Section 21.8
... a kind of randomized propagation takes place through genealogical networks. Before moving on to this, it is worth noting that randomized models can also sometimes be useful in studying social contagion, particularly in cases where the underlying decision processes of the individuals are hard to mode ...
... a kind of randomized propagation takes place through genealogical networks. Before moving on to this, it is worth noting that randomized models can also sometimes be useful in studying social contagion, particularly in cases where the underlying decision processes of the individuals are hard to mode ...
The Modelling of Random Phenomena
... Continuous laws have some features that contrast with those of discrete laws: • The law is not determined by the probability of the individual outcomes. • It is the density that determines the law. (This can be said to be true also for discrete laws, but the concept of “density function” is differen ...
... Continuous laws have some features that contrast with those of discrete laws: • The law is not determined by the probability of the individual outcomes. • It is the density that determines the law. (This can be said to be true also for discrete laws, but the concept of “density function” is differen ...
PDF
... This approach leaves open the question of how we construct . The simplest approach is to use model selection to pick a single high-scoring structure, and then use that as our approximation. If the amount of data is large relative to the size of the model, then the posterior will be sharply peaked ar ...
... This approach leaves open the question of how we construct . The simplest approach is to use model selection to pick a single high-scoring structure, and then use that as our approximation. If the amount of data is large relative to the size of the model, then the posterior will be sharply peaked ar ...
Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial... pages 201-210, Stanford, California, June 2000
... the structures examined during the search, and return the high scoring ones. However, the set of structures found in this manner is quite sensitive to the search procedure we use. For example, if we use greedy hill-climbing, then the set of structures we will collect will all be quite similar. Such ...
... the structures examined during the search, and return the high scoring ones. However, the set of structures found in this manner is quite sensitive to the search procedure we use. For example, if we use greedy hill-climbing, then the set of structures we will collect will all be quite similar. Such ...
Lecture Notes 7
... where (Wt ) is a one-dimensional Brownian motion, is an (Ft )-martingale. It follows that, if QT is the probability measure defined on the measurable space (Ω, FT ) by (22), then the process Wtϑ = ϑt + Wt , ...
... where (Wt ) is a one-dimensional Brownian motion, is an (Ft )-martingale. It follows that, if QT is the probability measure defined on the measurable space (Ω, FT ) by (22), then the process Wtϑ = ϑt + Wt , ...
Point and interval estimation of the population size
... all categorical covariate combinations (see Zelterman, 2002). In this paper we extend this work in a number of ways: by (1) proposing overall condence intervals for the population size, (2) estimating those intervals by tting the truncated Poisson regression model with covariates that can be both ...
... all categorical covariate combinations (see Zelterman, 2002). In this paper we extend this work in a number of ways: by (1) proposing overall condence intervals for the population size, (2) estimating those intervals by tting the truncated Poisson regression model with covariates that can be both ...
This PDF is a selection from an out-of-print volume from... of Economic Research
... can be found. For brevity, Table 1 includes both models, the partial differential equation of the probability generating functions and a mean-variance evolution of the random variable x(t). Given these (and higher order) moments, a "certainty equivalent" advertising strategy can theoretically be sel ...
... can be found. For brevity, Table 1 includes both models, the partial differential equation of the probability generating functions and a mean-variance evolution of the random variable x(t). Given these (and higher order) moments, a "certainty equivalent" advertising strategy can theoretically be sel ...
Efficient Importance Sampling for Reduced Form
... With the expansion in the corporate credit risk market and the surge in the trading of securitized products, such as Collateralized Debt Obligations (CDOs), there is a need for sophisticated credit risk models. The pricing and risk management of these products requires the computation of portfolio l ...
... With the expansion in the corporate credit risk market and the surge in the trading of securitized products, such as Collateralized Debt Obligations (CDOs), there is a need for sophisticated credit risk models. The pricing and risk management of these products requires the computation of portfolio l ...
Threshold Effects for Two Pathogens Spreading on a Network
... sizes S and "1 % S$C of the epidemic and the giant component on the residual graph as a function of transmissibility for the Poisson case. As the transmissibility increases from zero, the size of the residual giant component is initially equal to the size of the giant component of the entire graph, ...
