Interpretations of Probability.pdf
... theory — ‘standard’ both in the sense of being the orthodoxy, and in its employment of standard, as opposed to ‘non-standard’ real numbers. See Skyrms 1980.) In any case, our list is already long enough to help in our assessment of the leading interpretations on the ...
... theory — ‘standard’ both in the sense of being the orthodoxy, and in its employment of standard, as opposed to ‘non-standard’ real numbers. See Skyrms 1980.) In any case, our list is already long enough to help in our assessment of the leading interpretations on the ...
pdf
... still be accepted with high probability, as long as it is -close to some k-junta.) The tester also returns a set of k blocks (disjoint subsets of indices of the n variables) such that there is a k-junta h that is O()-close to f and has all its relevant variables in one of the k blocks, with no blo ...
... still be accepted with high probability, as long as it is -close to some k-junta.) The tester also returns a set of k blocks (disjoint subsets of indices of the n variables) such that there is a k-junta h that is O()-close to f and has all its relevant variables in one of the k blocks, with no blo ...
One-Way Functions, Hard on Average Problems, and Statistical Zero
... Suppose (towards the contradiction) that there exists a PPT algorithm A(; ; ) which, given (x i S b (x)(!0 ) " i) nds ! (almost) uniformly distributed among all ! which satisfy F bV (x; i; !) = (x i S b (x)(!0 ) " i). Using A as a subroutine, we construct A0 which can be used in place of ...
... Suppose (towards the contradiction) that there exists a PPT algorithm A(; ; ) which, given (x i S b (x)(!0 ) " i) nds ! (almost) uniformly distributed among all ! which satisfy F bV (x; i; !) = (x i S b (x)(!0 ) " i). Using A as a subroutine, we construct A0 which can be used in place of ...
Roulette
... Random variables are numerical values associated with outcomes of experiments. The letter X is the most common symbol used to represent a random variable. If we consider a straight bet of $1 to be an experiment and X to be the net winnings for the player, then X can take on either the value of 35 (i ...
... Random variables are numerical values associated with outcomes of experiments. The letter X is the most common symbol used to represent a random variable. If we consider a straight bet of $1 to be an experiment and X to be the net winnings for the player, then X can take on either the value of 35 (i ...
Introduction to forward algorithm
... The problem is that the number of possible paths increases exponentially with the length of the sequence # of possible paths = (number of underlying states)L Problems that grow exponentially with size can only be solved by brute force for remarkably small problem sizes We need a better way!! ...
... The problem is that the number of possible paths increases exponentially with the length of the sequence # of possible paths = (number of underlying states)L Problems that grow exponentially with size can only be solved by brute force for remarkably small problem sizes We need a better way!! ...
Statistical Tests for Contagion in Observational Social Network Studies
... Christakis and Fowler’s paper suggesting that obesity may spread along social ties [3] has sparked years of discussion about what constitutes evidence of contagion in observational social network studies (see, e.g., this recent review [2]). The most general result from the causal modeling perspectiv ...
... Christakis and Fowler’s paper suggesting that obesity may spread along social ties [3] has sparked years of discussion about what constitutes evidence of contagion in observational social network studies (see, e.g., this recent review [2]). The most general result from the causal modeling perspectiv ...
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.