Related papers: The Inference Framework
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a…
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
A thermodynamic framework for asymptotic inference is developed in which sample size and parameter variance define a state space. Within this description, Shannon information plays the role of entropy, and an integrating factor organizes…
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general…
In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be…
In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
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…
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…
Recently we presented a concise survey of the formulation of the induction and coinduction principles, and some concepts related to them, in five different fields mathematical fields, hence shedding some light on the precise relation…
Classical causal and statistical inference methods typically assume the observed data consists of independent realizations. However, in many applications this assumption is inappropriate due to a network of dependences between units in the…
This work is motivated by a question at the heart of unsupervised learning approaches: Assume we are collecting a number K of (subjective) opinions about some event E from K different agents. Can we infer E from them? Prima facie this seems…