Probability Theory
... Let us show that one of the events (1.3) and (1.4) will always take place, which would imply that the sum of their probabilities is at least 1, and hence prove (1.2). Indeed, assume that the event (1.3) does not take place, that is, some column contains only ...
... Let us show that one of the events (1.3) and (1.4) will always take place, which would imply that the sum of their probabilities is at least 1, and hence prove (1.2). Indeed, assume that the event (1.3) does not take place, that is, some column contains only ...
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... tandem exponent for many MGS–MGC pairs. We next observe that Theorems 1 and 2 can also be proved for memoryless Laplacian sources (MLSs) under the magnitude-error distortion measure. Using a similar approach, we establish upper and lower bounds for the JSCC excess distortion exponent for the lossy t ...
... tandem exponent for many MGS–MGC pairs. We next observe that Theorems 1 and 2 can also be proved for memoryless Laplacian sources (MLSs) under the magnitude-error distortion measure. Using a similar approach, we establish upper and lower bounds for the JSCC excess distortion exponent for the lossy t ...
Probability and Statistics Prof. Dr. Somesh Kumar Department of
... distribution of the discrete case.In the geometric distribution,we were considering Bernoullian trials and we were waiting for the first success or first occurrence. So, here also, it saysPoisson process and we are waiting for the first occurrence. So, in a sense,thisexponential distribution is a co ...
... distribution of the discrete case.In the geometric distribution,we were considering Bernoullian trials and we were waiting for the first success or first occurrence. So, here also, it saysPoisson process and we are waiting for the first occurrence. So, in a sense,thisexponential distribution is a co ...
ENTROPIES AND RATES OF CONVERGENCE
... estimates. Note that the Dirichlet process always selects discrete distributions and hence it cannot be directly used as a prior on densities. In a recent article, Ghosal, Ghosh and Ramamoorthi (1999a) showed that the Dirichlet mixture of normal prior gives rise to a consistent posterior under gener ...
... estimates. Note that the Dirichlet process always selects discrete distributions and hence it cannot be directly used as a prior on densities. In a recent article, Ghosal, Ghosh and Ramamoorthi (1999a) showed that the Dirichlet mixture of normal prior gives rise to a consistent posterior under gener ...
ENTROPIES AND RATES OF CONVERGENCE FOR MAXIMUM OF NORMAL DENSITIES
... estimates. Note that the Dirichlet process always selects discrete distributions and hence it cannot be directly used as a prior on densities. In a recent article, Ghosal, Ghosh and Ramamoorthi (1999a) showed that the Dirichlet mixture of normal prior gives rise to a consistent posterior under gener ...
... estimates. Note that the Dirichlet process always selects discrete distributions and hence it cannot be directly used as a prior on densities. In a recent article, Ghosal, Ghosh and Ramamoorthi (1999a) showed that the Dirichlet mixture of normal prior gives rise to a consistent posterior under gener ...
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... The sign of age was expected to be negative. The assumption is based on the research finding of Cordell et. al. (1996) which reports the inverse relationship between the age and participation in many outdoor recreation activities. It is hypothesized that age, which measures the activeness of people, ...
... The sign of age was expected to be negative. The assumption is based on the research finding of Cordell et. al. (1996) which reports the inverse relationship between the age and participation in many outdoor recreation activities. It is hypothesized that age, which measures the activeness of people, ...
New Perspectives on the Complexity of Computational Learning, and Other
... making any progress, but his enthusiasm for research and the excitement he brought to each discussion was infectious, and I would walk away with new ideas and new optimism. By not only advancing the state of the art in our field but also taking the time to explain our area to other mathematicians, ot ...
... making any progress, but his enthusiasm for research and the excitement he brought to each discussion was infectious, and I would walk away with new ideas and new optimism. By not only advancing the state of the art in our field but also taking the time to explain our area to other mathematicians, ot ...
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... the first to examine explanation. It has been has analyzed by philosophers for many years. Traditionally, it has been modeled by introducing a deductive relation between the explanation and the fact to be explained (explanandum) (Hempel and Oppenheim 1948). While perhaps applicable to scientific enq ...
... the first to examine explanation. It has been has analyzed by philosophers for many years. Traditionally, it has been modeled by introducing a deductive relation between the explanation and the fact to be explained (explanandum) (Hempel and Oppenheim 1948). While perhaps applicable to scientific enq ...
NBER WORKING PAPER SERIES Darrell Duffie
... In applications, random-matching models have also allowed for random mutation of agents, obviously in genetics, and in economics via random changes in preferences, productivity, or endowments. Typical models are also based on “random search,” meaning that the time at which a given agent is matched i ...
... In applications, random-matching models have also allowed for random mutation of agents, obviously in genetics, and in economics via random changes in preferences, productivity, or endowments. Typical models are also based on “random search,” meaning that the time at which a given agent is matched i ...
Mechanism Design with Selective Verification
... Due to the space limitations, some proofs and technical claims are omitted from this extended abstract. The full version of this work is available at [Fotakis et al. 2015b]. 1.3. Related Previous Work ...
... Due to the space limitations, some proofs and technical claims are omitted from this extended abstract. The full version of this work is available at [Fotakis et al. 2015b]. 1.3. Related Previous Work ...
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.