A Tutorial on Conformal Prediction
... textbook intervals as conformal prediction regions within the on-line Gaussian linear model, an on-line compression model that uses slightly weaker assumptions than the classical assumption of independent and normally distributed errors. 2.2 Confidence Says Less than Probability. Neyman’s notion of ...
... textbook intervals as conformal prediction regions within the on-line Gaussian linear model, an on-line compression model that uses slightly weaker assumptions than the classical assumption of independent and normally distributed errors. 2.2 Confidence Says Less than Probability. Neyman’s notion of ...
Induction, Rational Acceptance, and Minimally Inconsistent Sets
... a contradiction from the set of statements. A valid deductive argument that is also relevant is one such that the set of statements having as members the premises and the denial of the conclusion (or any truth functional equivalent) is not only logically inconsistent but minimally inconsistent. A se ...
... a contradiction from the set of statements. A valid deductive argument that is also relevant is one such that the set of statements having as members the premises and the denial of the conclusion (or any truth functional equivalent) is not only logically inconsistent but minimally inconsistent. A se ...
Harold Jeffreys`s Theory of Probability Revisited
... sion in those early pages are illustrated by the introduction of Ockham’s razor (the choice of the sim- 2.2 Foundational Principles plest law that fits the fact), as the meaning of what The text becomes more focused when dealing with a simplest law can be remains unclear, and the sec- the constructi ...
... sion in those early pages are illustrated by the introduction of Ockham’s razor (the choice of the sim- 2.2 Foundational Principles plest law that fits the fact), as the meaning of what The text becomes more focused when dealing with a simplest law can be remains unclear, and the sec- the constructi ...
The Applicability Problem for Chance
... What is the inductive strength of this argument? Given the connection between inductive strength and reasonable degree of confidence, the correct answer depends on how confident an agent should be that C* is true given that she is certain of P1 and P2 and has no other information that is relevant t ...
... What is the inductive strength of this argument? Given the connection between inductive strength and reasonable degree of confidence, the correct answer depends on how confident an agent should be that C* is true given that she is certain of P1 and P2 and has no other information that is relevant t ...
Arguments for–or against–Probabilism?
... leading to the axioms of probability], his choice would depend on the precise form in which the options were offered him, which would be absurd. He could have a book made against him by a cunning bettor and would then stand to lose in any event . . . Having degrees of belief obeying the laws of prob ...
... leading to the axioms of probability], his choice would depend on the precise form in which the options were offered him, which would be absurd. He could have a book made against him by a cunning bettor and would then stand to lose in any event . . . Having degrees of belief obeying the laws of prob ...
Pseudo-Bayesian Updating
... People often receive unexpected information. Even when they anticipate receiving information, they typically do not form priors over what information they will receive. Seldom, if ever, do decision makers bother to construct a joint prior on the set of signals and payoffrelevant states: waiting for ...
... People often receive unexpected information. Even when they anticipate receiving information, they typically do not form priors over what information they will receive. Seldom, if ever, do decision makers bother to construct a joint prior on the set of signals and payoffrelevant states: waiting for ...
A Puzzle About Degree of Belief
... theorems” that some Bayesians tout (see Earman 1992 for discussion). These theorems show, roughly, that in the long run, agents who give positive probability to all possibilities, and whose stream of evidence is sufficiently rich, will eventually be driven (by repeated conditionalization on the evid ...
... theorems” that some Bayesians tout (see Earman 1992 for discussion). These theorems show, roughly, that in the long run, agents who give positive probability to all possibilities, and whose stream of evidence is sufficiently rich, will eventually be driven (by repeated conditionalization on the evid ...
Continued misinterpretation of confidence intervals
... uncertainty that we have in whether a sampled interval will contain the true value. All the disagreement comes after the data are observed and an interval is computed. How do we then interpret a 95 % confidence interval? Does it have a 95 % probability of containing the true value? Neyman (1937) say ...
... uncertainty that we have in whether a sampled interval will contain the true value. All the disagreement comes after the data are observed and an interval is computed. How do we then interpret a 95 % confidence interval? Does it have a 95 % probability of containing the true value? Neyman (1937) say ...
Frequentism as a positivism: a three-tiered interpretation of probability
... probabilities can be “read off” from the actual history of real-world events, without the need to posit any unobservable entities. But taken literally, it clashes with many of our important intuitions about probability. In particular, it is a kind of operationalism about probability, and hence suffe ...
... probabilities can be “read off” from the actual history of real-world events, without the need to posit any unobservable entities. But taken literally, it clashes with many of our important intuitions about probability. In particular, it is a kind of operationalism about probability, and hence suffe ...
