I tend to define faith as belief which is evident through action.
Effective faith has to be more than just mental agreement to an idea.
The scriptures say "Faith is the evidence of things not seen and the substance of things hoped for." One aspect of that to me is that faith is evident, and substantive.
Faith ultimately flows to us, and through us, from God. We can choose to have faith.. but the choice to have faith is ultimately simply the choice to rely upon God. To take action upon his word, and trust that he will see to results and consequences, and ultimately that he will uphold your faith itself.
There is no salvation apart from faith and it is impossible to please God without faith. Anything that is not of faith is sin.
This is the idea that faith is tied to the will of God. Those who live by faith and act by faith, truly, do what God wills, not what they will.
When we indulge our own will it is not an act of faith, but rather of sin, no matter how 'good' we imagine our will to be.
this is why many peolpe who think they are living by faith and acting by faith are really fooling themselves, because they are trying to work up faith that God will give them what they want, and will give them success in doing what they want to do. Doing what you want, and hoping that God will prosper it, is not faith.
Here we come back again to Faith is the evidence of things not seen. The Spirit of God within us is not seen, his work in us is not seen, but Faith is the evidence of those things, which is seen. When God's work in us comes to fruition in our lives, that is faith.