The Entropy of Musical Classification A Thesis Presented to
... excitement of my fellow Reedies and their nearly ubiquitous enthusiasm for music. This year more than any other has proven to me that there is no other place quite like Reed, for me at least. I would also like to thank my “wallmate” in Old Dorm Block for playing the most ridiculous pop music, not ju ...
... excitement of my fellow Reedies and their nearly ubiquitous enthusiasm for music. This year more than any other has proven to me that there is no other place quite like Reed, for me at least. I would also like to thank my “wallmate” in Old Dorm Block for playing the most ridiculous pop music, not ju ...
A Probabilistic Boolean Logic and its Meaning
... known to be true with certainty, is Q true ?. For example, in several artificial intelligence applications and expert systems, rules and data are not known with certainty and only strongly indicated by evidence. With this as motivation, several researchers (see Cox [15], Nilsson [49], Fagin and Halp ...
... known to be true with certainty, is Q true ?. For example, in several artificial intelligence applications and expert systems, rules and data are not known with certainty and only strongly indicated by evidence. With this as motivation, several researchers (see Cox [15], Nilsson [49], Fagin and Halp ...
pdf
... for understanding much of the previous research in the area, as well as extending it to the first-order case. As we mentioned in the introduction, we have used plausibility in two other contexts; we briefly discuss these here. Probability theory offers many off-the-shelf tools, such as a a simple an ...
... for understanding much of the previous research in the area, as well as extending it to the first-order case. As we mentioned in the introduction, we have used plausibility in two other contexts; we briefly discuss these here. Probability theory offers many off-the-shelf tools, such as a a simple an ...
WEAK AND STRONG LAWS OF LARGE NUMBERS FOR
... By our analysis, we establish that laws of large numbers can be formulated under conditions that are much weaker than what is usually assumed. This will be explained in much more detail in the following sections, but it behoves us here to at least indicate in what way our assumptions are indeed much ...
... By our analysis, we establish that laws of large numbers can be formulated under conditions that are much weaker than what is usually assumed. This will be explained in much more detail in the following sections, but it behoves us here to at least indicate in what way our assumptions are indeed much ...
Chapter 6 of notes file
... A stationary stochastic process is a collection {ξn : n ∈ Z} of random variables with values in some space (X, B) such that the joint distribution of (ξn1 , · · · , ξnk ) is the same as that of (ξn1 +n , · · · , ξnk +n ) for every choice of k ≥ 1, and n, n1 , · · · , nk ∈ Z. Assuming that the space ...
... A stationary stochastic process is a collection {ξn : n ∈ Z} of random variables with values in some space (X, B) such that the joint distribution of (ξn1 , · · · , ξnk ) is the same as that of (ξn1 +n , · · · , ξnk +n ) for every choice of k ≥ 1, and n, n1 , · · · , nk ∈ Z. Assuming that the space ...
Logarithmic Concave Measures and Related Topics
... Inequality (2.4) gives an immediate proof for Theorem 2. The proof of the inequality is, however, very sophisticated. It can be established relatively easily for the case of logarithmic concave functions f , g which will suce for the proof of Theorem 2 and leads to a simplication in the proof of t ...
... Inequality (2.4) gives an immediate proof for Theorem 2. The proof of the inequality is, however, very sophisticated. It can be established relatively easily for the case of logarithmic concave functions f , g which will suce for the proof of Theorem 2 and leads to a simplication in the proof of t ...
Probabilistic reasoning with answer sets
... This paper is concerned with defining the syntax and semantics of P-log, and a methodology of its use for knowledge representation. Whereas much of the current research in probabilistic logical languages focuses on learning, our main purpose, by contrast, is to elegantly and straightforwardly repres ...
... This paper is concerned with defining the syntax and semantics of P-log, and a methodology of its use for knowledge representation. Whereas much of the current research in probabilistic logical languages focuses on learning, our main purpose, by contrast, is to elegantly and straightforwardly repres ...
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.