Related papers: The Art of Probability Assignment
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial…
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…
When a planner must decide whether it has enough evidence to make a decision based on probability, it faces the sample size problem. Current planners using probabilities need not deal with this problem because they do not generate their…
In using observed data to make inferences about a population quantity, it is commonly assumed that the sampling distribution from which the data were drawn belongs to a given parametric family of distributions, or at least, a given finite…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
The definition of preferences assigned to individuals is a concept that concerns many disciplines, from economics, with the search of an acceptable outcome for an ensemble of individuals, to decision making an analysis of vote systems. We…
The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
It is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls…
The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…
We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…