In this article, we derive a new covariance estimate. The estimate has a similar structure as the Brascamp-Lieb inequality and is optimal for ferromagnetic Gaussian measures. It can be naturally applied to deduce decay of correlations of lattice systems of continuous spins. We also discuss the relation of the new estimate with known estimates like a weighted estimate due to Helffer & Ledoux. Th...

The purpose of this paper is to investigate the short-run and long-run causality between renewable energy (RE) consumption and economic growth (EG) in nine OECD countries from the period between 1982 and 2011. To examine the linkage, this paper uses the autoregressive distributed lag (ARDL) bounds testing approach of cointegration test and vector error-correction models to test the causal relat...

So far we have talked about the expectation of random variables, and moved on to the variance or the second moment. However, neither of these methods is strong enough to produce the tight bounds needed for some applications. We have already stated that if all you are given is the variance of a r.v., then Chebyshev’s Inequality is essentially the best you can do. Thus, more information is needed...

This paper presents three new systematic approaches for computing coefficient matrices of the Heffron-Phillips multi-machine model (K1, …, K6). The amount of computations needed for conventional and three new approaches are compared by counting number of multiplications and divisions. The advantages of new approaches are: (1) their computation burdens are less than 73 percent of that of convent...

2. Query Uncertainty 4 2.1. Derivation of Special Case: Query Dependent on a Subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2. Derivation of Special Case: Independent Representation Elements . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3. Linear Query with Independent Elements Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4. Empirical Ent...