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This manuscript provides step-by-step instructions for implementing Bayesian functional regression models using Stan. Extensive simulations indicate that the inferential performance of the methods is comparable to that of state-of-the-art…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
I reject the following null hypothesis: {H0: your data are normal}. Such drastic decision is motivated by theoretical reasons, and applies to your current data, the past ones, and the future ones. While this situation may appear…
Null Hypothesis Significance Testing is the \textit{de facto} tool for assessing effectiveness differences between Information Retrieval systems. Researchers use statistical tests to check whether those differences will generalise to online…
AB testing aids business operators with their decision making, and is considered the gold standard method for learning from data to improve digital user experiences. However, there is usually a gap between the requirements of practitioners,…
Data analysis in HEP experiments often uses binned likelihood from data and finite Monte Carlo sample. Statistical uncertainty of Monte Carlo sample has been introduced in Frequentist Inference in some literatures, but they are not suitable…
Most of the statistical tests currently used to detect differentially expressed genes are based on asymptotic results, and perform poorly for low expression tags. Another problem is the common use of a single canonical cutoff for the…
Since its debut in the 18th century, the P-value has been an important part of hypothesis testing-based scientific discoveries. As the statistical engine accelerates, questions are beginning to be raised, asking to what extent scientific…
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…
Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial data sets that are exchangeable with the real data under the null hypothesis (but not under the…
Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
Bayesian neural networks (BNNs) are making significant progress in many research areas where decision-making needs to be accompanied by uncertainty estimation. Being able to quantify uncertainty while making decisions is essential for…
Model evaluation -- the process of making inferences about the performance of predictive models -- is a critical component of predictive modeling research in learning analytics. We survey the state of the practice with respect to model…
Attacks on the P-value are nothing new, but the recent attacks are increasingly more serious. They come from more mainstream sources, with widening targets such as a call to retire the significance testing altogether. While well meaning, I…
We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that…