Related papers: Beyond p values: practical methods for analyzing u…
This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
Large language models (LLMs) have been proposed as alternatives to human experts for estimating unknown quantities with associated uncertainty, a process known as Bayesian elicitation. We test this by asking eleven LLMs to estimate…
We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically,…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
Software packages usually report the results of statistical tests using p-values. Users often interpret these by comparing them to standard thresholds, e.g. 0.1%, 1% and 5%, which is sometimes reinforced by a star rating (***, **, *). We…
Investigators often use the data to generate interesting hypotheses and then perform inference for the generated hypotheses. P-values and confidence intervals must account for this explorative data analysis. A fruitful method for doing so…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
Estimating the effective sample size (ESS) of a prior distribution is an age-old yet pivotal challenge, with great implications for clinical trials and various biomedical applications. Although numerous endeavors have been dedicated to this…
In this study, we introduce a new approach to statistical decision theory. Without using a loss function, we select good decision rules to choice between two hypotheses. We call them "experts". They are globally unbiased but also…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been…