Mathematical Population Genetics
... In a pure drift model, genetic variation within a population can only be eliminated, but never created. To obtain even the most basic model for evolution, we need to include mutation as the ultimate source for new variation. Just these two evolutionary forces, mutation and drift, are the only ingred ...
... In a pure drift model, genetic variation within a population can only be eliminated, but never created. To obtain even the most basic model for evolution, we need to include mutation as the ultimate source for new variation. Just these two evolutionary forces, mutation and drift, are the only ingred ...
Stable Beliefs and Conditional Probability Spaces
... However, theories attempting to provide a quantitative probabilistic definition of belief come face to face with the fact that drifting away from the probability 1 principle (or in other words adapting a version of the so - called Lockean Thesis ([24])) is incompatible with maintaining the logical c ...
... However, theories attempting to provide a quantitative probabilistic definition of belief come face to face with the fact that drifting away from the probability 1 principle (or in other words adapting a version of the so - called Lockean Thesis ([24])) is incompatible with maintaining the logical c ...
MODEL UNCERTAINTY
... Priors and Decisions. We assume that the DMs’ ex-ante information also enables them to address model uncertainty through a subjective prior probability over models; in this we follow a key tenet of the Bayesian paradigm. Prior probabilities quantify DMs’ beliefs by using analogies with betting behav ...
... Priors and Decisions. We assume that the DMs’ ex-ante information also enables them to address model uncertainty through a subjective prior probability over models; in this we follow a key tenet of the Bayesian paradigm. Prior probabilities quantify DMs’ beliefs by using analogies with betting behav ...
Vertex and Hyperedge Connectivity in Dynamic Graph Streams
... Definition 1 (Linear Sketches). A linear measurement of a hypergraph on n vertices is defined by a set of coefficients {ce : e ∈ Pr (V )} where Pr (V ) is the set of all subsets P of V of size at most r. Given a hypergraph G = (V, E), the evaluation of this measurement is defined as e∈E ce . A sketc ...
... Definition 1 (Linear Sketches). A linear measurement of a hypergraph on n vertices is defined by a set of coefficients {ce : e ∈ Pr (V )} where Pr (V ) is the set of all subsets P of V of size at most r. Given a hypergraph G = (V, E), the evaluation of this measurement is defined as e∈E ce . A sketc ...
3. Invariant measures
... (i) The important hypotheses are (i) and (ii) (hypothesis (iii) says that the space X is σ-finite, a common technical assumption). Thus the Kolmogorov Extension Theorem says that if we have a function µ that looks like a measure on an algebra A, then it is indeed a measure when extended to B(A). (ii ...
... (i) The important hypotheses are (i) and (ii) (hypothesis (iii) says that the space X is σ-finite, a common technical assumption). Thus the Kolmogorov Extension Theorem says that if we have a function µ that looks like a measure on an algebra A, then it is indeed a measure when extended to B(A). (ii ...
Population recovery and partial identification
... fragments may be common to several. Even with knowledge of the complete description of each type (which we a-priori do not have), it is not clear how to determine the distribution from such partial descriptions. A modern-day version of this problem is analyzing the partial Netflix matrix, where spec ...
... fragments may be common to several. Even with knowledge of the complete description of each type (which we a-priori do not have), it is not clear how to determine the distribution from such partial descriptions. A modern-day version of this problem is analyzing the partial Netflix matrix, where spec ...
PDF
... are exactly the closed and dense sets, respectively [2]. This, for example, implies that every linear property can be expressed as a conjunction of a safety and a liveness property [2, 3]. From a practical point of view, reasoning about safety and liveness properties require different methodologies, ...
... are exactly the closed and dense sets, respectively [2]. This, for example, implies that every linear property can be expressed as a conjunction of a safety and a liveness property [2, 3]. From a practical point of view, reasoning about safety and liveness properties require different methodologies, ...
Learning and Risk Aversion"
... she chooses her alternative actions.1 The manner in which the agent responds to experience is described by a learning rule. For given behavior today, a learning rule is a mapping from the action played in this period and the payo¤ obtained to behavior in the next period. We refer to the payo¤ distri ...
... she chooses her alternative actions.1 The manner in which the agent responds to experience is described by a learning rule. For given behavior today, a learning rule is a mapping from the action played in this period and the payo¤ obtained to behavior in the next period. We refer to the payo¤ distri ...
sets of recurrence of z -actions and properties of sets of
... We now give some examples of sets of (strong!) recurrence in Z. Proofs can be found in [1]. 1. Thick sets. A set R a Z is called thick if it contains arbitrarily long intervals. 2. IP-sets. A subset of Z is called an /P-set if it consists of a sequence of (not necessarily distinct) integers nx, n2,. ...
... We now give some examples of sets of (strong!) recurrence in Z. Proofs can be found in [1]. 1. Thick sets. A set R a Z is called thick if it contains arbitrarily long intervals. 2. IP-sets. A subset of Z is called an /P-set if it consists of a sequence of (not necessarily distinct) integers nx, n2,. ...
1. Markov chains
... probability distributions incorporate a simple sort of dependence structure, where the conditional distribution of future states of the system, given some information about past states, depends only on the most recent piece of information. That is, what matters in predicting the future of the system ...
... probability distributions incorporate a simple sort of dependence structure, where the conditional distribution of future states of the system, given some information about past states, depends only on the most recent piece of information. That is, what matters in predicting the future of the system ...
FAST COMPRESSIVE SAMPLING WITH STRUCTURALLY RANDOM MATRICES Thong T. Do
... of solving a linear programming problem or employing greedy algorithms such as basis pursuit. This approach may be regarded as the efficient hybrid model of two current methods: completely random Gaussian/Bernoulli matrices and partial Fourier. It retains almost all desirable features of these afore ...
... of solving a linear programming problem or employing greedy algorithms such as basis pursuit. This approach may be regarded as the efficient hybrid model of two current methods: completely random Gaussian/Bernoulli matrices and partial Fourier. It retains almost all desirable features of these afore ...
Title of slide
... Suppose we toss the coin N = 20 times and get n = 17 heads. Region of data space with equal or lesser compatibility with H relative to n = 17 is: n = 17, 18, 19, 20, 0, 1, 2, 3. Adding up the probabilities for these values gives: ...
... Suppose we toss the coin N = 20 times and get n = 17 heads. Region of data space with equal or lesser compatibility with H relative to n = 17 is: n = 17, 18, 19, 20, 0, 1, 2, 3. Adding up the probabilities for these values gives: ...
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.