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Improving sampling efficacy on high-dimensional distributions with thin high-density regions using Conservative Hamiltonian Monte Carlo. [PDF]
McGregor G, Wan ATS.
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Tests for Categorical Data Beyond Pearson: A Distance Covariance and Energy Distance Approach. [PDF]
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Discrete Approximations of Probability Distributions
Management Science, 1983Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original ...
Allen C. Miller, III, Thomas R. Rice
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Approximation by Discrete GB-Splines
Numerical Algorithms, 2001Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided difference at the knots. They are a generalization both of smooth generalized splines and classic discrete cubic splines. The paper is devoted to the study of generalized splines.
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Approximating discrete probability distributions
IEEE Transactions on Information Theory, 1969The method of minimum discrimination information estimation is applied to the problem of estimating an n -dimensional discrete probability distribution in terms of lower order marginal distributions. The procedure provides a convergent iterative algorithm. The method yields regular best asymptotically normal (RBAN) estimates.
Harry H. Ku, Solomon Kullback
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Approximation by discrete hermite interpolation
2010 11th International Conference on Control Automation Robotics & Vision, 2010For a function f(t) defined on the discrete interval N[a, b + 2] = {a, a + 1, …, 6 + 2}, we develop a class of quintic discrete Hermite interpolate H ρ f(t) that involves only differences. Further, explicit error bounds are offered in the form of the inequality ||f-H ρ f||≤c j max/t∊N[a, b+2-j] | Δj f(t)|, 2≤j≤6 where the constants C j , 2 ≤ 6 are ...
Fengmin Chen, Patricia J. Y. Wong
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Discrete analogues of Laplace's approximation
Asymptotic Analysis, 2007An asymptotic formula is derived for the sum I n (1|q):=Σ n k=0 f n (k)q g n (k)
Wang, X.S., Wong, R.
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Discrete approximation of the Koch curve
Computers & Graphics, 1993Abstract Existing algorithms for Koch curve generation do not consider the discrete environment of the computer. They do not define the termination condition explicitly. Therefore, generation of the curve must be terminated in ad-hoc manners. This paper describes a new algorithm for discretely approximated Koch curve generation which produces only ...
Sam Chung Hwang, Hyun Seung Yang
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Approximation by discrete spline interpolation
2010 11th International Conference on Control Automation Robotics & Vision, 2010For a function f(t) defined on the discrete interval N[a, b + 2] = {a, a + 1, …, b + 2}, we develop a class of quintic discrete spline interpolate S ρ f(t) that involves only differences. Further, explicit error bounds are offered in the form of the inequality ||f-H ρ f||≤d j max/t∊N[a, b+2-j] |Δj f(t)|, 2≤j≤6 where the constants d j , 2 ≤ j ≤ 6 are
Fengmin Chen, Patricia J. Y. Wong
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Discrete Nonlinear Mean Approximation
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977AbstractBest approximation on a finite set by a non‐linear family of functions with respect to a general sum “norm”, which includes as a special case the Lp norms (1 < p < ∞), is considered. Properties of best approximations are given. It is shown that a local minimum of the error may not be a global minimum. Computation of best approximations is
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