Dangling modifiers are often hard to spot, and as a result frequently provide unintended comic relief, as this letter from a reader shows (Today, 15 May 2009).
As written, the sentence means the writer is a densely populated country.
This is because the non-finite clause, being a densely populated country, comes before the subject I in the main clause, and so is interpreted as modifying or adding to it. A clause or phrase that wrongly modifies a subject is called a dangling modifier or a dangling participle.
The writer could have avoided it by making the non-finite clause finite, with its own subject:
As Singapore is a densely populated country, I believe ...