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Regular conditional probabilities and strictly proper loss functions
Statistics & Probability Letters, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Nielsen
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Some results on regular conditional probabilities
Acta Mathematica Sinica, 1985 A necessary and sufficient condition for the existence of regular conditional probability on a separable probability space is obtained. Some equivalent conditions for a regular conditional probability to be continuous or discrete are also obtained. Blackwell's theorem is extended to an arbitrary separable measurable space in a slightly weaker form.
Zhi-Ming Ma
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The existence of regular conditional probabilities for Markov kernels
Statistics & Probability Letters, 2012 Abstract In this work, considering a Markov kernel (also called a stochastic kernel or transition probability) as a generalization of the concepts of the σ -field and the random variable, the concept of a conditional distribution (or regular conditional probability) of a Markov kernel given another is introduced.
Agustín García Nogales
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, 1994 Let (Ω, B, P) denote some probability space, where : stands for some Polish space with B as the corresponding Borel σ-algebra. Furthermore, (Ω,BP,P) is introduced as the completion of (Ω,B,P). It is proved that P is discrete if and only if there exists a regular version of the conditional distribution P(A\B), A ∈ Bp.
D. Plachky
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Existence of regular conditional probability measures
, 1966 J. Pfanzagl, W. Pierlo
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Products of Blackwell spaces and regular conditional probabilities
Real Analysis Exchange, 1984 Shortt
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Fuzzy c-means clustering with conditional probability based K–L information regularization
Journal of Statistical Computation and Simulation, 2021Fuzzy c-means with regularization by K–L information (KLFCM) is an objective function method for clustering, which is regarded as a fuzzy counterpart of Gaussian mixture models (GMMs) with EM algor...
Ouafa Amira, Jiang-She Zhang, Junmin Liu
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Regularizing Pattern Recognition with Conditional Probability Estimates
2020 International Joint Conference on Neural Networks (IJCNN), 2020Recent contributions in non-parametric statistical pattern recognition have investigated augmenting the task with information about the conditional probability distribution P(Y|X) away from the 0.5 level set, i.e. the decision boundary. Many hypothesis spaces satisfy generous smoothness criteria, so the behavior of a function away from the decision ...
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Communications in Partial Differential Equations, 2001
Let A = (aij ) be a matrix-valued Borel mapping on a domain Ω ⊂ R d , let b = (bi ) be a vector field on Ω, and let LA, b ϕ = a ij ∂ x i ∂ xj ϕ + bi ∂ xi ϕ. We study Borel measures μ on Ω that satisfy the elliptic equation LA, b *μ = 0 in the weak sense: ∫ LA, b ϕ dμ = 0 for all ϕ ∈ C 0 ∞ (Ω). We prove that, under mild conditions, μ has a density. If A
Bogachev, VI +2 more
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Let A = (aij ) be a matrix-valued Borel mapping on a domain Ω ⊂ R d , let b = (bi ) be a vector field on Ω, and let LA, b ϕ = a ij ∂ x i ∂ xj ϕ + bi ∂ xi ϕ. We study Borel measures μ on Ω that satisfy the elliptic equation LA, b *μ = 0 in the weak sense: ∫ LA, b ϕ dμ = 0 for all ϕ ∈ C 0 ∞ (Ω). We prove that, under mild conditions, μ has a density. If A
Bogachev, VI +2 more
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Petroleum Geostatistics 2019, 2019
Summary In this paper, we present a methodology to condition the prior probability field of the facies to the facies observations collected at the well locations. The prior probability field of the facies usually comes from seismic inversion and the facies observations are the result of the examination of the cores extracted at the well locations ...
B. Sebacher, R. Hanea, S. Marzavan
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Summary In this paper, we present a methodology to condition the prior probability field of the facies to the facies observations collected at the well locations. The prior probability field of the facies usually comes from seismic inversion and the facies observations are the result of the examination of the cores extracted at the well locations ...
B. Sebacher, R. Hanea, S. Marzavan
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