The Lighthouse Problem

The Lighthouse Problem

A lighthouse is somewhere off a piece of straight coastline at a position \(\alpha\) along the shore and a distance \(\beta\) out at sea. It emits a series of short highly collimate d flashes at random intervals and hence at random azimuths. These pulses are intercepted on the coast by photo-detectors that record only the fact that a flash has occurred, but not the angl e from which it came. \(N\) flashes have so far been recorded at positions \(\x_k\). Where is the lighthouse? - Text taken from [Sivia2006] (Example 3, 2nd Edition).

Lighthouse Sketch from Sivia2006


[Gull1988] - Bayesian Inductive Inference And Maximum Entropy, Stephen F. Gull [Sivia2006] - Data Analysis, A Bayesian Tutorial, Oxford University Press, D. Sivia, J. Skilling


Example 1 (distance \(\beta\) from shore known, location \(\alpha\) at coastline unknown)

python -m korali.plot --dir _results_example_1

Example 2 (distance \(\beta\) & location \(\alpha\) unknown)

python -m korali.plot --dir _results_example_2