Context
Where Qamar et al. 2013 sits in the field
The paper is one test in a long research programme: do people and animals use their own, trial-by-trial sensory uncertainty when they decide, as a Bayesian observer would? The map below places it among papers ( from the Ma lab), with "builds on" links.
The question the paper answered
A Bayesian observer weights evidence by its reliability. With a fixed reliability, though, an observer who is Bayesian cannot be told apart from one that has simply learned a good fixed criterion. Maloney and Mamassian called the way out "Bayesian transfer": make reliability change unpredictably from trial to trial, so that the optimal rule changes with it in a specific way. The Ma lab's tasks of the late 2000s share this design trick: visual search with item-by-item reliability (Ma et al. 2011), same–different judgements, working memory with variable precision, and categorisation, which is Qamar et al. 2013.
The categorisation task makes the prediction unusually sharp. Two categories with the same mean and different widths mean that the optimal boundary must move outward as noise grows, so an observer with a fixed boundary is measurably suboptimal. Humans and monkeys moved their boundaries with contrast. Subjects split between the optimal rule and simpler uncertainty-dependent heuristics (Lin-σ, Quad-σ), and Fixed always lost. On the neural side, a network with quadratic operations and divisive normalization on Poisson-like population input approximated the posterior, the same motif as the probabilistic population codes of Ma et al. 2006 and the search network of Ma et al. 2011.
What came after
- Heuristics vs Bayes became the main question. Shen and Ma (2016) found that several complex suboptimal rules are indistinguishable from optimal with lab-sized data: identifiability, not optimality, is the bottleneck. Qamar's split verdict (Opt for some subjects, Lin-σ or Quad-σ for others) is an early instance.
- Confidence. Adler and Ma (2018) used the same narrow-vs-wide categories with confidence reports; heuristic models beat Bayesian confidence. Denison et al. (2018) varied uncertainty through attention instead of contrast, and boundaries still moved.
- The same structure elsewhere. A binary latent variable choosing between a narrow and a wide distribution recurs in contour integration (Zhou et al. 2020), audiovisual synchrony and body ownership (Chancel et al. 2022).
- Neural implementation. Orhan and Ma (2017) trained generic networks on error feedback alone, including on this task, and found near-optimal probabilistic inference without a hand-built architecture. Walker et al. (2020) recorded V1 in monkeys doing this exact task (Monkey L is the same animal) and decoded trial-by-trial likelihood functions that predicted choices.
- Approximate observers. Point-estimate observers (Schütt et al. 2023) and a renewed look at fixed criteria (Lee et al. 2023) revisit the question of how much of the Bayesian computation is really performed.
The pattern. When Bayes makes a distinctive qualitative prediction, people are near-optimal in direction. Whether they are exactly Bayesian, or use a cheaper heuristic that tracks uncertainty, is usually unresolved at lab sample sizes. This replication's results fit that pattern: corrected fits keep the split between Opt and the heuristics, and model recovery (Phase 2) shows the design separates the paper's five models moderately well in humans (62–96% correct in the main experiment, 46–88% in the control) and well with Monkey L's trial count, while a near-Bayesian alternative (ImpSigma) is identifiable only at some subjects' parameters (Extensions).
The map
Select a paper to light up what it built on (blue) and what built on it (orange). Qamar et al. 2013 and its lineage are highlighted. Search, pan and zoom work inside the frame. Open the map full-screen.
Compiled in October 2026 by a research subagent (Opus); DOIs and years checked against Crossref and Europe PMC. Some entries are preprints.
Source: reports/malab_map/.