CHAPTER 1 0 Deductive Reasoning
... Implying with probability is the vaguer notion. Implying with probability admits of degrees. The probability usually cannot be measured with a number (the fancy phrase is ―cannot be quantified‖) but instead can only be measured as high, low, very high, and so forth. However, in those rare cases when ...
... Implying with probability is the vaguer notion. Implying with probability admits of degrees. The probability usually cannot be measured with a number (the fancy phrase is ―cannot be quantified‖) but instead can only be measured as high, low, very high, and so forth. However, in those rare cases when ...
pdf
... X = Y = {0, 1}. Suppose that our agent knows that EPrY [Y ] = PrY (Y = 1) = p for some fixed p. As before, let P be the set of distributions on X × Y with marginal PrY . Suppose further that the only actions are 0 and 1 (intuitively, these actions amount to predicting the value of Y ), and that the ...
... X = Y = {0, 1}. Suppose that our agent knows that EPrY [Y ] = PrY (Y = 1) = p for some fixed p. As before, let P be the set of distributions on X × Y with marginal PrY . Suppose further that the only actions are 0 and 1 (intuitively, these actions amount to predicting the value of Y ), and that the ...
RACSAM Rev. R. Acad. Cien. Serie A. Mat. V
... contrast, (9) and (18) can be quite small for large n if N is much larger than n. (Note that both (11) and (20) are near 1 for large n, but these probabilities refer to the event En that a further randomly chosen element will obey the stated law, not to the event that all elements in the population ...
... contrast, (9) and (18) can be quite small for large n if N is much larger than n. (Note that both (11) and (20) are near 1 for large n, but these probabilities refer to the event En that a further randomly chosen element will obey the stated law, not to the event that all elements in the population ...
Lesson 1 7•5
... standards in this cluster. A chance process is any process that is repeatable and results in one of two or more welldefined outcomes each time it is repeated. In the context of probability, observing a single outcome of a chance process is sometimes called a chance experiment. Because the term chanc ...
... standards in this cluster. A chance process is any process that is repeatable and results in one of two or more welldefined outcomes each time it is repeated. In the context of probability, observing a single outcome of a chance process is sometimes called a chance experiment. Because the term chanc ...
Logic and Fallacies
... Deductive validity is a relation between premises and conclusion. ‘Validity’ ordinarily means something like “true or relevant.” A ‘valid criticism’ is a criticism that is true or relevant to some issue being discussed. ...
... Deductive validity is a relation between premises and conclusion. ‘Validity’ ordinarily means something like “true or relevant.” A ‘valid criticism’ is a criticism that is true or relevant to some issue being discussed. ...
2CH10L1 - Kyrene School District
... numbers. The red one is more likely to land on one of the larger faces. So the likelihood is greater that you would roll a 5 with the red die than with the blue one. ...
... numbers. The red one is more likely to land on one of the larger faces. So the likelihood is greater that you would roll a 5 with the red die than with the blue one. ...
this paper - William M. Briggs
... refugee status in statistics, Franklin (2001). This is fully described Stove (1973, 1986). In any case, I do not follow Carnap’s terminology here, though I use deductive and non-deductive logic in what follows. The main purpose of this article is to survey the most common arguments used in assigning ...
... refugee status in statistics, Franklin (2001). This is fully described Stove (1973, 1986). In any case, I do not follow Carnap’s terminology here, though I use deductive and non-deductive logic in what follows. The main purpose of this article is to survey the most common arguments used in assigning ...
Confidence Sets - George Mason University
... We often want to identify a set in which a future observation on a random variable has a high probability of occurring. This kind of set is called a prediction set. For example, we may assume a given sample X1, . . . , Xn is from a N(µ, σ 2 ) and we wish to determine a measurable set C(X) such that ...
... We often want to identify a set in which a future observation on a random variable has a high probability of occurring. This kind of set is called a prediction set. For example, we may assume a given sample X1, . . . , Xn is from a N(µ, σ 2 ) and we wish to determine a measurable set C(X) such that ...
Use of WAAS for LAAS Ionosphere Threat Status Determination
... • Time averaging for slow-moving storms assumes a minimum practical speed of roughly 20 m/s – Below this speed, a hazardous gradient could persist for more than one approach (indefinitely for zero speed) ...
... • Time averaging for slow-moving storms assumes a minimum practical speed of roughly 20 m/s – Below this speed, a hazardous gradient could persist for more than one approach (indefinitely for zero speed) ...
1 1. Justification of analogical reasoning • an argument that it is
... “The supposition must be that m is an effect really dependent on some property of A, but we know not on which.” Derivative and ultimate properties: “every resemblance affords grounds for thinking that A and B share more ultimate properties” (and hence, possibly, m). Proportionality: if A and B agree ...
