37,974 research outputs found

    Bayesian estimation of one-parameter qubit gates

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    We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure. Bayesian inference is employed and compared with the ultimate quantum limits to precision, taking into account the biased nature of Bayes estimator in the non asymptotic regime. Besides, through the evaluation of the asymptotic a posteriori distribution for the gate parameter and the comparison with the results of Monte Carlo simulated experiments, we show that asymptotic optimality of Bayes estimator is actually achieved after a limited number of runs. The robustness of the estimation procedure against fluctuations of the measurement settings is investigated and the use of entanglement to improve the overall stability of the estimation scheme is also analyzed in some details.Comment: 10 pages, 5 figure

    Estimation of the Weibull Distribution Parameters and Reliability Using Kernel and Bayes Approaches

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    A new estimation technique based on the non-parametric kernel density estimation is introduced as an alternative and reliable technique for estimation in life testing models. This technique estimates the density functions of the parameters and reliability directly from the data without any prior assumptions about the underlying distribution parameters. The efficiency of this technique has been studied comparing to the Bayesian estimation of the parameters and reliability of the Weibull distribution based on the non-informative, informative and the informative conjugate priors, via Monte Carlo simulations, which indicated the robustness of the proposed method than the Bayesian approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper

    Bayesian Elastic Net based on Empirical Likelihood

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    Empirical likelihood is a popular nonparametric method for inference and estimation. In this article, we propose a Bayesian elastic net model that is based on empirical likelihood for variable selection. The proposed method incorporates interpretability and robustness from Bayesian empirical likelihood approach. We derive asymptotic distributions of coefficients for credible intervals. The posterior distribution of Bayesian empirical likelihood does not have a closed-form analytic expression and has nonconvex domain, which causes implementation of MCMC challenging. To solve this problem, we implement the Hamiltonian Monte Carlo approach. Simulation studies and real data analysis demonstrate the advantages of the proposed method in variable selection and prediction accuracy

    Fully Bayesian Penalized Regression with a Generalized Bridge Prior

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    We consider penalized regression models under a unified framework. The particular method is determined by the form of the penalty term, which is typically chosen by cross validation. We introduce a fully Bayesian approach that incorporates both sparse and dense settings and show how to use a type of model averaging approach to eliminate the nuisance penalty parameters and perform inference through the marginal posterior distribution of the regression coefficients. We establish tail robustness of the resulting estimator as well as conditional and marginal posterior consistency for the Bayesian model. We develop a component-wise Markov chain Monte Carlo algorithm for sampling. Numerical results show that the method tends to select the optimal penalty and performs well in both variable selection and prediction and is comparable to, and often better than alternative methods. Both simulated and real data examples are provided

    Robust approximate Bayesian inference

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    We discuss an approach for deriving robust posterior distributions from MM-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use MM-estimating functions to construct suitable summary statistics in ABC algorithms. The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method. An R implementation is also provided in the robustBLME package.Comment: This is a revised and personal manuscript version of the article that has been accepted for publication by Journal of Statistical Planning and Inferenc

    Assessing the Performance of Simple Contracts Empirically: The Case of Percentage Fees

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    This paper estimates the cost of using simple percentage fees rather than the broker optimal Bayesian mechanism, using data for real estate transactions in Boston in the mid-1990s. This counterfactual analysis shows that interme- diaries using the best percentage fee mechanisms with fees ranging from 5.4% to 7.4% achieve 85% or more of the maximum profit. With the empirically observed 6% fees intermediaries achieve at least 83% of the maximum profit and with an optimally structured linear fee, they achieve 98% or more of the maximum profit
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