Galactic Foreground Constraints on Primordial B-mode Detection for Ground-based Experiments

Contamination by polarized foregrounds is one of the biggest challenges for future polarized cosmic microwave background (CMB) surveys and the potential detection of primordial B-modes. Future experiments, such as Simons Observatory (SO) and CMB-S4, will aim at very deep observations in relatively small (f sky ∼ 0.1) areas of the sky. In this work, we investigate the forecasted performance, as a function of the survey field location on the sky, for regions over the full sky, balancing between polarized foreground avoidance and foreground component separation modeling needs. To do this, we simulate observations by an SO-like experiment and measure the error bar on the detection of the tensor-to-scalar ratio, σ(r), with a pipeline that includes a parametric component separation method, the Correlated Component Analysis, and the use of the Fisher information matrix. We forecast the performance over 192 survey areas covering the full sky and also for optimized low-foreground regions. We find that modeling the spectral energy distribution of foregrounds is the most important factor, and any mismatch will result in residuals and bias in the primordial B-modes. At these noise levels, σ(r) is not especially sensitive to the level of foreground contamination, provided the survey targets the least-contaminated regions of the sky close to the Galactic poles.

Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution

The process performance index (PPI) can be a simple metric to connect the conforming rate of products. The properties of the PPI have been well studied for the normal distribution and other widely used lifetime distributions, such as the Weibull, Gamma, and Pareto distributions. Assume that the quality characteristic of product follows power-normal distribution. Statistical inference procedures for the PPI are established. The maximum likelihood estimation method for the model parameters and PPI is investigated and the exact Fisher information matrix is derived. We discuss the drawbacks of using the exact Fisher information matrix to obtain the confidence interval of the model parameters. The parametric bootstrap percentile and bootstrap bias-corrected percentile methods are proposed to obtain approximate confidence intervals for the model parameters and PPI. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. One example about the flow width of the resist in the hard-bake process is used for illustration.

On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

This paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

Computation of the Exact Fisher Information Matrix of a Multiple Input Single Output Time Series Models

Klein, Mélard, and Zahaf (1998) have proposed the computation of the exact Fisher information matrix of a large class of Gaussian time series models called the single-input-single-output (SISO) model, includes dynamic regression with autocorrelated errors and the transfer function model, with autoregressive moving average errors. For computing the Fisher information matrix of a SISO model, they introduced an algorithm based on a combination of two computational procedures: recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters and the fast Kalman filter recursions used in the evaluation of the likelihood function. In this paper, we propose a generalization of this method for computing the Fisher information matrix of a MISO model.

Constrains on the electric charges of the binary black holes with GWTC-1 events

Testing black hole’s charged property is a fascinating topic in modified gravity and black hole astrophysics. In the first Gravitational-Wave Transient Catalog (GWTC-1), ten binary black hole merger events have been formally reported, and these gravitational wave signals have significantly enhanced our understanding of the black hole. In this paper, we try to constrain the amount of electric charge with the parameterized post-Einsteinian framework by treating the electric charge as a small perturbation in a Bayesian way. We find that the current limits in our work are consistent with the result of Fisher information matrix method in previous works. We also develop a waveform model considering a leading order charge effect for binary black hole inspiral.

FISHER INFORMATION MATRIX FOR CROVELLI'S AND GAMMA BETA II BIVARIATE DISTRIBUTIONS

In this paper, a system of nonlinear equations for the maximum likelihood estimators as wel as the exact forms of the Fisher information matrix for Crovelli's bivariate gamma distribution and bivariate gamma beta distribution of the second kind are determined. An application of the results to the rainfall data from the city of Passo Fundo are provided.