A CEP should be used in a situation where there is unmeasured uncertainty, where the model’s use of the CEP is to drive a deterministic response that directly determines the outcomes (i.e. CEP value x causes future a). A CEP is not required; however, in arguments by cases (especially where humans are involved) a model using CEPs often is the simplest and easiest way to get accurate-enough results, or to convey where uncertainty comes from (which enables the recognition of a gamble or even guess as resolution).
As such, the correct handling of a CEP depends on the model template:
– In Newtonian physics and other well-defined, often repeated experimental or real-life situations, with prediction accuracy over 99%, the CEP is bounded by the probability space of the surrounding physical measurements, and feasibility is proven by one example (or multiple as the case requires).
– In situations where prediction accuracy is over 99% but only in limited conditions and where an explanation for the limited applicability is not known, the CEP is the Bayesian variable (or depending on the measurement ability of the system, variables) in question, and the bounds are the logical range of the variable as suggested by solving for the operation of the system (in other words the bounds are the combination of hidden variables that make this system behave this way in this situation). So the correct handling of the CEPs likely is a joint probability type problem. The system usually is physically based, so strictly there always is feasibility of any individual variable (although historical data might establish a probability ranking).
– In situations where prediction accuracy in the short term is high but long-term prediction accuracy is low (e.g. the weather), any CEPs would depend on the specific models in question, but usually this inaccuracy is attributed to model error, model computational error, or measurement limitations/error. Hence unless you treat the missing measurements or measurement error as the CEP, and use that to validate the facts and model, there are no CEPs. The issue you run into with that approach is that the CEP might not be falsifiable, because the model is accurate regardless of the CEP in the short term and inaccurate regardless of the CEP in the long term, therefore you aren’t really estimating anything.
– In situations where the short-term prediction is unreliable but the long-term prediction is accurate, the CEP usually revolves around the convergence to the long-term prediction and tends to be purely synthetic, therefore dubious (unless it is characterized some other way, in which case it tends to be a fact). A sort of degenerate CEP can exist where the short-term noise factors are treated as CEPs and then the model is back-tested when the noise factors are known. However, since the noise factors aren’t noise, these degenerate CEPs wind up being effectively synthetic averages in prediction, which may not even be a CEP, but rather a historically-derived or empirically-derived fact or known behavior.
– In situations where the prediction accuracy is low but higher than a random distribution among cases, the CEP is the driver of the non-random distribution, and/or is the stochastic variable(s). Hence in predicting certain kinds of human behavior, the CEP is the probability of human decisions amongst the alternatives, which is the reduction of the probability distribution amongst the history of human beings; because this history for an individual is weighted on an individual as well, normally these items are identified as CEPs because various historical interpretations, in the short run, are noisy and so failure in short run isn’t even necessarily indicative of wrong values over the whole data set.
– With seemingly random events, with few or no clear correlations, the proposed CEPs usually wind up being posited facts or suppositions, and so don’t really admit of rigorous bound. This is not surprising since this class of phenomena is in general unpredictable, therefore there is high ambiguity between the pasts that prevents the bounds of a CEP, or really even the construction of an agreed-upon model.
There is one other situation where a CEP may be useful: there are some situations where it’s easier from a work perspective to transform a low-accuracy prediction problem into a set of higher-accuracy prediction models and a set of CEPs that represent the unknowns or gross error. This is somewhat sloppy practice, but if you just need a bounding box to make sure you aren’t going to head to a certain bad state, this may be a work-optimal way of approaching the prediction problem. Note the CEPs will be a mess and usually at least partially synthetic, therefore likely will be more heavily scrutinized. In that case it is helpful to show the sensitivity analysis indicating that even if you are way off, the overall conclusion most likely still is correct. Anyone that shows up with a better model ensemble will obsolete your analysis (although your analysis still may be helpful as a sanity check).
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Explanation
The “normal” definition of a CEP is somewhat synthetic, based on the concept that it cannot have a sufficiently narrow bound to be unambiguous (otherwise it would be a fact). That comes from the objective materialist intuition about there always being an unambiguous state.
From the functional perspective, the model or the value judgments on the model predictions are influenced by the various values the CEP could take. Hence the reason why we care about the bounds of the CEP is because they ripple to our conclusions.
How do we know the models are parameterized by the CEP variables? Why do we even believe the phenomena are not random, and that the CEP has meaningful bounds? We know that in some cases, the models need structured CEPs because the facts (with measured error bounds) do not strongly predict the outcomes, and because outcomes in these situations (i.e. past x+n) have discrete values and/or align to high-correlation model templates. To force the models to converge to the clearly predictable and limited futures (or pasts, as this is an explanation), we require structured or somehow controlling variables to eliminate the universe of other futures. A well-bounded, essential/fundamental CEP completes a model calculation (mathematically) and is the simplest way to represent the lack of knowledge or control over the situation. What does that mean in practice?
Consider the following example: you want to ban guns in a country. You may know how many guns are out there, how many people are in the country, how many criminals are out there, and so on. Usually you want to ban the guns to reduce the overall homicide rate (there are other reasons but I’m ignoring them for simplicity of explanation of concept). From a physical perspective, you know that a person shooting another person with a gun tends to have a higher lethality than other methods, and that your population of criminals is going to determine how many homicide attempts are made. In other words, you know basically every average input to a physically sound (99%+ correlation) system, and the transfer rules, except for how many criminals will actually get guns in the new regime and how lethal the alternative means of homicide will be.
The biggest issue is that you can’t just use the existing numbers for the alternative means of homicide because the criminals you are converting to alternative means may be more or less committed than the existing criminals; likewise the targets may be softer or harder. Depending on the present availability of guns and the ultimate effectiveness of the ban, you may be looking at a situation where your existing stabbing/poisoning/bludgeoning/car assault data has no relationship to the conversion, because your motivated criminals may be massively more capable than criminals of passion and stupidity. Likewise the data from other jurisdictions may not be directly applicable (or perhaps contradictory) either from an overall crime perspective or from the mix of crimes, and amongst the gun control levels in question.
In the gun control example, our decision hinges directly on those conversion factors because we all agree what the future will be given those conversions, we all agree the conversions are based on human behavior translated into physical action, yet the futures hugely diverge based on those values. In other words, we have a series of nearly 100% perfect models that we already know and use and that will work, and we know with reasonable bounds the set of futures that are possible (depends on situation, but likely under by previous less-lethal data and over by current lethality data), we just lack a few critical values (primarily based on human behavior) to complete the causality chain and allow us to compute the models from the mass of facts to the limited futures. Given the localization of the phenomena in question, indicating alternative hypotheses or approaches are unlikely to improve the prediction accuracy, the CEP is the simplest way to explain the uncertainty in the estimation that prevents us from knowing the future in advance.
It’s not correct to claim CEPs that invalidate model templates, since the model templates are pretty simple and very predictive of large swaths of at least physical phenomena. Hence for certain model templates, rather than accepting the effective supposition in contradiction to weight of evidence that the posited CEP (which by its nature is uncertain) dominates the template, we say that each model template has admissible CEP options that are compatible with the phenomena they predict. This is mathematically supported by the past x+n reasoning for each model template; a CEP cannot give a model template more or less predictive power than it inherently can hold, but it can provide an at least localized bounding of the uncertainty in a future prediction and give some hint as to what the future hinges on.