A note on the random greedy triangle-packing algorithm
... Wormald [11] also applied the differential-equation method to this problem, deriving an upper bound of n2−ǫ on |E(M )| for any ǫ < ǫ0 = 1/57 while stating that “some nontrivial modification would be required to equal or better Grable’s result.” Indeed, in a companion paper we combine the methods int ...
... Wormald [11] also applied the differential-equation method to this problem, deriving an upper bound of n2−ǫ on |E(M )| for any ǫ < ǫ0 = 1/57 while stating that “some nontrivial modification would be required to equal or better Grable’s result.” Indeed, in a companion paper we combine the methods int ...
BAYESIAN STATISTICS
... of the general form D = {x1 , . . . , xn }, where the xi ’s are somewhat “homogeneous” (possibly multidimensional) observations xi . Statistical methods are then typically used to derive conclusions on both the nature of the process which has produced those observations, and on the expected behaviou ...
... of the general form D = {x1 , . . . , xn }, where the xi ’s are somewhat “homogeneous” (possibly multidimensional) observations xi . Statistical methods are then typically used to derive conclusions on both the nature of the process which has produced those observations, and on the expected behaviou ...
May 24, 2000 13:43 WSPC/104-IJTAF 0034 MARKOV MARKET
... measures considered here are equivalent on null sets, in the usual sense, to the measure P , and thus admit a Radon derivative with respect to P . We denote by Ptb the value at time t of a discount bond maturing at time b ≥ t. We assume that for each given value of the maturity date the process Ptb ...
... measures considered here are equivalent on null sets, in the usual sense, to the measure P , and thus admit a Radon derivative with respect to P . We denote by Ptb the value at time t of a discount bond maturing at time b ≥ t. We assume that for each given value of the maturity date the process Ptb ...
7. Probability and Statistics Soviet Essays
... problems of the theory of probability and its most important applications. I shall therefore have to pass over in silence many special mathematical studies, and, when considering the applications, I shall pay more attention to problems of fundamental significance than to those playing an important p ...
... problems of the theory of probability and its most important applications. I shall therefore have to pass over in silence many special mathematical studies, and, when considering the applications, I shall pay more attention to problems of fundamental significance than to those playing an important p ...
Pdf - Text of NPTEL IIT Video Lectures
... 3 X , there are n random variables. Let m i be the mean of each of this random variables. And by taking two random variables at a time, we can define the covariance of these random variables, and I defines C i j as the covariance between the random variable X i and X j. This is given by expectation ...
... 3 X , there are n random variables. Let m i be the mean of each of this random variables. And by taking two random variables at a time, we can define the covariance of these random variables, and I defines C i j as the covariance between the random variable X i and X j. This is given by expectation ...
Epistemic Probability Logic Simplified
... Agent a knows φ if and only if the probability a assigns to φ equals 1. Our proposal has obvious relations to earlier proposals on combining knowledge and probability [10,15,14,7,5,13] and many more. A key difference is that these proposals do not equate knowledge with certainty. An exception to thi ...
... Agent a knows φ if and only if the probability a assigns to φ equals 1. Our proposal has obvious relations to earlier proposals on combining knowledge and probability [10,15,14,7,5,13] and many more. A key difference is that these proposals do not equate knowledge with certainty. An exception to thi ...
The expansion of random regular graphs
... η) > 4/d, the right-hand side is o(1), completing the proof. Note that we can take cd → 1/2 as d → ∞. In some ways, though, the most interesting case of Bollobás’ theorem is the d = 3 case. It implies that almost surely, h(G(n, 3)) ≥ 0.18. This was historically of great interest. In 1978, Buser had ...
... η) > 4/d, the right-hand side is o(1), completing the proof. Note that we can take cd → 1/2 as d → ∞. In some ways, though, the most interesting case of Bollobás’ theorem is the d = 3 case. It implies that almost surely, h(G(n, 3)) ≥ 0.18. This was historically of great interest. In 1978, Buser had ...
A classical measure of evidence for general null hypotheses
... data, we have problems with the conclusion, since we expected to have much more evidence against H03 than H01 and H02 . Notice that, p3 /p1 ∼ 3.3 and p3 /p2 ∼ 2.2. Many other examples for higher dimensions can be built on, but we think that these two instances are sufficient to illustrate the weakne ...
... data, we have problems with the conclusion, since we expected to have much more evidence against H03 than H01 and H02 . Notice that, p3 /p1 ∼ 3.3 and p3 /p2 ∼ 2.2. Many other examples for higher dimensions can be built on, but we think that these two instances are sufficient to illustrate the weakne ...
A Tale of Three Numbers
... One NAEP analysis of 100,000 American students found that science test scores for men were higher than the test scores for women, and this effect was statistically significant These results are unlikely if the null hypothesis, that gender plays no role in science scores, were ...
... One NAEP analysis of 100,000 American students found that science test scores for men were higher than the test scores for women, and this effect was statistically significant These results are unlikely if the null hypothesis, that gender plays no role in science scores, were ...
MARKOV CHAINS: BASIC THEORY 1.1. Definition and First
... of the transition probability matrix on the simplex is a contraction? First, it tells us that if we start the Markov chain in two different initial distributions, then the distributions after one step are closer than they were to start. Consequently, by induction, after n steps they are even closer: ...
... of the transition probability matrix on the simplex is a contraction? First, it tells us that if we start the Markov chain in two different initial distributions, then the distributions after one step are closer than they were to start. Consequently, by induction, after n steps they are even closer: ...
The Computational Power of Beeps
... The beeping model of network communication [1–3,10,14,19] assumes a collection of computational nodes, connected in a network, that interact by beeping in synchronous rounds. If a node decides to beep in a given round, it receives no feedback from the channel. On the other hand, if a node decides to ...
... The beeping model of network communication [1–3,10,14,19] assumes a collection of computational nodes, connected in a network, that interact by beeping in synchronous rounds. If a node decides to beep in a given round, it receives no feedback from the channel. On the other hand, if a node decides to ...
Full text in PDF form
... would be the most appropriate measure(s) of Ess. It seems that S(·, 1) = exp(H(·)), where H(·) is Shannon’s entropy, is the best choice; cf. Sect. 4 and 5. We also argued for expanding the key requirement P4 into a more general requirement P4∗ . The enhanced set of requirements is satisfied solely b ...
... would be the most appropriate measure(s) of Ess. It seems that S(·, 1) = exp(H(·)), where H(·) is Shannon’s entropy, is the best choice; cf. Sect. 4 and 5. We also argued for expanding the key requirement P4 into a more general requirement P4∗ . The enhanced set of requirements is satisfied solely b ...
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.