Complete Simultaneous Fiducial Distributions

Fiducial Inference for Discrete Distributions: Binomial and Poisson Cases

#p-complete Conditional Distributions

We study conditional probability from the perspective of complexity theory of functions and operators in analysis, building on work by Ko (1983), Friedman (1984), and Kawamura and Cook (2010). For some random variable X in {0, 1}N whose distribution is continuous and polynomial-time computable, and some polynomial-time computable function f : {0, 1}N → [0, 1] for which the random variable f(X) ...

Inference for functions of parameters in discrete distributions based on fiducial approach: Binomial and Poisson cases

In this article, we propose a simple method of constructing confidence intervals for a function of binomial success probabilities and for a function of Poisson means. The method involves finding an approximate fiducial quantity (FQ) for the parameters of interest. A FQ for a function of several parameters can be obtained by substitution. For the binomial case, the fiducial approach is illustrat...

Self-Calibration and Simultaneous Motion Estimation for C-Arm CT Using Fiducial

C-arm cone-beam CT systems have an increasing popularity in the clinical environment due to their highly flexible scan trajectories. Recent work used these systems to acquire images of the knee joint under weight-bearing conditions. During the scan, the patient is in a standing or in a squatting position and is likely to show involuntary motion, which corrupts image reconstruction. The state-of...

Fiducial prediction

A real-valued fiducial process is a process in the probabilistic sense, but the probability distributions are not defined on Borel sets. The adjective ‘fiducial’ indicates that a group acts on the observation spaces and the probability distributions are defined on the smaller σ-algebra of group-invariant Borel sets. Since a different group action determines a different σ-algebra, the group is a...