... “The supposition must be that m is an effect really dependent on some property of A, but we know not on which.” Derivative and ultimate properties: “every resemblance affords grounds for thinking that A and B share more ultimate properties” (and hence, possibly, m). Proportionality: if A and B agree ...
above - Anthropic Principle
... However, even with the stipulation that we take the reference class to be the class of all observers, our formulation of SSA is still vague in that it leaves open at least two important questions: What counts as an observer? And what is the sampling density with which you have been sampled? How thes ...
... However, even with the stipulation that we take the reference class to be the class of all observers, our formulation of SSA is still vague in that it leaves open at least two important questions: What counts as an observer? And what is the sampling density with which you have been sampled? How thes ...
Bayes` theorem
... Now consider the application of that line of reasoning to the examples of balls shot at random from a lottery machine. Suppose that you know that the balls in the machine are numbered sequentially (with no repeats) beginning with 1, but that you don't know how many balls there are in the machine. No ...
... Now consider the application of that line of reasoning to the examples of balls shot at random from a lottery machine. Suppose that you know that the balls in the machine are numbered sequentially (with no repeats) beginning with 1, but that you don't know how many balls there are in the machine. No ...
in-class exercises
... Instructions: Determine whether the statement, then use plus signs and Conclusion Indicators following are propositions. If some arrows to designate the argument are not propositions, see if they can structure as either a joint inference Therefore be rewritten as propositions. or an independent infe ...
... Instructions: Determine whether the statement, then use plus signs and Conclusion Indicators following are propositions. If some arrows to designate the argument are not propositions, see if they can structure as either a joint inference Therefore be rewritten as propositions. or an independent infe ...
Tools-Soundness-and-Completeness
... Answer: C. It doesn’t seem plausible to say that you have to breathe oxygen to be a whale. Suppose tomorrow a scientist discovers that one species which we have thus far been calling a species of “whale” actually breathes nitrogen. Suppose that the species is still very closely related to other whal ...
... Answer: C. It doesn’t seem plausible to say that you have to breathe oxygen to be a whale. Suppose tomorrow a scientist discovers that one species which we have thus far been calling a species of “whale” actually breathes nitrogen. Suppose that the species is still very closely related to other whal ...
how to predict future duration from present age - Philsci
... Given that Brian knows that the class will only last about another 5 minutes, it is ludicrous for Brian to assign probability 0.5 to the proposition that it will last at least another 45. The lesson here is that Gott’s argument does not have universal applicability. Gott is well aware of this: he sa ...
... Given that Brian knows that the class will only last about another 5 minutes, it is ludicrous for Brian to assign probability 0.5 to the proposition that it will last at least another 45. The lesson here is that Gott’s argument does not have universal applicability. Gott is well aware of this: he sa ...
The design argument
... So if we have good reason to believe in the multiverse, this has the makings of a good objection to the finetuning argument. But do we have good reason to believe in the multiverse? One might think that LIFE provides us with extremely strong evidence for the existence of the multiverse. After all, i ...
... So if we have good reason to believe in the multiverse, this has the makings of a good objection to the finetuning argument. But do we have good reason to believe in the multiverse? One might think that LIFE provides us with extremely strong evidence for the existence of the multiverse. After all, i ...
Doomsday argument
The Doomsday argument (DA) is a probabilistic argument that claims to predict the number of future members of the human species given only an estimate of the total number of humans born so far. Simply put, it says that supposing that all humans are born in a random order, chances are that any one human is born roughly in the middle.It was first proposed in an explicit way by the astrophysicist Brandon Carter in 1983, from which it is sometimes called the Carter catastrophe; the argument was subsequently championed by the philosopher John A. Leslie and has since been independently discovered by J. Richard Gott and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others. A more general form was given earlier in the Lindy effect, in which for certain phenomena the future life expectancy is proportional to (though not necessarily equal to) the current age, and is based on decreasing mortality rate over time: old things endure.Denoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that humans are equally likely (along with the other N − 1 humans) to find themselves at any position n of the total population N, so humans assume that our fractional position f = n/N is uniformly distributed on the interval [0, 1] prior to learning our absolute position.f is uniformly distributed on (0, 1) even after learning of the absolute position n. That is, for example, there is a 95% chance that f is in the interval (0.05, 1), that is f > 0.05. In other words we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n.If Leslie's Figure is used, then 60 billion humans have been born so far, so it can be estimated that there is a 95% chance that the total number of humans N will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1,140 billion humans will be born in 9,120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live on Earth. This problem is similar to the famous German tank problem.