... sizes S and "1 % S$C of the epidemic and the giant component on the residual graph as a function of transmissibility for the Poisson case. As the transmissibility increases from zero, the size of the residual giant component is initially equal to the size of the giant component of the entire graph, ...
Random Graphs
... descriptions of the processes that generate them. Describe such processes via random algorithms. The likelihood of generating a given graph via algorithm induces a probability distribution. Examine the properties of generated graphs; try to find models whose properties match those of the networks we ...
... descriptions of the processes that generate them. Describe such processes via random algorithms. The likelihood of generating a given graph via algorithm induces a probability distribution. Examine the properties of generated graphs; try to find models whose properties match those of the networks we ...
CS276A Text Information Retrieval, Mining, and Exploitation
... Tree-like networks are easily tractable Much other work on efficient exact and approximate ...
... Tree-like networks are easily tractable Much other work on efficient exact and approximate ...
Processes on complex networks. Percolation
... Note that for the power law distribution with the exponent 2 ≤ γ ≤ 3 the second moment is infinite, and hence the configuration model always has the giant component. Now we are interested in site percolation on the configuration model. I.e., each vertex in the configuration model with ν > 1 can be “open ...
... Note that for the power law distribution with the exponent 2 ≤ γ ≤ 3 the second moment is infinite, and hence the configuration model always has the giant component. Now we are interested in site percolation on the configuration model. I.e., each vertex in the configuration model with ν > 1 can be “open ...
Dp2007-08 - Research portal
... and assume that i and k share a group and that j and k share a group. Then, the probability that i and j also have a common group depends on the number of groups that the common neighbor k belongs to. Indeed, the fewer groups k belongs to, the more likely it is that i and j in fact share the same gr ...
... and assume that i and k share a group and that j and k share a group. Then, the probability that i and j also have a common group depends on the number of groups that the common neighbor k belongs to. Indeed, the fewer groups k belongs to, the more likely it is that i and j in fact share the same gr ...
1 CHANCE AND MACROEVOLUTION
... evolutionary conceptions of chance that are important in present-day evolutionary theory, I will follow Eble in focusing my attention on these conceptions. Eble’s conceptual scheme provides a useful starting point for a discussion of the meaning of chance in evolutionary theory, but it is in need of ...
... evolutionary conceptions of chance that are important in present-day evolutionary theory, I will follow Eble in focusing my attention on these conceptions. Eble’s conceptual scheme provides a useful starting point for a discussion of the meaning of chance in evolutionary theory, but it is in need of ...
Why should one expect to find long runs of (non)
... decay. Then color a decayed H-atom red if conditions (1.2) and (1.3) hold, otherwise blue. If one wants to be more formal, one can phrase this in terms of two independent, parallel Poisson processes, one of which has double the intensity of the other. But the point is that this model is equivalent, ...
... decay. Then color a decayed H-atom red if conditions (1.2) and (1.3) hold, otherwise blue. If one wants to be more formal, one can phrase this in terms of two independent, parallel Poisson processes, one of which has double the intensity of the other. But the point is that this model is equivalent, ...
Vortrag Graz
... Quotes indicating use of Quick‘s approach: ''To allow for the statistical nature of the detection process, the effects of probability summation must be incorporated. … A convenient way to compute the effects of spatial probability summation is based on Quick's (1974) parameterization of the psychom ...
... Quotes indicating use of Quick‘s approach: ''To allow for the statistical nature of the detection process, the effects of probability summation must be incorporated. … A convenient way to compute the effects of spatial probability summation is based on Quick's (1974) parameterization of the psychom ...
Line-of-Sight Networks.
... Most of today’s approaches to wireless computing and communications are built on architectures where base stations connect the wireless devices to a supporting infrastructure. However, since the overwhelming trend is to transmit information in packets, over standard protocols, a dominant focus in th ...
... Most of today’s approaches to wireless computing and communications are built on architectures where base stations connect the wireless devices to a supporting infrastructure. However, since the overwhelming trend is to transmit information in packets, over standard protocols, a dominant focus in th ...
