Electrophysiological recording data from multiple cells in motor cortex and elsewhere often are interpreted using the population vector method pioneered by Georgopoulos and coworkers. This paper proposes an alternative method for interpreting coding across populations of cells that may succeed under circumstances in which the population vector fails. 2. Population codes are analyzed using probability theory to find the complete conditional probability density of a movement parameter given the firing pattern of a set of cells. 3. The conditional probability density when a single cell fires is proportional to the shape of the cell's tuning curve of firing rate in response to different movement parameters. 4. The conditional density when multiple cells fire is proportional to the product of their tuning curves. 5. Movement parameters can be estimated from the conditional density using statistical maximum likelihood or minimum mean-squared error methods. 6. Simulations show that density estimation correctly finds movement directions for nonuniform distributions of preferred directions and noncosine cell tuning curves, whereas the population vector method fails for these cases. 7. Probability methods thus provide a statistically based alternative to the population vector for interpreting electrophysiological recording data from multiple cells.
