1. A method for troubleshooting based on a probability distribution model, the method comprising: establishing a speech-based conversation with a user; establishing at least one non-speech-based channel of interaction for obtaining behavioral information associated with a product during the speech-based conversation; for each of a plurality of component variables, maintaining via a processor a probability distribution for a state of the product based on a state of the speech-based conversation over time and a state of the behavioral information over time; and troubleshooting the product by responding based on the probability distribution.