Biomedical Engineering Reference
In-Depth Information
4.1
Introduction
During the past decades, neuroscience and neuroethology have experienced a
dramatic increase in the availability of methods to analyse neural data. Yet, compu-
tational data analysis has long been an integral part of this area of research, as
attested by many historical examples. Hodgkin and Huxley, for instance, used
numerical integration of differential equations to study the propagation of action
potentials in the giant squid axon. In another classical study, Katz and colleagues
applied probability theory to derive the properties of quantal synaptic release at the
neuromuscular junction. Recent progress in neural modelling has been in large part
fueled by an exponential increase in computing power, the widespread availability
of powerful numerical and simulation packages, such as MATLAB and NEURON, as
well as the need to cope with increasingly complex neural data sets spanning mul-
tiple spatio-temporal scales. The interested reader will ind a comprehensive treat-
ment of modelling techniques in Gabbiani and Cox [
2010
], including many
worked-out numerical and programming examples.
In this chapter, we focus on a speciic topic that has attracted renewed attention
and that is pertinent to neuroethology: Bayesian statistical modelling. The Bayesian
framework allows the computational analysis of neural data in the context of the
animal's environment using rigorous mathematical methods. In the following sec-
tions, we start with a brief introduction to Bayesian modelling before illustrating its
use to analyze the neural coding of natural sounds in the barn owl. The igures of
this chapter were generated using short MATLAB programs that are available online
and will help the reader assimilate the material covered. The name of these pro-
grams is speciied at the end of the igure legends using the notation: (
name.m
).
4.2
Bayesian Statistical Modelling
The Bayesian approach to statistics interprets probabilities as measures of belief
instead of empirical frequencies for event occurrence (Doya et al.
2007
, Hoff
2009
).
This framework centred on belief allows one to model decision making in a princi-
pled manner by (1) taking into account the sensory input experienced by an organ-
ism, (2) integrating previous information (e.g. memories or biases) and (3) deciding
on an appropriate motor output, based on this information.
In the Bayesian framework, the state of the outside world may be conceived as a
model indexed by a variable
θ
. In general, the variable
θ
will be multidimensional.
The main task of the organism is to infer from sensory data,
d
, an estimate of the
current state of the world,
q
, so as to react with an appropriate motor output. The
sensory data could for instance be the iring rate of sensory neurons activated in the
current state of the world. Because the transduction of external stimuli into neural
signals is noisy, due to both intrinsic and extraneous variability, and because the
processing of neural signals is noisy as well, the sensory data
d
will usually be a
random variable determined by
θ
and characterized by the conditional distribution
