The Idea of Laplace's Method
Assume that the function ƒ(x) has a unique global maximum at x0. Then, the value ƒ(x0) will be larger than other values ƒ(x). If we multiply this function by a large number M, the gap between Mƒ(x0) and Mƒ(x) will stay the same (since Mƒ(x0)/Mƒ(x) = ƒ(x0)/ƒ(x) ) -but it will grow exponentially in the function (see figure)
Thus, significant contributions to the integral of this function will come only from points x in a neighborhood of x0, which can then be estimated.
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