A classic inferential problem in statistics is the two-sample hypothesis test, where we test whether two samples of observations are either drawn from the same distribution or two distinct distributions. However, standard methods for performing this test require strong distributional assumptions on the two samples of data. We propose a semi-Bayesian nonparametric (semi-BNP) procedure for the two-sample hypothesis testing problem. First, we will derive a novel BNP maximum mean discrepancy (MMD) measure-based hypothesis test. Next, we will show that our proposed test will outperform frequentist MMD-based methods by yielding a smaller false rejection and acceptance rate of the null. Finally, we will show that we can embed our proposed hypothesis testing procedure within a generative adversarial network (GAN) framework as an application of our method. Using our novel BNP hypothesis test, this new GAN approach can help to mitigate the lack of diversity in the generated samples and produce a more accurate inferential algorithm compared to traditional techniques.
This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let x=(x1,…,xn) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ0, the goal is to test the null hypothesis H0:θ=θ0 against all possible alternatives. The proposed approach is based on using the well-known formula of the Kullback–Leibler divergence between two binomial distributions chosen in a certain way. Then, the difference of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Some theoretical properties of the method are developed. Examples and simulation results are included.
Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines, pattern recognition, data mining and tests of independence. The main goal of this paper is to provide an efficient estimator of the mutual information based on the approach of Al Labadi et. al. (2021). The estimator is explored through various examples and is compared to its frequentist counterpart due to Berrett et al. (2019). The results show the good performance of the procedure by having a smaller mean squared error.
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