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Ghahramani et al. model multisensory integration as a process minimizing uncertainty.

Human performance in combining slant and disparity cues for slant estimation can be explained by (optimal) maximum-likelihood estimation.

According to Landy et al., humans often combine cues (intra- or cross-sensory) optimally, consistent with MLE.

To estimate optimally, it is necessary to take into account the rate of each stimulus value. This is neglected by the efficient coding approach, which is recognized by the opponents.

Statistical decision theory and Bayesian estimation are used in the cognitive sciences to describe performance in natural perception.

A best estimator wrt. some loss function is an estimator that minimizes the average value of that loss function.

Given probability density functions (PDF) $P(X)$ and $P(X\mid M)$ for a latent variable $X$ and an observable $M$, an optimal estimator for $X$ wrt. the loss function $F$ is given by $$ f_{opt} = \mathrm{arg min}_f \int P(x) \int P(x\mid m) L(x,f(m))\;dx\;dm $$

The maxiumum a posteriori estimator (MAP) arises from an error function which penalizes all errors equally.

A weakness of empirical Bayes is that the prior which explains the data best is "not necessarily the one that leads to the best estimator".

Optimality of an estimator is relative to

  • loss function,
  • measurement probability,
  • prior,
  • (depending on the setting) a family of functions.

A representation of probabilities is not necessary for optimal estimation.

Weisswange et al. apply the idea of Bayesian inference to multi-modal integration and action selection. They show that online reinforcement learning can effectively train a neural network to approximate a Q-function predicting the reward in a multi-modal cue integration task.