This is an interesting question because it depends a lot on the nature of belief. It also gets (lightly) into the idea of duality.
Can one choose any belief? Can a person choose to believe that the sky is green? Does the use of the term "believe" not imply a perceived truth in the "belief"? If the person doesn't perceive truth in the belief then is it really a belief? Doesn't this lead to the question of whether or not a person can choose his perception of truth? "Choice" implies a conscious action, are you all willing to claim that truth is subject to a person's choice? The only way that a belief can be chosen is if the perception of truth can be chosen. I think that the grounds of intellectual honesty dictate that the perception of truth must be dynamically changeable in response to an ever-increasing store of stimuli, information, and experience. A person has the choice to actively pursue greater or lesser amounts of stimuli, information, and experiences and that choice has a dramatic impact on how quickly or how much a person's perception of truth changes but they don't have a direct control over their perception of truth.
In brief, a person cannot choose his beliefs because he cannot choose his perception of truth in any direct way but only through the very indirect method of limiting or encouraging diverse experiences which increase his ability to evaluate the truth and come ever closer to it as an asymptotic curve does approaches a given value.
ZV