Philosophy of Probability
... then Ω would be the set {1, 2, 3, 4, 5, 6}. From this set of elementary events, we can construct other, less fine–grained events. For example, there is the event that an odd number comes up. We represent this event with the set {1, 3, 5}. Or, there is the event that some number greater than two come ...
... then Ω would be the set {1, 2, 3, 4, 5, 6}. From this set of elementary events, we can construct other, less fine–grained events. For example, there is the event that an odd number comes up. We represent this event with the set {1, 3, 5}. Or, there is the event that some number greater than two come ...
The Principle of Sufficient Reason and Probability
... flipped a thousand times, and about 750 times the coin has landed heads. There is a very natural inference: The coin is loaded in such a way as to have approximately a 3/4 chance of landing heads. This natural inference leads to further predictions of the coin’s behavior. Frequency-to-chance inferen ...
... flipped a thousand times, and about 750 times the coin has landed heads. There is a very natural inference: The coin is loaded in such a way as to have approximately a 3/4 chance of landing heads. This natural inference leads to further predictions of the coin’s behavior. Frequency-to-chance inferen ...
The Topology of Change: Foundations of Probability with Black Swans
... theory to underestimate the likelihood of change. In a situation of change, events that are rare become frequent and events that are frequent become rare. Therefore by ignoring rare events we tend to underestimate the possibility of change. In a slight abuse of language it could be said that classic ...
... theory to underestimate the likelihood of change. In a situation of change, events that are rare become frequent and events that are frequent become rare. Therefore by ignoring rare events we tend to underestimate the possibility of change. In a slight abuse of language it could be said that classic ...
Inventory management
... depending on whether demand is continuous (e.g. normal) or discrete. We begin with continuous case. Suppose demand for apple cider at a downtown street stand varies continuously according to a normal distribution with a mean of 200 liters per week and a standard deviation of 100 liters per week: ...
... depending on whether demand is continuous (e.g. normal) or discrete. We begin with continuous case. Suppose demand for apple cider at a downtown street stand varies continuously according to a normal distribution with a mean of 200 liters per week and a standard deviation of 100 liters per week: ...
Dictatorships, Juntas, and Monomials
... many applications. Such variables are called relevant variables, and they arise in the study of natural phenomena, where there are numerous variables (or attributes) that describe the phenomena but only few of them are actually relevant. Typically, one does not know a priori which of the ℓ variables ...
... many applications. Such variables are called relevant variables, and they arise in the study of natural phenomena, where there are numerous variables (or attributes) that describe the phenomena but only few of them are actually relevant. Typically, one does not know a priori which of the ℓ variables ...
Philosophies of Probability
... In fact, despite Popper’s intentions, the propensity theory interprets probability defined over repeatable variables, not single-case variables. If, for example, V consists of repeatable variables A and B, where A stands for age of vehicles selected at random in London in 2010 and B stands for break ...
... In fact, despite Popper’s intentions, the propensity theory interprets probability defined over repeatable variables, not single-case variables. If, for example, V consists of repeatable variables A and B, where A stands for age of vehicles selected at random in London in 2010 and B stands for break ...
A Counterexample to Modus Tollens | SpringerLink
... Now it is clear that if this kind analysis is correct, the inference we began with is not plausibly an instance of MT. For on such an analysis, what is negated in (P2) is not even a constituent in (P1); a fortiori, what is negated is not the consequent of (P1). (I take it the consequent of a conditi ...
... Now it is clear that if this kind analysis is correct, the inference we began with is not plausibly an instance of MT. For on such an analysis, what is negated in (P2) is not even a constituent in (P1); a fortiori, what is negated is not the consequent of (P1). (I take it the consequent of a conditi ...
"Approximation Theory of Output Statistics,"
... Definition 6 (e.g., [3]): The variational distance or Iidistance between two distributions P and Q defined on the same measurable space (R, 9) is ...
... Definition 6 (e.g., [3]): The variational distance or Iidistance between two distributions P and Q defined on the same measurable space (R, 9) is ...
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... particular, we increase the probability that variables are set to 1 to 1/polylog n from 1/m by restricting the matchings to be contained in bipartite graphs G of polylog n degree. Thus we can keep as many as n/polylog n of the holes unmatched in each round. Therefore, by choosing the exponents in th ...
... particular, we increase the probability that variables are set to 1 to 1/polylog n from 1/m by restricting the matchings to be contained in bipartite graphs G of polylog n degree. Thus we can keep as many as n/polylog n of the holes unmatched in each round. Therefore, by choosing the exponents in th ...
Rectangles Are Nonnegative Juntas - Computer Science
... cannot be approximated point-wise with a low-degree polynomial, one obtains lower bounds against any bounded-error protocol computing f ◦ g n . A technical convenience that will be useful for us is that since randomized protocols are essentially linear combinations of 0/1-labeled rectangles R, it su ...
... cannot be approximated point-wise with a low-degree polynomial, one obtains lower bounds against any bounded-error protocol computing f ◦ g n . A technical convenience that will be useful for us is that since randomized protocols are essentially linear combinations of 0/1-labeled rectangles R, it su ...
Investment and Bargaining
... investment level is optimal and thus investment decisions cannot be the source of strategic uncertainty. In contrast we allow for the possibility that, in equilibrium, players cannot perfectly predict the investment decisions of each other. We also allow for interdependent values (investments with e ...
... investment level is optimal and thus investment decisions cannot be the source of strategic uncertainty. In contrast we allow for the possibility that, in equilibrium, players cannot perfectly predict the investment decisions of each other. We also allow for interdependent values (investments with e ...
Approximations of upper and lower probabilities by measurable
... shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The study of the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] can be split into two different subproblems: on the one hand, we need to study the convexity of the set P(Γ ...
... shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The study of the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] can be split into two different subproblems: on the one hand, we need to study the convexity of the set P(Γ ...
Schrödinger`s cat
... have the “nice” properties which would allow any reasonable model-theoretic treatment (as we understand it). The problematic part of this two-sorted structure seems S to be the sort of points: For example, given events {ai : i < ω}, the property a = i<ω ai , which is of fundamental importance to mea ...
... have the “nice” properties which would allow any reasonable model-theoretic treatment (as we understand it). The problematic part of this two-sorted structure seems S to be the sort of points: For example, given events {ai : i < ω}, the property a = i<ω ai , which is of fundamental importance to mea ...
Probability box
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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 modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.