Related papers: Statistical inference as Green's functions

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…

Statistical modeling is a powerful tool for developing and testing theories by way of causal explanation, prediction, and description. In many disciplines there is near-exclusive use of statistical modeling for causal explanation and the…

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically…

Likelihood-based inference, central in modern particle physics data analysis requires the extensive evaluation of a likelihood function that depends on set of parameters defined by the statistical model under consideration. If an analytical…

Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…

Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…

We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove…

The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to…

Causality is a subject of philosophical debate and a central scientific issue with a long history. In the statistical domain, the study of cause and effect based on the notion of `fairness' in comparisons dates back several hundred years,…

Feedforward neural networks (FNNs) are typically viewed as pure prediction algorithms, and their strong predictive performance has led to their use in many machine-learning applications. However, their flexibility comes with an…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…

Interpretable rationales for model predictions are crucial in practical applications. We develop neural models that possess an interpretable inference process for dependency parsing. Our models adopt instance-based inference, where…

Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

Given two views of data, we consider the problem of finding the features of one view which can be most faithfully inferred from the other. We find that these are also the most correlated variables in the sense of deep canonical correlation…

Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…

Generative models are capable of producing human-expert level content across a variety of topics and domains. As the impact of generative models grows, it is necessary to develop statistical methods to understand collections of available…

Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…