1 edition of **Estimation of multiple poisson means under entropy loss** found in the catalog.

- 163 Want to read
- 21 Currently reading

Published
**1986** .

Written in English

- Poisson distribution,
- Poisson processes

**Edition Notes**

Statement | by Ming-Chung Yang |

The Physical Object | |
---|---|

Pagination | vii, 69 leaves : |

Number of Pages | 69 |

ID Numbers | |

Open Library | OL25920671M |

OCLC/WorldCa | 15354732 |

Probabilistic Group Testing under Sum Observations: A Parallelizable 2-Approximation for Entropy Loss Weidong Han1, Purnima Rajan2, Peter I. Frazier3 and Bruno M. Jedynak4 1Department of Operations Research and Financial Engineering, Princeton University 2Department of Computer Science, Johns Hopkins University 3School of Operations Research and Information Engineering, Cornell University. Maximum likelihood. In this section we present the parametric estimation of the invariants based on the maximum likelihood approach and its flexible probabilities generalization.. In Section we extend the notion of maximum likelihood to the flexible probabilities framework, introducing the maximum likelihood with flexible probabilities estimates.

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For estimatingp(⩾ 2) independent Poisson means, the paper considers a compromise between maximum likelihood and empirical Bayes estimators. Such compromise estimators enjoy both good componentwise as well as ensemble by: 1.

This paper characterizes admissible linear estimators of multiple Poisson parameters under entropy loss. Estimators dominating some of the standard estimators are given.

Ghosh and Yang () considered entropy loss for simultaneous estimation of p-independent Poisson means. Rukhin and Ananda () considered the estimation problem of unknown variance of a multivariate nor- mal vector under quadratic loss and entropy by: In probability theory and statistics, the Poisson distribution (French pronunciation: ; in English often rendered / ˈ p w ɑː s ɒ n /), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate Support: k, ∈, N, 0, {\displaystyle k\in.

In estimation problems where over-estimation is more serious than under-estimation, the entropy loss is more appropriate than SEL and SISEL functions.

Some authors have used the following asymmetric and convex loss function (8) L (h (θ), δ) = δ h (θ) − ln δ h (θ) − 1, which is known as Stein's loss, to estimate the parameter Cited by: In various science/engineering applications, such as independent component analysis, image analysis, genetic analysis, speech recognition, manifold learning, evaluation of the status of biological systems and time delay estimation it is useful to estimate the differential entropy of a system or process, given some observations.

The simplest and most common approach uses histogram-based. Abstract. Let X 1, θ, X n (n > p) be a random sample from multivariate normal distribution N p (μ, Σ), where μ ε R p and Σ is a positive definite matrix, both μ and Σ being unknown.

We consider the problem of estimating the precision matrix Σ − this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of Σ −1 is Cited by: 5.

The paper deals with estimating shift point which occurs in any sequences of independent observations x1, x2,xm, xm+1,xn of poisson and geometric distributions. This shift point occurs in the sequence when xm i. m life data are observed.

With known shift point 'm', the Bayes estimator on befor and after shift process means θ1 and θ2 are derived for symmetric and assymetric. context of Kullback-Leibler loss in [34]. Under some conditions the analysis in [35] yields a root-nconsistent estimate of the entropy when 1 d 3.

The authors point out that the case d= 2 is of practical interest in projection pursuit. II.3 Estimates of entropy based on sample-spacings.

Since sample-spacings are de ned only for d= 1, we assume File Size: KB. X and a Poisson random variable with the same mean. By establishing monotonicity properties with respect to α, the maximum entropy result, Theoremfollows.

The action of U α is to thin X and then to add an independent Poisson random variable to it. In Section 4, we use U α to establish the maximum entropy property of the Poisson.

Binomial and Poisson Distributions as Maximum Entropy Distributions Peter Harremoës Abstract— The binomial and the Poisson distributions are shown to be maximum entropy distributions of suitably defined sets. Poisson’s law is considered as a case of entropy maximization, and also convergence in in-formation divergence is established.

