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Register a new userEstimation of Reliability in the Two-Parameter Geometric Distribution
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Added by
Sudhansu Sekhar Maiti
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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In this article, the reliabilities $R(t)=P(Xgeq t)$, when $X$ follows two-parameter geometric distribution and $R=P(Xleq Y)$, arises under stress-strength setup, when X and Y assumed to follow two-parameter geometric independently have been found out. Maximum Likelihood Estimator (MLE) and an Unbiased Estimator (UE) of these have been derived. MLE and UE of the reliability of k-out-of-m system have also been derived. The estimators have been compared through simulation study.
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Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean and covariance structure informs the proposed mechanism and is also used in a delayed-acceptance algorithm. Information on the resulting state of the system is given by a Gaussian mixture. In on-line mode, the algorithm is adaptive and uses a sliding window approach to accelerate sampling speed and to maintain appropriate acceptance rates. We apply the algorithm to joined state and parameter estimation in the case of irregularly sampled GPS time series data.
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Lighting estimation from a single image is an essential yet challenging task in computer vision and computer graphics. Existing works estimate lighting by regressing representative illumination parameters or generating illumination maps directly. However, these methods often suffer from poor accuracy and generalization. This paper presents Geometric Movers Light (GMLight), a lighting estimation framework that employs a regression network and a generative projector for effective illumination estimation. We parameterize illumination scenes in terms of the geometric light distribution, light intensity, ambient term, and auxiliary depth, and estimate them as a pure regression task. Inspired by the earth movers distance, we design a novel geometric movers loss to guide the accurate regression of light distribution parameters. With the estimated lighting parameters, the generative projector synthesizes panoramic illumination maps with realistic appearance and frequency. Extensive experiments show that GMLight achieves accurate illumination estimation and superior fidelity in relighting for 3D object insertion.
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