If you had been a security policy-maker in the world's greatest power in 1900, you would have been a Brit, looking warily at your age-old enemy, France.I think you could maybe nitpick some holes in it for historical accuracy, but the basic point - that geopolitical tides in the twentieth century varied dramatically at ten year intervals - is a cogent one, and its point is underscored by the fact that five months after it was written, the world's whole geopolitical outlook was upended catastrophically by 9/11.
By 1910, you would be allied with France and your enemy would be Germany.
By 1920, World War I would have been fought and won, and you'd be engaged in a naval arms race with your erstwhile allies, the U.S. and Japan.
By 1930, naval arms limitation treaties were in effect, the Great Depression was underway, and the defense planning standard said "no war for ten years."
Nine years later World War II had begun.
By 1950, Britain no longer was the worlds greatest power, the Atomic Age had dawned, and a "police action" was underway in Korea.
Ten years later the political focus was on the "missile gap," the strategic paradigm was shifting from massive retaliation to flexible response, and few people had heard of Vietnam.
By 1970, the peak of our involvement in Vietnam had come and gone, we were beginning détente with the Soviets, and we were anointing the Shah as our protégé in the Gulf region.
By 1980, the Soviets were in Afghanistan, Iran was in the throes of revolution, there was talk of our "hollow forces" and a "window of vulnerability," and the U.S. was the greatest creditor nation the world had ever seen.
By 1990, the Soviet Union was within a year of dissolution, American forces in the Desert were on the verge of showing they were anything but hollow, the U.S. had become the greatest debtor nation the world had ever known, and almost no one had heard of the internet.
Ten years later, Warsaw was the capital of a NATO nation, asymmetric threats transcended geography, and the parallel revolutions of information, biotechnology, robotics, nanotechnology, and high density energy sources foreshadowed changes almost beyond forecasting.
All of which is to say that I'm not sure what 2010 will look like, but I'm sure that it will be very little like we expect, so we should plan accordingly.
Epistemic uncertainty is something you don't know but is, at least in theory, knowable. If you wanted to predict the workings of a mystery machine, skilled engineers could, in theory, pry it open and figure it out. Mastering mechanisms is a prototypical clocklike forecasting challenge. Aleatory uncertainty is something you not only don't know; it is unknowable. No matter how much you want to know it will rain in Philadelphia one year from now, no matter how many great meteorologists you consult, you can't outguess the seasonal averages. You are dealing with an intractably cloud-like problem, with uncertainty that is impossible, even in theory, to eliminate.The issue with my investments career is that the problems I encounter fall under "aleatory uncertainty." No matter how much you try to guess where rents will be in Houston in five years, the truth is pretty fundamentally unknowable. I'd like a career where I focus on big, hairy, yet tangible issues that fall under "epistemic uncertainty."
We show that probability dilution is a symptom of a fundamental deficiency in probabilistic representations of statistical inference, in which there are propositions that will consistently be assigned a high degree of belief, regardless of whether or not they are true. We call this deficiency false confidence. [...] We introduce the Martin–Liu validity criterion as a benchmark by which to identify statistical methods that are free from false confidence. Such inferences will necessarily be non-probabilistic.From Section 3(d):
False confidence is the inevitable result of treating epistemic uncertainty as though it were aleatory variability. Any probability distribution assigns high probability values to large sets. This is appropriate when quantifying aleatory variability, because any realization of a random variable has a high probability of falling in any given set that is large relative to its distribution. Statistical inference is different; a parameter with a fixed value is being inferred from random data. Any proposition about the value of that parameter is either true or false. To paraphrase Nancy Reid and David Cox,3 it is a bad inference that treats a false proposition as though it were true, by consistently assigning it high belief values. That is the defect we see in satellite conjunction analysis, and the false confidence theorem establishes that this defect is universal.From Section 5:
This finding opens a new front in the debate between Bayesian and frequentist schools of thought in statistics. Traditional disputes over epistemic probability have focused on seemingly philosophical issues, such as the ontological inappropriateness of epistemic probability distributions [15,17], the unjustified use of prior probabilities [43], and the hypothetical logical consistency of personal belief functions in highly abstract decision-making scenarios [13,44]. Despite these disagreements, the statistics community has long enjoyed a truce sustained by results like the Bernstein–von Mises theorem [45, Ch. 10], which indicate that Bayesian and frequentist inferences usually converge with moderate amounts of data.
The false confidence theorem undermines that truce, by establishing that the mathematical form in which an inference is expressed can have practical consequences. This finding echoes past criticisms of epistemic probability levelled by advocates of Dempster–Shafer theory, but those past criticisms focus on the structural inability of probability theory to accurately represent incomplete prior knowledge, e.g. [19, Ch. 3]. The false confidence theorem is much broader in its implications. It applies to all epistemic probability distributions, even those derived from inferences to which the Bernstein–von Mises theorem would also seem to apply.
