Lec 11
... Probabilities provide a principled foundation for uncertain reasoning. Can we use probabilities to quantify our uncertainties? ...
... Probabilities provide a principled foundation for uncertain reasoning. Can we use probabilities to quantify our uncertainties? ...
Building large-scale Bayesian Networks``, The Knowledge
... to node ``correctness of solution''. We shall talk about parents and children when referring to links. We say that an edge goes from the parent to the child. The nodes in the BN represent random variables. A random variable has a number of states (e.g. ``yes'' and ``no'') and a probability distribut ...
... to node ``correctness of solution''. We shall talk about parents and children when referring to links. We say that an edge goes from the parent to the child. The nodes in the BN represent random variables. A random variable has a number of states (e.g. ``yes'' and ``no'') and a probability distribut ...
The contact process in a dynamic random environment - DIM
... been considered. In particular, the literature includes several different versions of contact processes in random environments. One class of these processes corresponds to contact processes where the birth and death rates are not homogeneous in space, and they are chosen according to some probabilit ...
... been considered. In particular, the literature includes several different versions of contact processes in random environments. One class of these processes corresponds to contact processes where the birth and death rates are not homogeneous in space, and they are chosen according to some probabilit ...
Pushed beyond the brink: Allee effects, environmental stochasticity
... as a function of its density and the environmental state ξ , and the environmental fluctuations ξt are given by a sequence of independent and identically distributed (i.i.d.) random variables. Here we determine when these deterministic and stochastic forces result in unconditional stochastic persist ...
... as a function of its density and the environmental state ξ , and the environmental fluctuations ξt are given by a sequence of independent and identically distributed (i.i.d.) random variables. Here we determine when these deterministic and stochastic forces result in unconditional stochastic persist ...
![arXiv:math/0512009v3 [math.PR] 8 Aug 2006](http://s1.studyres.com/store/data/016729012_1-9d9901e66bf10ac7b7dd218d84b67638-300x300.png)
arXiv:math/0512009v3 [math.PR] 8 Aug 2006
... integer. Every site of Zd is either occupied by a pathogen or empty. Each model is started with a single pathogen at the origin of Zd and with all other sites empty. Rules for births and mutations are the same for the three spatial models. Let x be a site occupied by a pathogen and y be one of its 2 ...
... integer. Every site of Zd is either occupied by a pathogen or empty. Each model is started with a single pathogen at the origin of Zd and with all other sites empty. Rules for births and mutations are the same for the three spatial models. Let x be a site occupied by a pathogen and y be one of its 2 ...
Stochastic Processes from 1950 to the Present
... restricted sense of random evolutions governed by time (continuous or discrete time). Moreover, we must leave aside (for lack of competence) the study of classes of special processes. I have presented the parts of probability that I myself came in contact with, and their development as it appeared t ...
... restricted sense of random evolutions governed by time (continuous or discrete time). Moreover, we must leave aside (for lack of competence) the study of classes of special processes. I have presented the parts of probability that I myself came in contact with, and their development as it appeared t ...
Notes on stochastic processes
... the natural numbers as its state space and the non-negative numbers as its index set, so S = 0, 1, 2, . . . and T = [0, ∞) [151, pages 1 and 2]. If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process [151, pages 1 and 2][121, page 24 ...
... the natural numbers as its state space and the non-negative numbers as its index set, so S = 0, 1, 2, . . . and T = [0, ∞) [151, pages 1 and 2]. If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process [151, pages 1 and 2][121, page 24 ...
Information Theoretic Analysis of the Structure
... be achieved by means of information theory. To this end, with concepts from Kolmogorov complexity and from Shannon’s information theory, we create novel analysis methods of the structure-dynamics relationships in two models of complex systems: an executable model of the human immune systems and the ...
... be achieved by means of information theory. To this end, with concepts from Kolmogorov complexity and from Shannon’s information theory, we create novel analysis methods of the structure-dynamics relationships in two models of complex systems: an executable model of the human immune systems and the ...
Almost Tight Bounds for Rumour Spreading with Conductance
... The first result is a significant improvement with respect to best current bound of O(log4 n/φ6 ) [4]. (The proof of [4] is based on an interesting connection with spectral sparsification [20]. The approach followed here is entirely different.) The result is almost tight because Ω(log n/φ) is a lowe ...
... The first result is a significant improvement with respect to best current bound of O(log4 n/φ6 ) [4]. (The proof of [4] is based on an interesting connection with spectral sparsification [20]. The approach followed here is entirely different.) The result is almost tight because Ω(log n/φ) is a lowe ...
IMITATION DYNAMICS WITH PAYOFF SHOCKS
... expected payoffs, a strategy survives with a probability that does not depend on the random variance of its payoffs: a strategy’s survival probability is simply its initial frequency. Similarly, even if a strategy which is strictly dominant in expectation is subject to arbitrarily high noise, it wil ...
