Related papers: Fiducial inference then and now
Building a safety case is a common approach to make expert judgement explicit about safety of a system. The issue of confidence in such argumentation is still an open research field. Providing quantitative estimation of confidence is an…
Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee, et al. (2016), allows for valid inference after model selection if the model selection event can be described by…
Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. Within this paper we will propose and present two forms of inclusion: The…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
Since the mid-2000s, there has been a resurrection of interest in modern modifications of fiducial inference. To date, the main computational tool to extract a generalized fiducial distribution is Markov chain Monte Carlo (MCMC). We propose…
The following discussion is inspired by the paper Nonparametric generalized fiducial inference for survival functions under censoring by Cui and Hannig. The discussion consists of comments on the results, but also indicates it's importance…
Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We…
Censored data, where the event time is partially observed, are challenging for survival probability estimation. In this paper, we introduce a novel nonparametric fiducial approach to interval-censored data, including right-censored, current…
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Wasserman et al. (2020, PNAS, vol. 117, pp. 16880-16890) constructed estimator agnostic and finite-sample valid confidence sets and hypothesis tests, using split-data likelihood ratio-based statistics. We demonstrate that the same approach…
This paper tries to tell the story of the general linear model, which saw the light of day 200 years ago, and the assumptions underlying it. We distinguish three principal stages (ignoring earlier more isolated instances). The model was…
Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…