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Joram Soch

Publications and source records attributed to Joram Soch.

6 recordsLinked to original sources

On Agentic Behavioral Modeling

Integrating theoretical neuroscience, decision theory, and probabilistic inference offers a promising route to understanding human cognition, yet concrete methodological bridges between agentic AI models and behavioral data analysis remain formally underdeveloped. We advance this synthesis under the framework of agentic behavioral modeling (ABM), which treats artificial agents as latent, generative hypotheses about cognitive mechanisms and evaluates them by their statistical adequacy in explaining human behavior. After outlining its conceptual foundations, we apply the framework to two minimal laboratory paradigms: a binary perceptual contrast-discrimination task and a symmetric two-armed bandit learning task. We formalize each task-agent-data system as a joint probability model, derive explicit conditional log-likelihoods for behavioral inference, validate different model variants using model and parameter recovery simulations, and evaluate them in light of empirical data. Using these minimal examples, we provide an agent-centric interpretation of the psychometric function, derive optimal policies for both tasks, and show the equivalence between Rescorla-Wagner learning and Bayesian inference in symmetric bandits. More broadly, this work may serve as a conceptual and practical foundation for applying ABM to cognitive behavioral science.

q-bio.NC

cvBMS and cvBMA: filling in the gaps

With this technical report, we provide mathematical and implementational details of cross-validated Bayesian model selection (cvBMS) and averaging (cvBMA) that could not be communicated in the corresponding peer-reviewed journal articles. This will allow statisticians and developers to comprehend internal functionalities of cvBMS and cvBMA for further development of these techniques.

stat.ME

Linear Algebraic Number Theory, Part I: Foundations

We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space, therefore replaces multiplication with addition and allows to capture variation in the natural numbers from variation in the prime numbers. This automatically puts prime numbers to their designated place of atomic particles of natural numbers and enables fruitful new formulations of number-theoretic functions. We outline the theory, derive some basic results, make connections to standard number theory and give an outlook regarding the Riemann hypothesis, number theory's long-standing enigma.

math.GM

Solution for the Indefinite Integral of the Standard Normal Probability Density Function

Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this anti-derivative in infinite elementary terms that, when being differentiated, directly yields the standard normal density function. We derive this function using infinite partial integration and review its relation to the cumulative distribution function for the standard normal distribution and the error function.

stat.OT

Kullback-Leibler Divergence for the Normal-Gamma Distribution

We derive the Kullback-Leibler divergence for the normal-gamma distribution and show that it is identical to the Bayesian complexity penalty for the univariate general linear model with conjugate priors. Based on this finding, we provide two applications of the KL divergence, one in simulated and one in empirical data.

math.ST

Exceedance Probabilities for the Dirichlet Distribution

We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to a sampling approach which is the current practice in neuroimaging model selection.

stat.AP