... expected payoffs, a strategy survives with a probability that does not depend on the random variance of its payoffs: a strategy’s survival probability is simply its initial frequency. Similarly, even if a strategy which is strictly dominant in expectation is subject to arbitrarily high noise, it wil ...
Tomasz R. Bielecki (Chicago, IL) Marek Rutkowski (Warszawa
... desired properties runs as follows. In the first step, we assume that we are given a family of F-predictable intensity processes λ1 , . . . , λp , and we produce a collection τ1 , . . . , τp of F-conditionally independent random times by the canonical method (see, e.g., Section 9.1.2 of Bielecki and ...
... desired properties runs as follows. In the first step, we assume that we are given a family of F-predictable intensity processes λ1 , . . . , λp , and we produce a collection τ1 , . . . , τp of F-conditionally independent random times by the canonical method (see, e.g., Section 9.1.2 of Bielecki and ...
Probability and Stochastic Processes
... inform conclusions. Consider, for example, computer network analysis, models based on large data sets, and actuarial analysis. Whatever a probability student's potential future career, she or he will be better served by having been exposed to many ways in which probability theory and computing inter ...
... inform conclusions. Consider, for example, computer network analysis, models based on large data sets, and actuarial analysis. Whatever a probability student's potential future career, she or he will be better served by having been exposed to many ways in which probability theory and computing inter ...
Stochastic Processes - Institut Camille Jordan
... Definition 4.3. A consequence of Property 2) above is that, given any collection C of subsets of Ω, there exists a smallest δ-system S on Ω which contains C. This δ-system is simply the intersection of all the δ-systems containing C (the intersection is non-empty for P(Ω) is always a δ-system contai ...
... Definition 4.3. A consequence of Property 2) above is that, given any collection C of subsets of Ω, there exists a smallest δ-system S on Ω which contains C. This δ-system is simply the intersection of all the δ-systems containing C (the intersection is non-empty for P(Ω) is always a δ-system contai ...
Linear birth/immigration-death process with binomial
... Birth-death processes have a rich history in probabilistic modeling, including applications in ecology, genetics, and evolution, see [18, 52, 59, 73] and the references therein. Moreover, populations can suffer dramatic declines from disease or food shortage but, perhaps surprisingly, such populatio ...
... Birth-death processes have a rich history in probabilistic modeling, including applications in ecology, genetics, and evolution, see [18, 52, 59, 73] and the references therein. Moreover, populations can suffer dramatic declines from disease or food shortage but, perhaps surprisingly, such populatio ...
May 24, 2000 13:43 WSPC/104-IJTAF 0034 MARKOV MARKET
... σ i of the forward Libor rates are allowed to be path-dependent. We note that this result can also be derived via the method of Brace, Gatarek and Musiela based on stochastic differential equations (cf. [2]). In Sec. 3, we construct multi-factor Markov Market Models for which the forward Libor rates ...
... σ i of the forward Libor rates are allowed to be path-dependent. We note that this result can also be derived via the method of Brace, Gatarek and Musiela based on stochastic differential equations (cf. [2]). In Sec. 3, we construct multi-factor Markov Market Models for which the forward Libor rates ...
Non-Uniform Distribution of Nodes in the Spatial Preferential
... such as the Jaccard coefficient [19], gave way to iterative graph theoretic measures, in which two objects are similar if they are related to similar objects, such as SimRank [15]. Many such measures also incorporate co-citation, the number of common neighbours of two nodes, as proposed in the conte ...
... such as the Jaccard coefficient [19], gave way to iterative graph theoretic measures, in which two objects are similar if they are related to similar objects, such as SimRank [15]. Many such measures also incorporate co-citation, the number of common neighbours of two nodes, as proposed in the conte ...
pdf
... for the objective of satisfying stability in probability. Their discussion was for bounded-noise signals. The authors of [59] also observed a parallel discussion, again for bounded-noise signals. With a departure from the bounded-noise assumption, [58] extended the discussion in [78] and studied a m ...
... for the objective of satisfying stability in probability. Their discussion was for bounded-noise signals. The authors of [59] also observed a parallel discussion, again for bounded-noise signals. With a departure from the bounded-noise assumption, [58] extended the discussion in [78] and studied a m ...
On the Diameter of Hyperbolic Random Graphs - Hasso
... Euclidean Random Graphs. It is not new to study graphs in a geometric space. In fact, graphs with Euclidean geometry have been studied intensively for more than a decade. The standard Euclidean model are random geometric graphs which result from placing n nodes independently and uniformly at random ...
... Euclidean Random Graphs. It is not new to study graphs in a geometric space. In fact, graphs with Euclidean geometry have been studied intensively for more than a decade. The standard Euclidean model are random geometric graphs which result from placing n nodes independently and uniformly at random ...