An estimation problem of the mean µ of an inverse Gaussian distribution IG(µ, C µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. A class of Bayes estimators is constructed, and shown to include MRSE estimator as its closure.

Two important members of this class can easily be computed using continued fractions. The c-Loss Function: Balancing Total and Individual Risk in the Simultaneous Estimation of Poisson Means Emil Aas Stoltenberg THESIS for the degree of.

The information entropy, often just entropy, is a basic quantity in information theory associated to any random variable, which can be interpreted as the average level of "information", "surprise", or "uncertainty" inherent in the variable's possible concept of information entropy was introduced by Claude Shannon in his paper "A Mathematical Theory of Communication".

e.g. repeat the entropy estimation experiment many times and compute the average. The entropy estimator using plug-in values under -estimates the true entropy value (MM=Miller-Madow) No unbiased estimator of entropy exists for discrete case Ref: “Estimation of Entropy and Mutual Information”, Liam Paninski () Filename/RPS Number Maximum Entropy Priors for Estimation Problems.

94 Mutual Information, Data Processing Intrinsic Loss Functions and Density Estimation Problems. Foundational Aspects: The Likelihood, Conditionality, and made under a state of uncertainty, and its goal is to provide a rational File Size: 1MB. Multivariate and multiple Poisson distributions Carol Bates Edwards Iowa State University Follow this and additional works at: Part of theMathematics Commons This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University.

Entropy, an international, peer-reviewed Open Access journal. We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations.

{(Yi,ξi),Yi∈ Π} is the Poisson marked point process we will work with.Ψ can be seen as a random variable with values in N:= {ϕlocally ﬁnite counting measure on Rd× M}. An important property of this process is stationarity, meaning that TyΨ = Ψd for all y∈ Rd, where the translation operator T y is deﬁned as Tyϕ(B× L):= ϕ(B+y× L) for any Borel set B× L⊂ Rd× M and ϕ∈ by: 3.

Page 28References j Nonparametric entropy estimation j References I.A. Ahmad and P.E. Lin, A nonparametric estimation of the entropy for absolutely continuous distributions, IEEE Trans.

Information Theory IT (), no. 3, – P. Alonso-Ruiz and E. Spodarev, Estimation of entropy for poisson marked point. The Poisson distribution describes the number of occurrences of an event in a fixed interval, under the assumption that occurrences are independent. In particular, the constraint that the events should be independent means that not every discrete distribution is a valid candidate for describing this system, and motivates the choice of the union.

The function accepts the following options. accessor: accessor function for accessing array values.; dtype: output typed array or matrix data type. Default: float copy: boolean indicating if the function should return a new data structure.

Default: true. path: deepget/deepset key path.; sep: deepget/deepset key path separator. Default: '.'. For non-numeric arrays, provide an accessor. This thesis is devoted to the simultaneous estimation of the means of p> 1 independent Poisson distributions.

A novel loss function that penalizes bad estimates of each of the means and the sum of the means is introduced. Under this loss function, a class of. Selectivity Estimation; Histograms; Entropy Models 1. INTRODUCTION Selectivity estimation is the task of estimating the size of the result set of a relational algebra operator.

For a partic-ular query, multiple execution plans can be generated with This author’s research has been funded in. Probability Estimation with Maximum Entropy Principle Yupeng Li and Clayton V. Deutsch The principle of Maximum Entropy is a powerful and versatile tool for inferring a probability distribution from constraints that do not completely characterize the distribution.

The principle of Minimum RelativeFile Size: 93KB. Entropy is a concept that originated in thermodynamics, and later, via statistical mechanics, motivated entire branches of information theory, statistics, and machine learning. Maximum entropy is the state of a physical system at greatest disorder or a statistical model of least encoded information, these being important theoretical analogs.

Maximum entropy may refer to. Estimation of Entropy and Mutual Information ducing anything particularly novel, but merely formalizing what statis-ticians have been doing naturally since well before Shannon wrote his papers.