On the Genealogy of Large Populations Author(s): J. F. C. Kingman
... Section 5 onwards. Before embarking on this, we indicate very briefly the way in which it relates to previous work on the neutral mutation problem, and the fact that it arises from other models than the Wright-Fisher. The assumption that N is constant is not essential. If N varies because of externa ...
... Section 5 onwards. Before embarking on this, we indicate very briefly the way in which it relates to previous work on the neutral mutation problem, and the fact that it arises from other models than the Wright-Fisher. The assumption that N is constant is not essential. If N varies because of externa ...
Full report
... to develop models that capture essential features of the real networks. A natural candidate to model a network is a random graph, and, to fit with the empirical observations, such a graph should have a heavy-tailed degree distribution and considerable clustering. We will quantify the clustering in a ...
... to develop models that capture essential features of the real networks. A natural candidate to model a network is a random graph, and, to fit with the empirical observations, such a graph should have a heavy-tailed degree distribution and considerable clustering. We will quantify the clustering in a ...
paper
... (N , A), where N is the set of nodes and A is the set of arcs. Each arc (i, j) represents a lossy point-to-point link. Some subset of the packets injected into arc (i, j) by node i are lost; the rest are received by node j without error. The process by which packets are injected into an arc is taken ...
... (N , A), where N is the set of nodes and A is the set of arcs. Each arc (i, j) represents a lossy point-to-point link. Some subset of the packets injected into arc (i, j) by node i are lost; the rest are received by node j without error. The process by which packets are injected into an arc is taken ...
Branching Processes with Negative Offspring Distributions
... the Galton-Watson branching process, and had been studied thoroughly in literature, for example, [2, 6, 7, 10]. Some interesting details on the early history of branching processes can be found in [9]. Another model for the branching processes was based on the interpretation of the random walk Sn − ...
... the Galton-Watson branching process, and had been studied thoroughly in literature, for example, [2, 6, 7, 10]. Some interesting details on the early history of branching processes can be found in [9]. Another model for the branching processes was based on the interpretation of the random walk Sn − ...
Influential Nodes in a Diffusion Model for Social Networks.
... model [3], this probability is a constant pv (u), independent of the history of the process. In general, however, v’s propensity for being activated may change as a function of which of its neighbors have already attempted (and failed) to influence it; if S denotes the set of v’s neighbors that have ...
... model [3], this probability is a constant pv (u), independent of the history of the process. In general, however, v’s propensity for being activated may change as a function of which of its neighbors have already attempted (and failed) to influence it; if S denotes the set of v’s neighbors that have ...
4.4 Occupation measures and local times
... processes using the theory of local nondeterminism introduced by Berman (1973), and later extended to non-Gaussian stable processes by Nolan (1982). The following proposition shows existence of jointly continuous local times for certain self-similar processes with stationary increments. ...
... processes using the theory of local nondeterminism introduced by Berman (1973), and later extended to non-Gaussian stable processes by Nolan (1982). The following proposition shows existence of jointly continuous local times for certain self-similar processes with stationary increments. ...
Random Dot Product Graph Models for Social Networks
... They proceed to show that for higher dimensions the probability of an arbitrary edge is independent of the dimension, but the degree distribution develops a “bend” in the power law. That is, the slope of the log-log plot of the degree distribution in numerical studies (and confirmed analytically for ...
... They proceed to show that for higher dimensions the probability of an arbitrary edge is independent of the dimension, but the degree distribution develops a “bend” in the power law. That is, the slope of the log-log plot of the degree distribution in numerical studies (and confirmed analytically for ...
bayesian networks in video games
... calculate the probabilities that the agent's best move would be forward, backward, left, or right. For each probability that was ultimately calculated by the network, the agent would have that probability of traveling in that direction; therefore the agent did not always travel in the direction that ...
... calculate the probabilities that the agent's best move would be forward, backward, left, or right. For each probability that was ultimately calculated by the network, the agent would have that probability of traveling in that direction; therefore the agent did not always travel in the direction that ...
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.