Empirical Implications of Arbitrage-Free Asset Markets
... In particular, suppose µ is the probability measure for the differentiable process and suppose that we generate a sequence of random times tj, j=1,...,∞, from a Poisson process that makes the probability of an event generating a new tj .01 per unit time. (That is, at any date t, the p.d.f. of the ti ...
... In particular, suppose µ is the probability measure for the differentiable process and suppose that we generate a sequence of random times tj, j=1,...,∞, from a Poisson process that makes the probability of an event generating a new tj .01 per unit time. (That is, at any date t, the p.d.f. of the ti ...
Quality of service parameters and link operating point estimation
... traffic engineering in Multiprotocol Label Switching (MPLS) networks. We point out the need of a good estimation of the bandwidth in order to optimize the resource sharing. In section 3 we show how the operating point of a link can be estimated from its EB, the consistency of this estimation and its ...
... traffic engineering in Multiprotocol Label Switching (MPLS) networks. We point out the need of a good estimation of the bandwidth in order to optimize the resource sharing. In section 3 we show how the operating point of a link can be estimated from its EB, the consistency of this estimation and its ...
The Effects of Causation Probability on the Ship
... could be stated that the model reflected well the actual situation. However, it should be noted that it is hard to compare the results to statistics since analyzed time interval should be long but the traffic would have to remain constant. The return periods were estimated based on one summer month ...
... could be stated that the model reflected well the actual situation. However, it should be noted that it is hard to compare the results to statistics since analyzed time interval should be long but the traffic would have to remain constant. The return periods were estimated based on one summer month ...
MA3H2 Markov Processes and Percolation theory
... √ i 6= j. Hence, E(Sn ) = n, and the expected distance from the origin is ∼ c n for some constant c > 0. In order to get more detailed information of the random walk at a given time n we consider the set of possible sample paths. The probability that the first n steps of the walk follow a given path ...
... √ i 6= j. Hence, E(Sn ) = n, and the expected distance from the origin is ∼ c n for some constant c > 0. In order to get more detailed information of the random walk at a given time n we consider the set of possible sample paths. The probability that the first n steps of the walk follow a given path ...
Bayesian Networks
... see exercise 3.2). This formula is very natural, since it computes the posterior probability ratio of c 1 versus c2 as a product of their prior probability ratio (the first term), multiplied by a set of terms ~i::lg:~~~ that measure the relative support of the finding Xi for the two classes. This mo ...
... see exercise 3.2). This formula is very natural, since it computes the posterior probability ratio of c 1 versus c2 as a product of their prior probability ratio (the first term), multiplied by a set of terms ~i::lg:~~~ that measure the relative support of the finding Xi for the two classes. This mo ...
Lecture 5. Stochastic processes
... sufficiently detailed information to determine how the system behaves, or the behavior of the system is so complicated that an exact description of it becomes irrelevant or impossible. In that case, a probabilistic model is often useful. Probability and randomness have many different philosophical i ...
... sufficiently detailed information to determine how the system behaves, or the behavior of the system is so complicated that an exact description of it becomes irrelevant or impossible. In that case, a probabilistic model is often useful. Probability and randomness have many different philosophical i ...
Lecture Notes CH. 2 - Electrical and Computer Engineering
... Processes In this chapter we will begin with a formal definition of what a stochastic process is and how it can be characterized. We will then study certain properties related to classes of processes which have simple probabilistic characterizations both in terms of their so-called sample-path prope ...
... Processes In this chapter we will begin with a formal definition of what a stochastic process is and how it can be characterized. We will then study certain properties related to classes of processes which have simple probabilistic characterizations both in terms of their so-called sample-path prope ...
Stochastic geometry models of wireless networks
In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.In the early 1960s a pioneering stochastic geometry model was developed to study wireless networks. This model is considered to be the origin of continuum percolation. Network models based on geometric probability were later proposed and used in the late 1970s and continued throughout the 1980s for examining packet radio networks. Later their use increased significantly for studying a number of wireless network technologies including mobile ad hoc networks, sensor networks, vehicular ad hoc networks, cognitive radio networks and several types of cellular networks, such as heterogeneous cellular networks. Key performance and quality of service quantities are often based on concepts from information theory such as the signal-to-interference-plus-noise ratio, which forms the mathematical basis for defining network connectivity and coverage.The principal idea underlying the research of these stochastic geometry models, also known as random spatial models, is that it is best to assume that the locations of nodes or the network structure and the aforementioned quantities are random in nature due to the size and unpredictability of users in wireless networks. The use of stochastic geometry can then allow for the derivation of closed-form or semi-closed-form expressions for these quantities without resorting to simulation methods or (possibly intractable or inaccurate) deterministic models.