On the relationship between a Gamma distributed precision parameter and the associated standard deviation in the context of Bayesian parameter inference
This addresses a specific technical issue in Bayesian parameter inference, making it easier to incorporate prior knowledge on standard deviation, but it is incremental as it focuses on a transformation method without broader applications.
The paper tackles the impracticality of using a Gamma distributed precision parameter when prior information on the standard deviation is needed in Bayesian inference, by introducing a numerical optimisation method for transformation between them, showing adequate results across various scenarios.
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be utilised during inference. This paper thus introduces a method for transforming between a gamma distributed precision parameter and the distribution of the associated standard deviation. The proposed method is based on numerical optimisation and shows adequate results for a wide range of scenarios.