On the assumptions behind metacognitive measurements: Implications for theory and practice

Theory of visual confidence has largely been grounded in the gaussian signal detection framework. This framework is so dominant that people could be rather ignorant of idiosyncratic consequences from this distributional assumption. By contrasting gaussian and logistic signal detection models, this paper systematically evaluates the consequences of auxiliary distributional assumptions in the measurement of metacognitive accuracy and its theoretical implications. We found that these models can lead to opposing conclusions regarding the efficiency of confidence rating relative to objective decision (whether meta-d’ is larger or smaller than d’) as well as the metacognitive efficiency along the internal evidence continuum (whether meta-d’ is larger or smaller for higher levels of confidence). These demonstrations may call for reconsideration of hitherto established theories of metacognition that are critically dependent on auxiliary modeling assumptions. We deem there is no instant solution for this matter as our quantitative model comparisons on a large dataset did not decide on a clear victor between gaussian and logistic metacognitive models. Yet, being aware of the hidden modeling assumptions and their systematic consequences would facilitate cumulative development of the science of metacognition.

ROC Asymmetry Is Not Diagnostic of Unequal Residual Variance in Gaussian Signal Detection Theory

Signal detection theory (SDT) is used to analyze yes/no judgment accuracy in many research domains of psychology. SDT yields separate estimates for response bias/criterion (c) and for sensitivity/discriminability (d'). Discrimination performance can be displayed in Receiver Operating Characteristics (ROCs) plotting hit and false alarm rates at various levels of confidence. We provide formal proof and simulations showing that asymmetric ROCs in Gaussian SDT are not exclusively diagnostic of unequal residual variance but may as well result from equal-variance models with c and d' systematically varying across subjects and/or items. Falsely attributing zROC slopes to unequal residual variance while neglecting true group-level variability introduces systematic and unsystematic statistical error. We show that ordinal regression models minimize such errors while estimating all SDT parameters and statistical criteria in a single model.

A Hierarchical Unequal-Variance Signal Detection Model for Binary Data

Gaussian signal detection models with equal variance are typically used for detection and discrimination data whereas models with unequal variance rely on data with multiple response categories or multiple conditions. Here a hier- archical signal detection model with unequal variance is suggested that requires only binary responses from a sample of participants. Introducing plausible constraints on the sampling distributions for sensitivity and response criterion makes it possible to estimate signal variance at the population level. This model was applied to existing data from memory and reasoning tasks and the results suggest that parameters can be reliably estimated, allowing a direct comparison of signal detection models with equal- and unequal-variance.

On Energy–Information Balance in Automatic Control Systems Revisited

We revise and slightly generalize some variational problems related to the “informational approach” in the classical optimization problem for automatic control systems which was popular from 1970–1990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax relations. The main example of such functionals is given by the Gelfand–Pinsker–Yaglom formula for the information quantity contained in one random process in another one. We find some balance relations in a linear stationary one-dimensional system with Gaussian signal and interpret them in terms of Legendre duality.

A Single-Judge Solution to Beauty Contests

We show that the equilibrium policy rule in beauty contest models is equivalent to that of a single agent’s forecast of the economic fundamental. This forecast is conditional on a modified information process, which simply discounts the precision of idiosyncratic shocks by the degree of strategic complementarity. The result holds for any linear Gaussian signal process (static or persistent, stationary or nonstationary, exogenous or endogenous), and also extends to network games. Theoretically, this result provides a sharp characterization of the equilibrium and its properties under dynamic information. Practically, it provides a straightforward method to solve models with complicated information structures. (JEL C72, D82, D83, D84)

Sensing system with an artificial neural network based on floating-gate metal oxide semiconductor transistors

This paper shows a novel design of a gas sensor system based on artificial neural networks and Floating-gate MOS Transistors (FGMOS). Two types of circuits with FGMOS transistors of minimum dimensions were designed and simulated by Simulink of Matlab; simulations and experimental measurements results were compared obtaining good expectations. The reason of using FGMOS is that ANN can also be implemented with these kinds of devices, since ANN’s based on FGMOS are able to produce pseudo Gaussian-functions. These functions give a reliable option to determine the gas concentration. A sensitive thin film can be deposited on the FGMOS’s floating gate, which produces a charge variation due to the chemical reaction between the sensitive layer and the gas species, modifying the threshold voltage thereby a correlation of drain current of the FGMOS with gas concentration can be obtained. Therefore, a generator circuit was implemented for the pseudo Gaussian signal with FGMOS. This system can be applied in environments with dangerous species such as CO2, CO, methane, propane, among others. Simulations demonstrated that the implemented proposal has a good performance as an alternative method for sensing gas concentrations, compared with conventional sensors.

Nonlinear and non-Gaussian signal processing

Linear, time-invariant (LTI) Gaussian DSP, has substantial mathematical conveniences that make it valuable in practical DSP applications and machine learning. When the signal really is generated by such an LTI-Gaussian model then this kind of processing is optimal from a statistical point of view. However, there are substantial limitations to the use of these techniques when we cannot guarantee that the assumptions of linearity, time-invariance and Gaussianity hold. In particular, signals that exhibit jumps or significant non-Gaussian outliers cause substantial adverse effects such as Gibb's phenomena in LTI filter outputs, and nonstationary signals cannot be compactly represented in the Fourier domain. In practice, many real signals show such phenomena to a greater or lesser degree, so it is important to have a `toolkit' of DSP methods that are effective in many situations. This chapter is dedicated to exploring the use of the statistical machine learning concepts in DSP.