Model neurons
... Homogeneous Poisson process! The probability of having the remaining M-n bins without any spikes in them! is! ...
... Homogeneous Poisson process! The probability of having the remaining M-n bins without any spikes in them! is! ...
MCMCRev.pdf
... In (3.4), cλ are the change of basis coefficients in expressing the Jack symmetric functions in terms of the power-symmetric functions. The normalizing constant in (3.4) involves closed form, combinatorially-defined terms which will not be detailed further. Here is an aside on the cλ (·). Classical ...
... In (3.4), cλ are the change of basis coefficients in expressing the Jack symmetric functions in terms of the power-symmetric functions. The normalizing constant in (3.4) involves closed form, combinatorially-defined terms which will not be detailed further. Here is an aside on the cλ (·). Classical ...
UNIT 12 Counting and Probability
... 2 trophies left to choose from, so he can fill the second spot in 2 ways. Now he has 1 trophy left, so he has only 1 way to fill the last spot. To get the total number of ways that Ishmael can arrange the trophies, multiply all the numbers of ways: 3 · 2 · 1 = 6 ways. ■ In this example, each possibl ...
... 2 trophies left to choose from, so he can fill the second spot in 2 ways. Now he has 1 trophy left, so he has only 1 way to fill the last spot. To get the total number of ways that Ishmael can arrange the trophies, multiply all the numbers of ways: 3 · 2 · 1 = 6 ways. ■ In this example, each possibl ...
A Puzzle about Knowing Conditionalsi Daniel Rothschild University
... You might think that considerations along the lines of Williamson’s (2000) safety principle (or his margin for error principles) precludes you from knowing that you know that the first n coins didn’t land heads (where n is, again, the least number such that you know that the first n coins didn’t lan ...
... You might think that considerations along the lines of Williamson’s (2000) safety principle (or his margin for error principles) precludes you from knowing that you know that the first n coins didn’t land heads (where n is, again, the least number such that you know that the first n coins didn’t lan ...
Reflections on Fourteen Cryptic Issues Concerning the Nature
... the pathologist whose statements we should respect: they are the experts who are engaged to codify their behaviour, to calibrate their opinions, to discuss basic principles, and thus form well-balanced conclusions that are to be considered as ‘scientifically sound’. They are the professionals in the ...
... the pathologist whose statements we should respect: they are the experts who are engaged to codify their behaviour, to calibrate their opinions, to discuss basic principles, and thus form well-balanced conclusions that are to be considered as ‘scientifically sound’. They are the professionals in the ...
The Limits of Supposing: Semantic Illusions and Conditional Probability
... How, then, could reasoners resolve this impossible tension? Our hypothesis is that they would tend to respond with a failure of hypothetical thinking or, in slightly more technical terms, the ‘null model’ (i.e., the ‘vacuous’ or ‘empty’ model): previous work demonstrates (Elqayam, in press) that thi ...
... How, then, could reasoners resolve this impossible tension? Our hypothesis is that they would tend to respond with a failure of hypothetical thinking or, in slightly more technical terms, the ‘null model’ (i.e., the ‘vacuous’ or ‘empty’ model): previous work demonstrates (Elqayam, in press) that thi ...
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.