Lecture 6: State-Based Methods (cont 2)
... Recall that for DTMCs, * = *P. For CTMCs, we can let Pˆ =Q I and then * =* Pˆ. Converting this to an iterative method, we write (k + 1) = (k)P. This is called the power method. – Simple, natural for DTMCs – Gets to an answer slowly – Can find a non-unique solution ...
... Recall that for DTMCs, * = *P. For CTMCs, we can let Pˆ =Q I and then * =* Pˆ. Converting this to an iterative method, we write (k + 1) = (k)P. This is called the power method. – Simple, natural for DTMCs – Gets to an answer slowly – Can find a non-unique solution ...
Ideology and existence of 50%-majority equilibria in multidimensional spatial voting models ∗
... religion (the ideological position in the ‘laïcity’ dimension) was clearly the only way to explain another (orthogonal) split of the gaullist party. Another type of political debates often builds on more than three underlying dimensions: proxy Þghts in publicly traded corporations in a context of ma ...
... religion (the ideological position in the ‘laïcity’ dimension) was clearly the only way to explain another (orthogonal) split of the gaullist party. Another type of political debates often builds on more than three underlying dimensions: proxy Þghts in publicly traded corporations in a context of ma ...
Probabilistic Algorithms
... Let 0 1. Then for any polynomial p(n) and a probabilistic TM PT1 that operates with error probability , there is a probabilistic TM PT2 that operates with an error probability 2 p ( n ) ...
... Let 0 1. Then for any polynomial p(n) and a probabilistic TM PT1 that operates with error probability , there is a probabilistic TM PT2 that operates with an error probability 2 p ( n ) ...
October 6th, 2015
... Seminar on Free Probability and Random Matrices Speaker: Mario Diaz Title: On the Speed at which Asymptotic Liberation Sequences Deliver Freeness Abstract: It is well known that certain ensembles of unitary matrices deliver asymptotic freeness under suitable conditions. Related to the intuitive ques ...
... Seminar on Free Probability and Random Matrices Speaker: Mario Diaz Title: On the Speed at which Asymptotic Liberation Sequences Deliver Freeness Abstract: It is well known that certain ensembles of unitary matrices deliver asymptotic freeness under suitable conditions. Related to the intuitive ques ...
stat11t_Chapter4S
... 1) Suppose a high school consists of 25% juniors, 15% seniors, and the remaining 60% is students of other grades. The relative frequency of students who are either juniors and seniors is 40%. We can add the relative frequencies of juniors (P(J)=0.25) and seniors (P(S)=0.15) because no student can be ...
... 1) Suppose a high school consists of 25% juniors, 15% seniors, and the remaining 60% is students of other grades. The relative frequency of students who are either juniors and seniors is 40%. We can add the relative frequencies of juniors (P(J)=0.25) and seniors (P(S)=0.15) because no student can be ...
Spectral characterization of the optional quadratic varation process (revised vers ion) ET
... As is well known in the statistical analysis of time series in discrete or continuous time, t h e periodogram can be used for estimation problems in t h e frequency domain. It follows from t h e results of the present paper that the periodogram can also be used to estimate the variance of the innova ...
... As is well known in the statistical analysis of time series in discrete or continuous time, t h e periodogram can be used for estimation problems in t h e frequency domain. It follows from t h e results of the present paper that the periodogram can also be used to estimate the variance of the innova ...
A Conditional Probability Model for Groundwater Risk Assessment
... Further, if this arguably intuitive definition of a successful mitigation effort is accepted, as it is in Bolster et al.8, aquifer contamination is only certain if all three basic events occur together, implying the alternative logic that we propose, ...
... Further, if this arguably intuitive definition of a successful mitigation effort is accepted, as it is in Bolster et al.8, aquifer contamination is only certain if all three basic events occur together, implying the alternative logic that we propose, ...
Bruno de Finetti and Imprecision
... and data one works with in applied mathematics. The jointly authored 1962 paper [14], Sul modo di scegliere le probabilità iniziali, adds some arguments to de Finetti’s ideas on imprecise probabilities while discussing Smith’s then recently published paper [36]. Recall that Smith proposed a modifica ...
... and data one works with in applied mathematics. The jointly authored 1962 paper [14], Sul modo di scegliere le probabilità iniziali, adds some arguments to de Finetti’s ideas on imprecise probabilities while discussing Smith’s then recently published paper [36]. Recall that Smith proposed a modifica ...
The ancestral process of long
... constant m and being small when compared to the total population size (resp. during passage to a scaling limit). Under such circumstances, it is then shown that the ancestral process of the population can be approximately described by a time-changed Kingman coalescent, where the (constant) time cha ...
... constant m and being small when compared to the total population size (resp. during passage to a scaling limit). Under such circumstances, it is then shown that the ancestral process of the population can be approximately described by a time-changed Kingman coalescent, where the (constant) time cha ...
Confidence analysis for nuclear arms control: SMT
... inspect only one of these two boxes. The inspecting party, say nation N2 or some third party, is given a radiation detector with a specific, known sensitivity and known false-error reporting rate. The detector shows a green or red light based on whether nuclear materials in a particular ratio of a p ...
... inspect only one of these two boxes. The inspecting party, say nation N2 or some third party, is given a radiation detector with a specific, known sensitivity and known false-error reporting rate. The detector shows a green or red light based on whether nuclear materials in a particular ratio of a p ...
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.