Related papers: Incorporating Nuisance Parameters in Likelihoods f…
Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…
We often estimate a parameter of interest psi when the identifying conditions involve a nuisance parameter theta. Examples from causal inference are Inverse Probability Weighting, Marginal Structural Models and Structural Nested Models. To…
This paper proposes a simple unified inference approach on moment restrictions in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters and…
Supervised machine learning models often associate irrelevant nuisance factors with the prediction target, which hurts generalization. We propose a framework for training robust neural networks that induces invariance to nuisances through…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Individuals may differ in their parameter values. This article discusses a three-step method of studying such differences by calculating and then modeling "individual parameter contributions", making the study of heterogeneity in arbitrary…
Profile likelihood is the key tool for dealing with nuisance parameters in likelihood theory. It is often asserted, however, that profile likelihood is not a 'true' likelihood. One implication is that likelihood theory lacks the generality…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a…
We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
A recent literature considers causal inference using noisy proxies for unobserved confounding factors. The proxies are divided into two sets that are independent conditional on the confounders. One set of proxies are `negative control…
The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
The analysis of screening experiments is often done in two stages, starting with factor selection via an analysis under a main effects model. The success of this first stage is influenced by three components: (1) main effect estimators'…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Pooling multiple neuroimaging datasets across institutions often enables improvements in statistical power when evaluating associations (e.g., between risk factors and disease outcomes) that may otherwise be too weak to detect. When there…
The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter…