# 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).

References

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

## Setup¶

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

./example_1
python -m korali.plotter --dir _results_example_1


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

./example_2
python -m korali.plotter --dir _results_example_2