Paper:
Multiscale Semi-Markov Dynamics for Intracortical Brain-Computer Interfaces
Intracortical brain-computer interfaces (iBCIs) have allowed people with tetraplegia to control a computer cursor by imagining the movement of their paralyzed arm or hand. State-of-the-art decoders deployed in human iBCIs are derived from a Kalman filter that assumes Markov dynamics on the angle of intended movement, and a unimodal dependence on intended angle for each channel of neural activity. Due to errors made in the decoding of noisy neural data, as a user attempts to move the cursor to a goal, the angle between cursor and goal positions may change rapidly. We propose a dynamic Bayesian network that includes the on-screen goal position as part of its latent state, and thus allows the person's intended angle of movement to be aggregated over a much longer history of neural activity. This multiscale model explicitly captures the relationship between instantaneous angles of motion and long-term goals, and incorporates semi-Markov dynamics for motion trajectories. We also introduce a multimodal likelihood model for recordings of neural populations which can be rapidly calibrated for clinical applications. In offline experiments with recorded neural data, we demonstrate significantly improved prediction of motion directions compared to the Kalman filter. We derive an efficient online inference algorithm, enabling a clinical trial participant with tetraplegia to control a computer cursor with neural activity in real time. The observed kinematics of cursor movement are objectively straighter and smoother than prior iBCI decoding models without loss of responsiveness.

Review:
The paper describes a novel brain-computer-interface algorithm for controlling movement of a cursor to random locations on a screen using neuronal activity (power in the "spike-spectrum" of intra-cortically implanted selected electrodes).
The algorithm uses a dynamic Bayesian network model that encodes possible target location (from a set of possible positions on a 40x40 grid, layed out on the screed). Target changes can only occur once a countdown timer reaches zero (time intervals are drawn at random) at which time the target has a chance of switching location. This forces slow target location dynamics.
Observations (power in spike spectrum) are assumed to be drawn from a multi modal distribution (mixture of von Mises functions) as multiple neurons may affect the power recording on a single electrode and are dependent on the current movement direction. The position is simply the integration over time of the movement direction variable (with a bit of decay).
The novel method is compared with several variations of a Kalman filter (using same movement state space but missing the latent target location) and an HMM. Experiments are performed off line (using data from closed loop BCI session using either a Kalman filter or an HMM) and also in 2 online closed-loop sessions (alternating between Kalman filter and the new method). Experiments performed an a tetraplegic human subject.
Overall the paper (sans supplementary material with is essential to understanding the experiment) is well written. The new model vastly outperforms the standard Kalman Filter, as is clear from the multiple figures and supplementary movies (!).
Some comments:
- I gather that the von Mieses distribution was used both for modelling the observations given the intended movement direction and for modelling the next goal position. I found the mathematical description of the selection of the goal position unclear. Is there a distribution over possible goal positions or is a single goal position selected at each time point during inference? Can you clarify?
- Once a timer is set, can the goal be changed before the timer expires? My understanding is that it cannot, no matter what the observations show. I find this to be a strange constraint. There should be more straightforward ways of inducing slow switch rates that would not force the estimate of the target position to stay fixed as new evidence accumulates. e.g. forced transition rates or state cascades. 
- My understanding is that the model has no momentum. I.e., the cursor can "turn on a dime". most objects we control can not (e.g hand movements). Would it not make more sense to use a model that preserves some of the velocity and controls some of the accelleration? It is known that some neurons in motor cortex are direction sensitive and other are force sensitive. Would it not be more natural?
- After an initial model learning period, the model is fixed for the rest of the session. It would be interesting to see how the level of performance changes as time passes. Is the level of performance maintained? Is there some degredation as the network / recordings drift? Is there some improvement as the subject masters control of the system? Would an adaptive system perform better? These questions are not addressed. 
- The paper is geared at an engineering solution to the BCI problem. There is no attempt at providing insights into what the brain encodes most naturally or how the subject (and neural system) adapt / learn to make the most out of the provided BCI. 
- citations are in the wrong format should be numerical [1] , [1-4] etc... not Author et al (2015).