37,974 research outputs found
Bayesian estimation of one-parameter qubit gates
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
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
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
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
We discuss an approach for deriving robust posterior distributions from
-estimating functions using Approximate Bayesian Computation (ABC) methods.
In particular, we use -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
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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