ROC Curves within the Framework of Neural Network Assembly Memory Model: Some Analytic Results

On the basis of convolutional (Hamming) version of recent Neural Network Assembly Memory Model (NNAMM) for intact two-layer autoassociative Hopfield network optimal receiver operating characteristics (ROCs) have been derived analytically. A method of taking into account explicitly a priori probabilities of alternative hypotheses on the structure of information initiating memory trace retrieval and modified ROCs (mROCs, a posteriori probabilities of correct recall vs. false alarm probability) are introduced. The comparison of empirical and calculated ROCs (or mROCs) demonstrates that they coincide quantitatively and in this way intensities of cues used in appropriate experiments may be estimated. It has been found that basic ROC properties which are one of experimental findings underpinning dual-process models of recognition memory can be explained within our one-factor NNAMM.

Sensitivity and Bias within the Binary Signal Detection Theory, BSDT

Similar to classic Signal Detection Theory (SDT), recent optimal Binary Signal Detection Theory (BSDT) and based on it Neural Network Assembly Memory Model (NNAMM) can successfully reproduce Receiver Operating Characteristic (ROC) curves although BSDT/NNAMM parameters (intensity of cue and neuron threshold) and classic SDT parameters (perception distance and response bias) are essentially different. In present work BSDT/NNAMM optimal likelihood and posterior probabilities are analytically analyzed and used to generate ROCs and modified (posterior) mROCs, optimal overall likelihood and posterior. It is shown that for the description of basic discrimination experiments in psychophysics within the BSDT a ‘neural space’ can be introduced where sensory stimuli as neural codes are represented and decision processes are defined, the BSDT’s isobias curves can simultaneously be interpreted as universal psychometric functions satisfying the Neyman-Pearson objective, the just noticeable difference (jnd) can be defined and interpreted as an atom of experience, and near-neutral values of biases are observers’ natural choice. The uniformity or no-priming hypotheses, concerning the ‘in-mind’ distribution of false-alarm probabilities during ROC or overall probability estimations, is introduced. The BSDT’s and classic SDT’s sensitivity, bias, their ROC and decision spaces are compared.

A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.