Related papers: Robust Bayesian Method for Refutable Models
We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…
This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…
Some drawbacks of the formalism of Bayes Theorem can be avoided by the rMPE-Method, a modification of the cMPE-Method that permits (i): Adding probabilities in spite of non-linearity. (ii): Taking into account extensional evidence and…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
This paper proposes a new Bayesian approach for analysing moment condition models in the situation where the data may be contaminated by outliers. The approach builds upon the foundations developed by Schennach (2005) who proposed the…
Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…
Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…
This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based…
Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
Outliers can seriously distort statistical inference by inducing excessive sensitivity in the likelihood function, thereby compromising the reliability of Bayesian estimation. To address this issue, we develop a robust Bayesian estimation…