Types of approximation for probabilistic cognition : sampling and variational

A basic challenge for probabilistic models of cognition is explaining how probabilistically correct solutions are approximated by the limited brain, and how to explain mismatches with human behavior. An emerging approach to solving this problem is to use the same approximation algorithms that were been developed in computer science and statistics for working with complex probabilistic models. Two types of approximation algorithms have been used for this purpose: sampling algorithms, such as importance sampling and Markov chain Monte Carlo, and variational algorithms, such as mean-field approximations and assumed density filtering. Here I briefly review this work, outlining how the algorithms work, how they can explain behavioral biases, and how they might be implemented in the brain. There are characteristic differences between how these two types of approximation are applied in brain and behavior, which points to how they could be combined in future research

Levels of biological plausibility

Notions of mechanism, emergence, reduction and explanation are all tied to levels of analysis. I cover the relationship between lower and higher levels, suggest a level of mechanism approach for neuroscience in which the components of a mechanism can themselves be further decomposed and argue that scientists' goals are best realized by focusing on pragmatic concerns rather than on metaphysical claims about what is 'real'. Inexplicably, neuroscientists are enchanted by both reduction and emergence. A fascination with reduction is misplaced given that theory is neither sufficiently developed nor formal to allow it, whereas metaphysical claims of emergence bring physicalism into question. Moreover, neuroscience's existence as a discipline is owed to higher-level concepts that prove useful in practice. Claims of biological plausibility are shown to be incoherent from a level of mechanism view and more generally are vacuous. Instead, the relevant findings to address should be specified so that model selection procedures can adjudicate between competing accounts. Model selection can help reduce theoretical confusions and direct empirical investigations. Although measures themselves, such as behaviour, blood-oxygen-level-dependent (BOLD) and single-unit recordings, are not levels of analysis, like levels, no measure is fundamental and understanding how measures relate can hasten scientific progress. This article is part of the theme issue 'Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'

Behavioralizing the Black-Scholes Model

In this article, I incorporate the anchoring-and-adjustment heuristic into the Black-Scholes option pricing framework, and show that this is equivalent to replacing the risk-free rate with a higher interest rate. I show that the price from such a behavioralized version of the Black-Scholes model generally lies within the no-arbitrage bounds when there are transaction costs. The behavioralized version explains several phenomena (implied volatility skew, countercyclical skew, skew steepening at shorter maturities, inferior zero-beta straddle return, and superior covered-call returns) which are anomalies in the traditional Black-Scholes framework. Six testable predictions of the behavioralized model are also put forward

Where do hypotheses come from?

Why are human inferences sometimes remarkably close to the Bayesian ideal and other times systematically biased? One notable instance of this discrepancy is that tasks where the candidate hypotheses are explicitly available result in close to rational inference over the hypothesis space, whereas tasks requiring the self-generation of hypotheses produce systematic deviations from rational inference. We propose that these deviations arise from algorithmic processes approximating Bayes' rule. Specifically in our account, hypotheses are generated stochastically from a sampling process, such that the sampled hypotheses form a Monte Carlo approximation of the posterior. While this approximation will converge to the true posterior in the limit of infinite samples, we take a small number of samples as we expect that the number of samples humans take is limited by time pressure and cognitive resource constraints. We show that this model recreates several well-documented experimental findings such as anchoring and adjustment, subadditivity, superadditivity, the crowd within as well as the self-generation effect, the weak evidence, and the dud alternative effects. Additionally, we confirm the model's prediction that superadditivity and subadditivity can be induced within the same paradigm by manipulating the unpacking and typicality of hypotheses, in 2 experiments.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF – 1231216