A Sharp Test of the Portability of Expertise ∗ Etan A. Green
... Two sets of studies on experts, one with professional soccer players and a second with chess grandmasters, examine the portability of expertise to traditional laboratory games. Chiappori, Levitt and Groseclose (2002) and Palacios-Huerta (2003) show that in professional soccer, penalty kicks are cons ...
... Two sets of studies on experts, one with professional soccer players and a second with chess grandmasters, examine the portability of expertise to traditional laboratory games. Chiappori, Levitt and Groseclose (2002) and Palacios-Huerta (2003) show that in professional soccer, penalty kicks are cons ...
Tolerance Intervals With Improved Coverage Probabilities for
... For a binomial or Poisson distribution with an unknown parameter, θ , the level (1 − α) of the confidence interval for θ are usually determined by a large-sample approximate method. TIs are then constructed based on these confidence intervals. When the sample size is large, the true coverage probabi ...
... For a binomial or Poisson distribution with an unknown parameter, θ , the level (1 − α) of the confidence interval for θ are usually determined by a large-sample approximate method. TIs are then constructed based on these confidence intervals. When the sample size is large, the true coverage probabi ...
6= BPP on the hardness of PAC learning On basing ZK
... the hidden labelling function rather than simply deciding whether it exists, as well as deal with the fact that in standard PAC learning one does not have access to the circuit generating labelled examples. In this paper we show that many standard proof techniques do not suffice to prove that the ha ...
... the hidden labelling function rather than simply deciding whether it exists, as well as deal with the fact that in standard PAC learning one does not have access to the circuit generating labelled examples. In this paper we show that many standard proof techniques do not suffice to prove that the ha ...
Full text in PDF form
... Equality obtains on the left in (10) if and only if p(Ci ) = 1 for some i: if you already know in advance that ξ will come up with state Ci , then you gain no knowledge by performing the experiment. Equality obtains on the right in (10) if and only if p(Ci ) = r−1 for each i: the most informative ex ...
... Equality obtains on the left in (10) if and only if p(Ci ) = 1 for some i: if you already know in advance that ξ will come up with state Ci , then you gain no knowledge by performing the experiment. Equality obtains on the right in (10) if and only if p(Ci ) = r−1 for each i: the most informative ex ...
PROBABILITY THEORY - PART 2 INDEPENDENT RANDOM
... is called Chebyshev’s inequality. Higher the moments that exist, better the asymptotic tail bounds that we get. For example, if E[eλX ] < ∞ for some λ > 0, we get exponential tail bounds by P(X > t) = P(eλX > eλt ) ≤ e−λt E[eλX ]. Note that X is not assumed to be non-negative in these examples as Ma ...
... is called Chebyshev’s inequality. Higher the moments that exist, better the asymptotic tail bounds that we get. For example, if E[eλX ] < ∞ for some λ > 0, we get exponential tail bounds by P(X > t) = P(eλX > eλt ) ≤ e−λt E[eλX ]. Note that X is not assumed to be non-negative in these examples as Ma ...
Conditioning using conditional expectations: The Borel
... The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which looses its mea ...
... The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which looses its mea ...
Probability Sections 12.1, 12.2, 12.3 Lecture 21 Robb T. Koether
... The “probability” that a fair coin lands head is 21 . What exactly does that mean? If I toss the coin 10 times, I will get 5 heads? That is simply not true. ...
... The “probability” that a fair coin lands head is 21 . What exactly does that mean? If I toss the coin 10 times, I will get 5 heads? That is simply not true. ...
Uncertainty171
... “A25 will get me there on time if there's no accident on the bridge and it doesn't rain and my tires remain intact etc etc.” (A1440 might reasonably be said to get me there on time but I'd have to stay overnight in the airport …) ...
... “A25 will get me there on time if there's no accident on the bridge and it doesn't rain and my tires remain intact etc etc.” (A1440 might reasonably be said to get me there on time but I'd have to stay overnight in the airport …) ...
The Markov Chain Monte Carlo revolution
... The stationary distribution is the left eigenvector proportional to (1, θ, θ, θ, θ 2, θ 2 ). This example bears a passing resemblance to the cryptography example: the set of one-to-one functions of an m-set to an n-set is replaced by the symmetric group. Presumably, the stationary distribution in th ...
... The stationary distribution is the left eigenvector proportional to (1, θ, θ, θ, θ 2, θ 2 ). This example bears a passing resemblance to the cryptography example: the set of one-to-one functions of an m-set to an n-set is replaced by the symmetric group. Presumably, the stationary distribution in th ...
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.