a more balanced article. The current rating of the article is C class, hardly perfect by Wikipedia standards. And, "AIC is an index used to score fit functions to identical data for ranking." That, and similar simple language you do not have a good excuse for ignoring, it is helpful, and I am helpful, and you are ignoring me and my suggestions because you can, not because you should. The word 'ignorant' is related to ignoring, and it is not I who am ignoring you.

Talk Pages

Click "new section" to start a new section on a talk page this way it automatically goes to the bottom of page. All new talk page entries go at the bottom of the page. You didn't put your entry at the bottom. I moved it. Mr. C.C.^{Hey yo!}_{I didn't do it!} 00:44, 28 March 2018 (UTC)

Variable volume distribution

Variable_volume_pharmacokinetic_models needs significant improvement. We need independent sources for this model please! I strongly advise that you rewrite the article in plain English. I will propose the article for deletion if no independent sources can be located as this is not a place for fringe /novel models. PainProf (talk) 01:52, 5 July 2020 (UTC) the editor indicated they want this on the article talk page only PainProf (talk) 03:27, 5 July 2020 (UTC)

Nomination of Variable volume pharmacokinetic models for deletion

A discussion is taking place as to whether the article Variable volume pharmacokinetic models is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Wikipedia:Articles for deletion/Variable volume pharmacokinetic models until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. PainProf (talk) 04:05, 5 July 2020 (UTC)