Abstract
The nature of human behavior makes Bayesian methods particularly well-suited for its automated analysis. It is complex, highly variable, frequently inconsistent and is often the consequence of thought processes that we know not of. Advanced modeling techniques that specifically take uncertainty into account are therefore highly desirable. If it were not for the associated computational cost, whether real or perceived, fully Bayesian methods would probably be dominating the field. It can therefore be expected that, as computational power becomes ever more easily and cheaply available, we will see a growing trend towards the wide use of these methods. This chapter introduces the basics of Bayesian methods, and focuses specifically on two major techniques which have received increasing attention in recent years, thanks to their flexibility, ease of use and computational tractability: Dirichlet processes and Gaussian processes.
This chapter introduces the basics of Bayesian methods, and focuses specifically on two major techniques which have received increasing attention in recent years, thanks to their flexibility, ease of use and computational tractability: Dirichlet processes and Gaussian processes.
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- 1.
For the remainder of this chapter, we handle the convention that vectors are denoted by lowercase bold letters (a,θ,…), while matrices are denoted by uppercase bold letters (A,Σ,…).
- 2.
That is, the prior probability distribution that we had defined over the parameter values. In Bayesian statistics, probabilities are seen as a measure of our belief in the possible values of a variable.
- 3.
With infinite amounts of training data, the prior vanishes and both ML and MAP converge to the same solution.
- 4.
We may nevertheless not be certain which cluster a data point belongs to, so that neither the prior nor the posterior probability that a given data point belongs to a given cluster need to be zero or one.
- 5.
For the purpose of this explanation, we will consider functions of a single, scalar variable, but the concept easily extends to multiple dimensions.
- 6.
To be more formally exact, it is defines the distribution over any finite subset of the variables in that vector to be Gaussian.
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Englebienne, G. (2011). Bayesian Methods for the Analysis of Human Behaviour. In: Salah, A., Gevers, T. (eds) Computer Analysis of Human Behavior. Springer, London. https://doi.org/10.1007/978-0-85729-994-9_1
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