Related papers: Bayesianize Fuzziness in the Statistical Analysis …
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory.…
We propose a new mathematical framework for the evolution and propagation of opinions, called Fuzzy Opinion Network, which is the connection of a number of Gaussian Nodes, possibly through some weighted average, time-delay or logic…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes;…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
This paper develops a mathematical and computational framework for analyzing the expected performance of Bayesian data fusion, or joint statistical inference, within a sensor network. We use variational techniques to obtain the posterior…
Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
Sensitivity Analysis is a framework to assess how conclusions drawn from missing outcome data may be vulnerable to departures from untestable underlying assumptions. We extend the E-value, a popular metric for quantifying robustness of…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
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…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…