On the Hierarchical Bernoulli Mixture Model Using Bayesian Hamiltonian Monte Carlo

The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli’s constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation utilizing the HMC/NUTS to analyze the Bayesian Bernoulli mixture aggregate regression model (BBMARM) and Hibermimo. In the model estimation, Hibermimo yielded a result of ~90% compliance with the modeling of each district and a small Widely Applicable Information Criteria (WAIC) value.

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

Dirichlet series expansions of p-adic L-functions

We study p-adic L-functions $$L_p(s,\chi )$$ L p ( s , χ ) for Dirichlet characters $$\chi $$ χ . We show that $$L_p(s,\chi )$$ L p ( s , χ ) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of $$\chi $$ χ . The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for $$c=2$$ c = 2 , where we obtain a Dirichlet series expansion that is similar to the complex case.

Pandemic Metric with Confidence (PMC) Model to Predict Trustworthy Probability of Utilized COVID-19 Pandemic Trajectory across the Global

Lots of works aim to reveal the driving factors of COVID-19 pandemic trajectory yet ignore the confidence of utilized trajectory data, making consequent results suspicious. Hereby, we proposed a pandemic metric with confidence (PMC) model in the hypothesis of Bernoulli Distribution of nine trajectories reported from 113 countries. Results exhibit the average confidence of trajectories across the global not in excess of 12.1% with the error threshold configuration of 1E-5. In contrast, the 95% high confidence setting also failed to predict the trajectory containing the acceptable error not beyond 1E-3. Thus, a proposed trade-off strategy between two contradictory expections (>50% confidence, <1E-3 error) supports 61% of investigated countries to predict the varying trajectory with confidence beyond 50%. Moreover, PMC model recommend the remanent 39% countries to extend the proportion of populaces in COVID-19 detecting-pool to a suggested-value (>1% of populations), ensuing the average confidence up to 70%.

UFIR Filtering Under Uncertain One-Step Delayed and Missing Data

This paper develops the unbiased finite impulse response (UFIR) filter for wireless sensor network (WSN) systems whose measurements are affected by random delays and packet dropout due to inescapable failures in the transmission and sensors. The Bernoulli distribution is used to model delays in arrived measurement data with known transmission probability. The effectiveness of the UFIR filter is compared experimentally to the KF and game theory recursive H1 filter in terms of accuracy and robustness employing the GPS-measured vehicle coordinates transmitted with latency over WSN.

Improved Bernoulli Sampling for Discrete Gaussian Distributions over the Integers

Discrete Gaussian sampling is one of the fundamental mathematical tools for lattice-based cryptography. In this paper, we revisit the Bernoulli(-type) sampling for centered discrete Gaussian distributions over the integers, which was proposed by Ducas et al. in 2013. Combining the idea of Karney’s algorithm for sampling from the Bernoulli distribution Be−1/2, we present an improved Bernoulli sampling algorithm. It does not require the use of floating-point arithmetic to generate a precomputed table, as the original Bernoulli sampling algorithm did. It only needs a fixed look-up table of very small size (e.g., 128 bits) that stores the binary expansion of ln2. We also propose a noncentered version of Bernoulli sampling algorithm for discrete Gaussian distributions with varying centers over the integers. It requires no floating-point arithmetic and can support centers of precision up to 52 bits. The experimental results show that our proposed algorithms have a significant improvement in the sampling efficiency as compared to other rejection algorithms.

Bernoulli multi-armed bandit problem under delayed feedback

Online learning under delayed feedback has been recently gaining increasing attention. Learning with delays is more natural in most practical applications since the feedback from the environment is not immediate. For example, the response to a drug in clinical trials could take a while. In this paper, we study the multi-armed bandit problem with Bernoulli distribution in the environment with delays by evaluating the Explore-First algorithm. We obtain the upper bounds of the algorithm, the theoretical results are applied to develop the software framework for conducting numerical experiments.