Related papers: Prior Distributions for Ranking Problems
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
We study the ranking problem in generalized linear bandits. At each time, the learning agent selects an ordered list of items and observes stochastic outcomes. In recommendation systems, displaying an ordered list of the most attractive…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…
Recommendation algorithms typically build models based on historical user-item interactions (e.g., clicks, likes, or ratings) to provide a personalized ranked list of items. These interactions are often distributed unevenly over different…
A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are…
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items…