Related papers: A simple two-sample Bayesian t-test for hypothesis…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…
In Bayesian statistics the precise point-null hypothesis $\theta=\theta_0$ can be tested by checking whether $\theta_0$ is contained in a credible set. This permits testing of $\theta=\theta_0$ without having to put prior probabilities on…
I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…
A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…
Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation…
In this paper, a problem of testing is discussed when the samples have been drawn from the normal distribution. The study of hypothesis testing is also extended to Baye's set up.
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
With the advent of so-called default Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise,…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…
Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…
In this paper we proposed the alternative test to the two independent and normally distributed samples t test based on the cross variance concept. We present the simulation results of the power and the error rate of the special case of the…