# Climate change and The Burglar's Stopping Problem

The climate change hypothesis is that global changes in climate leading to significantly higher number of severe weather events are predominantly man-made, and in particular, the release of greenhouse gases such as carbon-dioxide into the atmosphere is a leading cause. After conveniently escaping the national spotlight in the US during the presidential campaigns, climate change has once again appeared in the news, thanks to Hurricane Sandy. Munich-Re, the reinsurance giant released a report, somewhat presciently on Oct 17, that says:

Nowhere in the world is the rising number of natural catastrophes more evident than in North America. The study shows a nearly quintupled number of weather-related loss events in North America for the past three decades, compared with an increase factor of 4 in Asia, 2.5 in Africa, 2 in Europe and 1.5 in South America.

Unambiguously proving that man-made climate change has a role to play in a specific event such as Sandy is more of an ideological debate, than a statistical exercise. And so there are many many people who can boldly claim that man-made climate change is fiction.

A few industrialized nations are responsible for the bulk of CO2 emissions.

Some of these nations have refused to ratify the Kyoto Protocol, which calls for reduction in CO2 emissions. No points for guessing which colors in the map below denote countries that have not ratified the treaty.

(Brown = No intention to ratify. Red = Countries which have withdrawn from the Protocol. Source: Wikipedia)

Most of the world apparently believes in man-made climate change. When will these other countries wake up? I can't help but think of the following stopping problem:

Taken from G. Haggstrom (1966) “Optimal stopping and experimental design”, Ann. Math. Statist. 37, 7-29.

A burglar contemplates a series of burglaries. He may accumulate his larcenous earnings as long as he is not caught, but if he is caught during a burglary, he loses everything including his initial fortune, if any, and he is forced to retire. He wants to retire before he is caught. Assume that returns for each burglary are i.i.d. and independent of the event that he is caught, which is, on each trial, equally probable. He wants to retire with a maximum expected fortune. When should the burglar stop?