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Bayesian Methods for Optimization of Radiation Monitoring Networks
Šmídl, Václav; Hofman, Radek
2011 - English
Release of radioactive material into the atmosphere is the last possible resort of any accident in a nuclear power plant. It is an extremely rare event, however with severe consequences for potentially many people living in proximity of the power plant. Awareness of radiation security has been increased after the Chernobyl accident, and almost every country is now equipped with monitoring network of on-line connected receptors continually measuring radiation levels. Initial configurations of the network were designed by experts using their experience.In this report, we are concerned with local scale modeling of less severe accident in the range of tens of kilometers from the nuclear power plant. Both the stationary and mobile groups will be discussed. The preferred model of uncertainty is the empirical density which will be assimilated with measurements using the sequential Monte Carlo methodology. We will discuss influence of various loss functions.
Keywords:
radiation monitoring; UAV; data assimilation
Fulltext is available at external website.
Bayesian Methods for Optimization of Radiation Monitoring Networks
Release of radioactive material into the atmosphere is the last possible resort of any accident in a nuclear power plant. It is an extremely rare event, however with severe consequences for ...
On polyhedral approximations of polytopes for learning Bayes nets
Studený, Milan; Haws, D.
2011 - English
We review three vector encodings of Bayesian network structures. The first one has recently been applied by Jaakkola et al., the other two use special integral vectors, called imsets. The central topic is the comparison of outer polyhedral approximations of the corresponding polytopes. We show how to transform the inequalities suggested by Jaakkola et al. to the framework of imsets. The result of our comparison is the observation that the implicit polyhedral approximation of the standard imset polytope suggested in (Studený Vomlel 2010) gives a closer approximation than the (transformed) explicit polyhedral approximation from (Jaakkola et al. 2010). Finally, we confirm a conjecture from (Studený Vomlel 2010) that the above-mentioned implicit polyhedral approximation of the standard imset polytope is an LP relaxation of the polytope.
Keywords:
learning Bayesian networks; imsets; polytopes
Fulltext is available at external website.
On polyhedral approximations of polytopes for learning Bayes nets
We review three vector encodings of Bayesian network structures. The first one has recently been applied by Jaakkola et al., the other two use special integral vectors, called imsets. The central ...
Stable distributions: On parametrizations of characteristic exponent
Karlová, Andrea
2011 - English
In this report we investigate theory of stable distributions and their role in probability theory. We are interested in derivation of canonical measure, semigroup operator and mainly in parametrizations of characteristic exponents. We finally introduce a new parametrization.
Keywords:
stable distribution; characteristic function; characteristic exponent
Fulltext is available at external website.
Stable distributions: On parametrizations of characteristic exponent
In this report we investigate theory of stable distributions and their role in probability theory. We are interested in derivation of canonical measure, semigroup operator and mainly in ...
Approximate Dynamic Programming based on High Dimensional Model Representation
Pištěk, Miroslav
2011 - English
In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric function approximation is used not only to reduce memory demands necessary to store Bellman function, but also to allow its fast approximate minimization. On that account, a clear connection between HDMR minimization and discrete optimization is newly established. In each time step of the backward evaluation of the Bellman function, we relax the parameterized discrete minimization subproblem to obtain parameterized trust region problem. We observe that the involved matrix is the same for all parameters owning to the structure of HDMR approximation. We find eigenvalue decomposition of this matrix to solve all trust region problems effectively.
Keywords:
HDMR approximation; Bellman equation; minimization of HDMR functions
Fulltext is available at external website.
Approximate Dynamic Programming based on High Dimensional Model Representation
In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric ...
Notes on projection based modelling of beta-distributed weights of a two-component mixture
Dedecius, Kamil
2011 - English
This report contains brief notes on estimation of beta-distributed weight of a Gaussian mixture. The results are directly applied in paper Kárný, M.: On approximate Bayesian recursive estimation]. First, we develop a method to update the beta distribution of weights by new data (evidences) and show, that a projection is needed to preserve the low modelling complexity. Then, we show how forgetting may be applied to improve adaptivity. The results can be immediately applied to multicomponent mixtures.
