Mineral resource modelling using an unequal sampling pattern: An improved practice based on factorization techniques

This work addresses the problem of geostatistical simulation of cross-correlated variables by factorization approaches in the case when the sampling pattern is unequal. A solution is presented, based on a Co-Gibbs sampler algorithm, by which the missing values can be imputed. In this algorithm, a heterotopic simple cokriging approach is introduced to take into account the cross-dependency of the undersampled variable with the secondary variable that is more available over the entire region. A real gold deposit is employed to test the algorithm. The imputation results are compared with other Gibbs sampler techniques for which simple cokriging and simple kriging are used. The results show that heterotopic simple cokriging outperforms the other two techniques. The imputed values are then employed for the purpose of resource estimation by using principal component analysis (PCA) as a factorization technique, and the output compared with traditional factorization approaches where the heterotopic part of the data is removed. Comparison of the results of these two techniques shows that the latter leads to substantial losses of important information in the case of an unequal sampling pattern, while the former is capable of reproducing better recovery functions.

A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve

The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.

Bayesian Hetero-Elasticnet (A Gibbs Sampler Approach)

Combined heteroscedasticity and multicollinearity as dual non-spherical disturbances were experimented asymptotically. A Gibbs Sampler technique was used to investigate the asymptotic properties of hetero-elasticnet estimator with mean squares error (MSE) and bias as performance metrics. The seed was set to 12345; is set at ; Xs variables were generated as follow: the design matrix was generated from the multivariate normal distribution with mean > 0 and variance . and are truncated with Harvey (1976) heteroscedastic error structure; are collinear covariate with pairwise correlation between 0.6 and 0.9, the sample sizes were 25, 100 and 1000. The number of replications of the experiment was set at 10,000 with burn-in of 1000 which specified the draws that were discarded to remove the effects of the initial values. The thinning was set at 5 to ensure the removal of the effects of autocorrelation in the MCMC simulation. The study found that there is consistency of estimator asymptotically as the sample sizes increases from 25 to 50 so also to 1000, the larger sample size depicted least bias. The estimator exhibited efficiency asymptotically as larger sample sizes depicted least mean squares error. The study therefore recommended Bayesian hetero-elasticnet when data exhibit both heteroscedasticity and multicollinearity. Keywords: Elasticnet; Bayesian Inference and Gibbs sampler

Multi-qubit correction for quantum annealers

We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels—i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value—and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.