R code for the Bayesian methodology proposed in “Probabilistic Detection and Estimation of Conic Sections from Noisy Data” by Subharup Guha and Suit K. Ghosh. The manuscript is available at https://arxiv.org/abs/1910.14078
The code reproduces the results of Simulation Study 2 of Section 3.2. Specifically, it performs three functions: (a) generates artificial datasets, (b) analyzes the generated data using the proposed Bayesian methodology to detect the underlying conic type, and (c) provides a summary of the method’s accuracy of detection, presented in Table 3.
The artificial datasets consist of noisy data generated by conics in non-standard form, i.e., hyperbolas, ellipses, and parabolas with unknown focuses and arbitrarily rotated axes of symmetry. To increase the difficulty of making calls from a visual inspection, all the datasets correspond to partial conics, such as half-ellipses that may be incorrectly detected as hyperbolas or parabolas. Additional variability is introduced into the simulation by randomly generating the true conics parameters for each artificial dataset. Assuming all conic parameters to be unknown, the MCMC procedure described in the paper is implemented to identify the unknown type of conic in each dataset. Finally, summary details are provided about the estimated posterior probabilities and standard errors of detection and misclassification for each type of conic.
To obtain the Table 3 result of the paper, simply run "master.R".