On the Unfortunate Problem of the Nonobservability
... and magnitude of adverse outcomes) subjects agents to just such mistakes. We argue below that, for various reasons, risk managers cannot rule out “catastrophic events”. We then show that this ever-present possibility of black swan events means that, in most situations, Risk managers are essentially ...
... and magnitude of adverse outcomes) subjects agents to just such mistakes. We argue below that, for various reasons, risk managers cannot rule out “catastrophic events”. We then show that this ever-present possibility of black swan events means that, in most situations, Risk managers are essentially ...
Is it a Crime to Belong to a Reference Class?
... signi®cant should have been obvious, given that 17 of an original 142 data points from the Drug Enforcement Administration contained inconsistent information (net weights greater than or equal to gross weights).10 We shall not dwell on such matters here. Although these details are important, the rea ...
... signi®cant should have been obvious, given that 17 of an original 142 data points from the Drug Enforcement Administration contained inconsistent information (net weights greater than or equal to gross weights).10 We shall not dwell on such matters here. Although these details are important, the rea ...
12. Probability
... S are the edge sets of the k possible subgraphs Kk . We obtain only a factor 2 improvement, but it gives the best bound known. To prove theorem 4.2, we colour the points of S blue or red independently and with equal probability. For each subset Ei , let Ai be the event that Ei is monochromatic. Then ...
... S are the edge sets of the k possible subgraphs Kk . We obtain only a factor 2 improvement, but it gives the best bound known. To prove theorem 4.2, we colour the points of S blue or red independently and with equal probability. For each subset Ei , let Ai be the event that Ei is monochromatic. Then ...
Document
... “The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is soug ...
... “The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is soug ...
Decentralized learning from failure 夡 Andreas Blume , April Mitchell Franco
... We study decentralized learning in organizations. We require agents to learn by trial and error. They can only observe success or failure and not the actions taken by other agents. A failure means that the organization will want to explore a novel action combination. Decentralization means that agen ...
... We study decentralized learning in organizations. We require agents to learn by trial and error. They can only observe success or failure and not the actions taken by other agents. A failure means that the organization will want to explore a novel action combination. Decentralization means that agen ...
Tomasz R. Bielecki (Chicago, IL) Marek Rutkowski (Warszawa
... to the familiar results concerning the case of conditionally independent random times through a judicious choice of an equivalent probability measure. Finally, it should be stressed that in our approach the migration process can also be seen as a standard Markov chain (or a conditional Markov chain) ...
... to the familiar results concerning the case of conditionally independent random times through a judicious choice of an equivalent probability measure. Finally, it should be stressed that in our approach the migration process can also be seen as a standard Markov chain (or a conditional Markov chain) ...
PDF
... reasonable one. However, as we discussed in the introduction, there are many interesting domains (e.g., our biological application) where the amount of data is small relative to the size of the model. In this case, there is usually a large number of high-scoring models, so using a single model as ou ...
... reasonable one. However, as we discussed in the introduction, there are many interesting domains (e.g., our biological application) where the amount of data is small relative to the size of the model. In this case, there is usually a large number of high-scoring models, so using a single model as ou ...
arXiv
... optimization problems, the set of stationary policies is the smallest structured set of control policies in which one can find a globally optimal policy. However, computing an optimal policy even in this class is in general computationally prohibitive for non-finite Polish (that is, complete and sep ...
... optimization problems, the set of stationary policies is the smallest structured set of control policies in which one can find a globally optimal policy. However, computing an optimal policy even in this class is in general computationally prohibitive for non-finite Polish (that is, complete and sep ...
Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial... pages 201-210, Stanford, California, June 2000
... reasonable one. However, as we discussed in the introduction, there are many interesting domains (e.g., our biological application) where the amount of data is small relative to the size of the model. In this case, there is usually a large number of high-scoring models, so using a single model as ou ...
... reasonable one. However, as we discussed in the introduction, there are many interesting domains (e.g., our biological application) where the amount of data is small relative to the size of the model. In this case, there is usually a large number of high-scoring models, so using a single model as ou ...
The Optimal Sample Complexity of PAC Learning
... Probably approximately correct learning (or PAC learning; Valiant, 1984) is a classic criterion for supervised learning, which has been the focus of much research in the past three decades. The objective in PAC learning is to produce a classifier that, with probability at least 1 − δ, has error rate ...
... Probably approximately correct learning (or PAC learning; Valiant, 1984) is a classic criterion for supervised learning, which has been the focus of much research in the past three decades. The objective in PAC learning is to produce a classifier that, with probability at least 1 − δ, has error rate ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.