Most social science research about beliefs excludes atheist participant samples . . .

If I look out my window and see a bear running by my house, I can say, “I believe I just saw a bear." Perfectly fine usage, backed up by sufficient evidence. Has the usage of this word changed in recent years, to become less broad? :confused:
But where do you "suspect " the bear is going? What do you "suspect" is his motive for being in your yard in the first place? Also perfectly fine usage! Cap't Jack