Related papers: Subjective inference
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…
Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning.…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
To investigate the structure of individual differences in performance on behavioral tasks, Haaf and Rouder (2017) developed a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual effects. The…
Bayes's rule deals with hard evidence, that is, we can calculate the probability of event $A$ occuring given that event $B$ has occurred. Soft evidence, on the other hand, involves a degree of uncertainty about whether event $B$ has…
In this work a quantum analogue of Bayesian inference is considered. Based on the notion of instrument, we propose a quantum analogue of Bayes' rule, which elaborates how a prior normal state updates under observations. Besides, we…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
To make decisions we are guided by the evidence we collect, as well as the opinions of friends and neighbors. How do we integrate our private beliefs with information we obtain from our social network? To understand the strategies humans…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…
The aim of this paper is to firmly establish subjective fiducial inference as a rival to the more conventional schools of statistical inference, and to show that Fisher's intuition concerning the importance of the fiducial argument was…
A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states,…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…