arXiv subjects

Richard Clare

Publications and source records attributed to Richard Clare.

3 recordsLinked to original sources

arXiv2026

Bounds on Intrinsic Bayes Factors and Least Favorable Intrinsic Priors for General Statistical Hypothesis Testing

Hypothesis Testing is the most contentious procedure in statistical Methodology. P values rejects Null Hypotheses far too easily, specially for large samples. On the other hand, Bayes Factors depends on assumptions, for example regarding Intrinsic Bayes Factors, which average? Arithmetic, Geometric, Median? Our bound is the infimum over all the averages. We develop a lower bound on Intrinsic Bayes Factors that adjust authomatically with the sample size. Furthermore, we introduce the new idea of {\it{\textbf{Least Favorable Intrinsic Prior}}}, which corresponds to the least favourable possible training samples. The bound sets a bridge between Intrinsic Bayes Factors and Adrian Smith and David Spiegelhalter methodology.

math.ST↗

arXiv2024

The GPU-based High-order adaptive OpticS Testbench

The GPU-based High-order adaptive OpticS Testbench (GHOST) at the European Southern Observatory (ESO) is a new 2-stage extreme adaptive optics (XAO) testbench at ESO. The GHOST is designed to investigate and evaluate new control methods (machine learning, predictive control) for XAO which will be required for instruments such as the Planetary Camera and Spectrograph of ESOs Extremely Large Telescope. The first stage corrections are performed in simulation, with the residual wavefront error at each iteration saved. The residual wavefront errors from the first stage are then injected into the GHOST using a spatial light modulator. The second stage correction is made with a Boston Michromachines Corporation 492 actuator deformable mirror and a pyramid wavefront sensor. The flexibility of the bench also opens it up to other applications, one such application is investigating the flip-flop modulation method for the pyramid wavefront sensor.

astro-ph.IM↗

arXiv2024

A universal robust bound for the intrinsic Bayes factor

In this work, we undertake a comprehensive reformulation, modification, and extension of Smith and Spiegelhalter's (1980) and (1982) Bayes Factor work within the evolving subject of Objective Bayes Factors. Our primary focus centers on defining and computing empirical and theoretical bounds for the Intrinsic Bayes Factor (IBF) across various models, including normal, exponential, Poisson, geometric, linear, and ANOVA. We show that our new bounds are useful, feasible, and change with the amount of information. We also propose a methodology to construct the least favorable (for the null model) intrinsic priors that result in the lower and upper bounds of the Intrinsic Bayes Factors under certain conditions. Notably, our lower bounds exhibit superior performance compared to the well-known -ep log(p) bound proposed by Sellke et al. (2001) (Sellke et al., 2001) based on p-values.

math.ST↗