Keywords:
beta mixtures; projection; Bayesian modelling
Fulltext is available at external website.
Notes on projection based modelling of beta-distributed weights of a two-component mixture
This report contains brief notes on estimation of beta-distributed weight of a Gaussian mixture. The results are directly applied in paper Kárný, M.: On approximate Bayesian recursive estimation]. ...
Evaluation of tight bounds for divergences
Harremoes, P.; Vajda, Igor
2010 - English
The paper presents a general method for evaluation of the joint range of pairs of f-divergences. This range provides tight maxima and minima for one f-divergence for given value of the other. Applications in information theory, identification and detection are mentioned. Práce prezentuje obecnou metodu pro stanovení oblasti hodnot dvojic f-divergencí. Tato oblast poskytuje těsná maxima a minima jedné divergence pro danou hodnotu druhé. Jsou zmíněny aplikace takových mezí v teorii informace, identifikaci a detekci.
Keywords:
Divergence bounds; Conditional divergence maxima; Conditional divergence minima
Fulltext is available at external website.
Evaluation of tight bounds for divergences
The paper presents a general method for evaluation of the joint range of pairs of f-divergences. This range provides tight maxima and minima for one f-divergence for given value of the other. ...
Goodness-of-Fit Disparity Statistics Obtained by Hypothetical and Empirical Quantizations
Boček, Pavel; Vajda, Igor; van der Meulen, E.
2010 - English
Goodness-of-fit disparity statistics are defined as appropriately scaled phi-disparities or phi-divergences of quantized hypothetical and empirical distributions. It is shown that the classical Pearson-type statistics are obtained if we quantize by means of hypothetical percentiles, and that new spacings-based disparity statistics are obtained if we quantize by means of empirical percentiles.
Keywords:
power divergences; goodness-of-fit; asymptotic normality,
Fulltext is available at external website.
Goodness-of-Fit Disparity Statistics Obtained by Hypothetical and Empirical Quantizations
Goodness-of-fit disparity statistics are defined as appropriately scaled phi-disparities or phi-divergences of quantized hypothetical and empirical distributions. It is shown that the classical ...
Generalized information criteria for optimal Bayes decisions
Morales, D.; Vajda, Igor
2010 - English
Upper and lower levels of Byes decision errors and risk achieved under given lelvels of generalized information are evaluated. Quadratic information is shown to be optimal error and risk characteristic in infinite class of the most common generalized information measures including the measure of Shannon. Vypočteny jsou horní a dolní meze pro bayesovské chyby a rizika při daných hodnotách zobecněných informačních obsažností dat. Bylo prokázáno, že kvadratická informace určuje tyto meze nejpřesněji v nekonečné třídě nejběžnějších měr informace včetně Shannonovy informace.
Keywords:
Generalized informations; Bayes decision error; Bayes decision risk; Information risk and error criteria; Inaccuracies of information criteria
Fulltext is available at external website.
Generalized information criteria for optimal Bayes decisions
Upper and lower levels of Byes decision errors and risk achieved under given lelvels of generalized information are evaluated. Quadratic information is shown to be optimal error and risk ...
On weak solutions of stochastic differential equations
Hofmanová, M.; Seidler, Jan
2010 - English
A new proof of existence of weak solutions to stochastic differential equations with continuous coefficients based on ideas from infinite-dimensional stochastic analysis is presented.
Keywords:
weak solutions; stochastic differential equations
Fulltext is available at external website.
On weak solutions of stochastic differential equations
A new proof of existence of weak solutions to stochastic differential equations with continuous coefficients based on ideas from infinite-dimensional stochastic analysis is presented.
Implementation of partial forgetting in Mixtools
Dedecius, Kamil
2010 - English
The report describes the implementation of the partial forgetting in the Mixtools software package.
Keywords:
partial forgetting
Fulltext is available at external website.
Implementation of partial forgetting in Mixtools
The report describes the implementation of the partial forgetting in the Mixtools software package.
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