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Spatial

by Travis Monk (Submitted: 10/30/2013)

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## WHAT IS IT?

This model illustrates how spatial distributions of spiking sensors (small black circles) can, in principle, use Bayesian inference about some state of the world. In this model, the state of the world considered is the location of a prey (small red circle) with respect to a predator (large red circle). Watch how spatial distributions of spiking sensors can represent a probability distribution of prey location that converges on its actual location

## HOW IT WORKS

The predator has S neurones (S is user-defined) that are equally spaced around the circumference of the predator. Each sensor fires a spike on a time step with probability Pr(S|r,theta), where (r, theta) is the position of the prey with respect to the predator, as outlined in the manuscript. Given this conditional probability and a prior distribution, we can infer the prey location by Bayes' rule with the individual spikes and non-spikes of the individual neurones.

Since the posterior distribution is in two dimensions, the probability that the prey is on a certain square patch is indicated by the colour of that patch. If the patch is blue, then the prey is unlikely to be on that patch, given the output of the sensors. If the patch is white, then the prey is highly likely to be on that patch, given the output of the sensors.

## HOW TO USE IT

To start, set the parameters of the model to your desired values. Choose the location of the prey using the `distance-from-predator' and 'angle' sliders and the number of sensors S that the predator possesses. Choose the gain and noise of each sensor; sensors are defined to be equivalent, so every sensor will have the same gain and noise parameter values.

Next, click the 'setup' button and then click 'go.' Click the 'go' button once to start running a simulation, and click again to pause it. Use the speed slider at the top of the screen to control the speed of the simulation. Every time step is one millisecond in duration. When a neurone spikes in a time step, that neurone flashes white, and when a neuron does not spike on a time step, that neurone is black. The posterior distribution of prey location is modified accordingly (see the manuscript) and the simulation proceeds to the next time step.

## THINGS TO TRY

Investigate how the gain/noise ratio affects the speed of convergence of the posterior to the actual prey location. The higher the gain/noise ratio, the fewer time steps required for the posterior to accurately estimate prey location.

Investigate how the proximity of the prey to the predator affects the speed of convergence of the posterior to the actual prey location. The smaller r is, the fewer time steps required for the posterior to accurately estimate prey location.

Investigate how the number of sensors S affects the speed of convergence of the posterior to the actual prey location. Generally speaking, the higher S is, the fewer time steps required for the posterior to accurately estimate prey location.

## EXTENDING THE MODEL

To relax the assumption that prey is stationary, we need to utilise some basic theory from particle filtering (sequential Monte Carlo approximation algorithms).

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