Inverse kinematics is about reconstructing body motion from position marker data, not really about modeling. For example, glue some tennis balls to a person's arms and legs, track their position from video of the person walking around, and use inverse kinematics to reconstruct their joint angles (their skeletal pose) across time. It's also possible to do this with marker-free methods.
Inverse dynamics takes the kinematics data from above and, in combination with ground reaction forces measured from a force plate (or instrumented footwear, etc.), calculates the forces and moments on each joint. Since control of the human musculoskeletal system is over-determined (the same motion, forces, and moments can be produced by multiple muscle activation patterns), EEG data or even ultrasound elastography is sometimes used to better constrain estimates of muscle activation patterns.
In your example the usual approach would be to use (elements of) the above methods to find out if a patient had unusual motion patterns, like the suspected abnormal leg motion in your back pain patient. Statistics comes into play once you have population data to classify as "good" or "bad", and when you're trying to determine if the hypothesized relationships between symptoms and particular motion / muscle activation patterns genuinely exist. Of course, it's fine to try different approaches (but don't forget to obtain IRB review and comply with the various regulations on human subjects research).
Inverse dynamics takes the kinematics data from above and, in combination with ground reaction forces measured from a force plate (or instrumented footwear, etc.), calculates the forces and moments on each joint. Since control of the human musculoskeletal system is over-determined (the same motion, forces, and moments can be produced by multiple muscle activation patterns), EEG data or even ultrasound elastography is sometimes used to better constrain estimates of muscle activation patterns.
In your example the usual approach would be to use (elements of) the above methods to find out if a patient had unusual motion patterns, like the suspected abnormal leg motion in your back pain patient. Statistics comes into play once you have population data to classify as "good" or "bad", and when you're trying to determine if the hypothesized relationships between symptoms and particular motion / muscle activation patterns genuinely exist. Of course, it's fine to try different approaches (but don't forget to obtain IRB review and comply with the various regulations on human subjects research).