Related papers: Logical coherence in Bayesian simultaneous three-w…
In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
In the classical literature on infinite series there are various tests to determine if a given infinite series converges, diverges, or oscillates. But unfortunately, for very many infinite series all the existing tests can fail to provide…
The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
Despite their impressive capabilities, large pre-trained language models (LMs) struggle with consistent reasoning; recently, prompting LMs to generate explanations that self-guide the inference has emerged as a promising direction to amend…
Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a…
Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…
The nature of intelligence in both humans and machines is a longstanding question. While there is no universally accepted definition, the ability to reason causally is often regarded as a pivotal aspect of intelligence (Lake et al., 2017).…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
Temporary syntactic ambiguities arise when the beginning of a sentence is compatible with multiple syntactic analyses. We inspect to which extent neural language models (LMs) exhibit uncertainty over such analyses when processing…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially…
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
Usually one compares the accuracy of two competing classifiers via null hypothesis significance tests (nhst). Yet the nhst tests suffer from important shortcomings, which can be overcome by switching to Bayesian hypothesis testing. We…
We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method…
Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…
While Large language models (LLMs) have proved able to address some complex reasoning tasks, we also know that they are highly sensitive to input variation, which can lead to different solution paths and final answers. Answer consistency…
We demonstrate that any logical problem can be solved by Bayesian inference. In this approach, the distinction between complexity classes vanishes. The method is illustrated by solving the 3-SAT problem in polynomial time. Beyond this,…