Abstract

Individuals experience varying densities of negative thoughts (N.T.) throughout their daily lives, influenced by a multitude of internal factors such as mood, sleep quality, and cognitive patterns, as well as external elements like stressors, recent events, and immediate situational contexts. This variability makes accurate quantification challenging, yet essential for evidence based mental health research, self-monitoring, and clinical interventions.

This article introduces a comprehensive, rigorous, and transparent mathematical model specifically designed to quantify the number of negative thoughts per day. The model emphasizes practicality, making it accessible for researchers, clinicians, and even individuals seeking self-monitoring compassionate AI tools. It is adaptable to incorporate diverse data sources, including self-reported experiences, passive sensing from wearables, and ecological momentary assessments (EMA) that capture real-time data in natural environments.

This article introduces the Negative Thought Quantification Framework (NTQF), a comprehensive, rigorous, and transparent mathematical model designed to measure and estimate the frequency and intensity of negative thoughts per day. NTQF conceptualizes thoughts as discrete stochastic events, integrating both deterministic and stochastic modeling approaches, and leveraging hierarchical Bayesian inference to account for real-time uncertainty and individual variability.

The framework is highly adaptable, providing precise definitions and a suite of parametric tools capable of incorporating diverse multimodal data sources. These sources include self-reports, passive sensing from wearable physiological signals (e.g., HRV, EEG, EDA), and inference derived from voice or text inputs. NTQF yields a standardized, quantifiable metric: the Negative Thought Density Index (NTDI). This index captures both the frequency and duration-weighted intensity of N.T.s, offering actionable, reproducible insights into cognitive health for applications spanning research, clinical monitoring, and personalized therapeutic interventions.