We present a new method to estimate the Hubble constant H0 from the measured time delays in quadruply imaged gravitational lens systems. We show how it is possible to get an estimate of H0 without the need to completely reconstruct the lensing potential thus avoiding any a priori hypothesis on the expression of the galaxy lens model. Our method only needs to assume that the lens potential may b...

The problem of reconciling the frequentist and Bayesian evidence in testing statistical hypotheses has been extensively studied in the literature. Most of the existing work considers cases without the nuisance parameters which is not the frequently encountered situation since the presence of the nuisance parameters is very common in practice. In this paper, we consider the reconcilability of th...

When hypothesis tests of H0 : θ = 0 have low power, it is possible that their rejection can frequently be accompanied by an estimate θ̂ that has the wrong sign and significantly exaggerated magnitude. Such sign errors are less likely when the confidence interval for θ is well separated from 0, as measured in units of the confidence interval’s width. Sign errors can be controlled by declaring con...

We address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis H0 that a given bit sequence is generated by Bernoulli source with equal probabilities of 0 and 1 and the alternative hypothesis H1 that the sequence is generated by a stationary and erg...

Specific statistical tests are used when the null hypothesis (H0) is to be tested using nonparametric nominal or ordinal data. With nominal data, experimental results are expressed by proportions or frequencies. Chi-square or related tests (the Fisher's exact test or the rows by columns test) are appropriate for testing H0 with nominal data. Ordinal data permit arrangement of statistical result...