Simply put, it is not always sensible, nor even harmless, to try to compute the probability of a non-random event. In satellite conjunction analysis, we have a clear real-world example in which the deleterious effects of false confidence are too large and too important to be overlooked. In other applications, there will be propositions similarly affected by false confidence. The question that one must resolve on a case-by-case basis is whether the affected propositions are of practical interest. For now, we focus on identifying an approach to satellite conjunction analysis that is structurally free from false confidence.
The work presented in this paper has been done from a fundamentally frequentist point of view, in which θ (e.g. the satellite states) is treated as having a fixed but unknown value and the data, x, (e.g. orbital tracking data) used to infer θ are modelled as having been generated by a random process (i.e. a process subject to aleatory variability). Someone fully committed to a subjectivist view of uncertainty [13,44] might contest this framing on philosophical grounds. Nevertheless, what we have established, via the false confidence phenomenon, is that the practical distinction between the Bayesian approach to inference and the frequentist approach to inference is not so small as conventional wisdom in the statistics community currently holds. Even when the data are such that results like the Bernstein-von Mises theorem ought to apply, the mathematical form in which an inference is expressed can have large practical consequences that are easily detectable via a frequentist evaluation of the reliability with which belief assignments are made to a proposition of interest (e.g. ‘Will these two satellites collide?’).[boldface emphasis mine]
[...]
There are other engineers and applied scientists tasked with other risk analysis problems for which they, like us, will have practical reasons to take the frequentist view of uncertainty. For those practitioners, the false confidence phenomenon revealed in our work constitutes a serious practical issue. In most practical inference problems, there are uncountably many propositions to which an epistemic probability distribution will consistently accord a high belief value, regardless of whether or not those propositions are true. Any practitioner who intends to represent the results of a statistical inference using an epistemic probability distribution must at least determine whether their proposition of interest is one of those strongly affected by the false confidence phenomenon. If it is, then the practitioner may, like us, wish to pursue an alternative approach.
Aleatory uncertainty is typically what is associated with uncertainty and is known as irreducible uncertainty since enough information is known to describe a continuous random variable X by a CDF given by (1) F (x, θ) = ∫ − ∞ x f (x, θ) d x where x is a data point of a random variable X and f represents the probability density function (PDF) of x occurring in the data set . Therefore, aleatory uncertainty can be defined as the internal randomness of phenomena . Key features of Epistemic and Aleatory Uncertainty. Key features characterizing pure epistemic and pure aleatory uncertainty are distinguished according to judgement and decision making. Representation The effects of aleatory uncertainty can also be characterized using probabilities, however, the specific outcomes are not predictable with any level of certainty. This kind of uncertainty is considered as irreducible although its effects can be mitigated by introducing margins in the form of such things as extra resources, time, and capacity to help mitigate the effects. Pure aleatory uncertainty, in contrast: (1) is represented in relation to a class of possible outcomes, (2) is focused on assessing an event’s propensity, (3) is naturally measured by relative frequency, and (4) is attributed to stochastic behavior. Epistemic! Uncertainty is conveyed in only half of patient consultations. When uncertainty is communicated, oncologists mainly refer to aleatory uncertainty. This is also the type of uncertainty that most patients perceive and seem comfortable discussing. Given that it is increasingly common for clinicians to … Aleatory variability is the natural randomness in a process. For discrete variables, the randomness is parameterized by the probability of each possible value. For continuous variables, the randomness is parameterized by the probability density function. Epistemic uncertainty is the scientific uncertainty in the model of the process. It is due to Deriving from the Latin noun alea, which refers to a kind of dice game, aleatory was first used in English in the late 17th century to describe things that are dependent on uncertain odds, much like a roll of the dice. The term now describes things that occur by sheer chance or accident, such as the unlucky bounce of a golf shot or the unusual ... 6 Aleatory Uncertainty and Epistemic Uncertainty • Aleatory uncertainty is an inherent variation associated with the physical system or the environment – Also referred to as variability, irreducible uncertainty, and stochastic uncertainty, random uncertainty • Examples: – Variation in atmospheric conditions and angle of attack for inlet conditions – Variation in fatigue life of ... Aleatory Uncertainty. Let us start with the overfitting most machine learning practitioners are familiar with: overfitting caused by aleatory uncertainty, simply said overfitting caused by noisy data. Here we have to deal w ith the fact, that the process generating real data, oftentimes, exhibits intrinsic randomness. "Aleatory" and "Epistemic" Uncertainties Terminology/concepts built into multiple documents, e.g., • ASME/ANS PRA Standard • Regulatory Guides 1 200 aleatory uncertainty: the uncertainty inherent in a nondeterministic (s tochastic, random) phenomenon… is reflected by modeling the – 1.200 phenomenon in terms of a probabilistic – 1.174
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty ... Skip navigation Sign in. Search "See You on the Other Side" is a brand new composition by John Dorhauer written specifically for remote recording, and it uses aleatory and Ligeti-inspired textures to reflect on life in quarantine. Visualizing high-dimensional spheres to understand a surprising puzzle.Home page: https://www.3blue1brown.com/Brought to you by Brilliant: https://brilliant....
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