This strategy bears a striking resemblance to regularization methods em-ployed in abstract statistical inference (Grenander, ), generally known. 1 Maximum Entropy estimation of probability distribution of variables in higher dimensions from lower dimensional data Jayajit Das, Sayak Mukherjee1,2, and, Susan E.

Hodge1,2 1Battelle Center for Mathematical Medicine, Research Institute at the Nationwide Children's Hospital. on robust empirical Bayes estimation in nite population sampling under my supervision (). Yang of the University of Florida has written his Ph.D. dissertation on simultaneous estimation of Poisson means under entropy loss, under my supervision ().

Lily L. Mantelle of the University of Florida has written her Ph.D. Marginal Likelihood Estimation with the Cross-Entropy Method Chan, Joshua and Eisenstat, Eric Australian National University, Spiru Haret University Online at MPRA Paper No.

posted 13 Jul UTC. choose the distribution that minimizes entropy relative to the default estimate q0. When q0 is uniform this is the same as maximizing the entropy. Here, as usual, the entropy of a distribution p is deﬁned as H(p) = p[ln(1=p)] and the relative entropy, or Kullback-Leibler divergence, as D(p k q) = p[ln(p=q)].

Thus, the maximum entropy principle. The Entropy of a Poisson Distribution Problem *, by C. ROBERT APPLEDORN (Indiana University). The following problem arose during a study of data compression schemes for digitally encoded radiographic images. Specifically, Huffman optimum (minimum) codes are employed to reduce the storage requirements for high resolution gray-levelCited by: In this case, the loss function is the negative log loss: loss(q;X) = logq(X).

The expected value of this loss function is the risk: Risk(q) = E p[log 1 q(x)]:We want to nd a distribution qthat minimizes the risk. However, notice that minimizing the risk with respect to a distribution qis exactly minimizing the relative entropy between pand q.

Entropy and Probability (A statistical view) Entropy ~ a measure of the disorder of a system. A state of high order = low probability A state of low order = high probability In an irreversible process, the universe moves from a state of low probability to a state of higher probability.

We will illustrate the concepts byFile Size: 44KB. Statistics & Risk Modeling with Applications in Finance and Insurance. Editor-in-Chief: Stelzer, RobertCited by: 7. I hate to disagree with other answers, but I have to say that in most (if not all) cases, there is no difference, and the other answers seem to miss this.

For instance, in the binary classification case as stated in one of the answers. Let’s start. Chapter 8 Estimation of Parameters and Fitting of Probability Distributions !. 0 P (x) x. FIGURE Gaussian ﬁt of current ﬂow across a cell membrane to a frequency polygon.

The use of the normal distribution as a model is usually justiﬁed using someFile Size: KB. In probability theory and statistics, the Poisson distribution (French pronunciation: [pwasɔ̃]; in English often rendered /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and.

Maximum Likelihood and Entropy Cosma Shalizi posted recently about optimization for learning. This is a recurring theme in statistics 1: set up a functional combining empirical risk and a regularization term for smoothing, then use optimization to find a parameter value that minimizes this functional.

The most common estimators of MI are based on plug-in density estimation, e.g., using the histogram, kernel density or kNN density estimators [21,22]. Motivated by ensemble methods applied to divergence estimation [23,24], in an ensemble method for combining multiple KDE bandwidths was proposed for estimating MI.

Under certain smoothness Cited by: 5. See page of Paninski's Estimation of Entropy and Mutual Information for a slick proof. Thus, all we can do is attempt to mitigate 4 the bias, but we can never hope to remove it completely. In a future post, I'll discuss two methods for dealing with the bias, one very old, the other much more recent.Estimation of Smoothed Entropy Paul Cuff, Peter Park, Yucel Altug, Lanqing Yu (Princeton University) Estimation of Smoothed Support Paul Cuff, Peter Park, Yucel Altug, Lanqing Yu (Princeton University) Problem Take n samples from an unknown distribution () .Estimation.

Chapter E.3Estimation. Mixture of invariants model as hidden Markov model Glivenko-Cantelli theorem: theory.