Bayesian Updating Based on Hausdorff Outer Measures and the Role of Emotions in Decision Process During the Therapeutic Phase of Alliance

Serena Doria¹, Iolanda Angelucci²

1. Department of Enginnering and Geology, University G.D’Annunzio, 63013 Chieti, Italy.
2. Graduate School in Clinical Psychology and Psychotherapy (S.S.P.I.G.; I.F.R.E.P.); via Reggio Emilia, 52 ,00198, Roma, Italy.

Abstract:

A probabilistic approach of the diagnostic process is proposed in which the subject’s degree of knowledge is represented with coherent upper conditional probabilities defined by Hausdorff outer measures.

Using this model the diagnosis is assumed to be positive when it produces a change, that is when the subject’s level of knowledge is defined by an a posterior Hausdorff outer measure different from the initial Hausdorff outer measure.

The psychotherapist-patient system is interpreted as a complex system, whose evolution, representing the phase of alliance, is described by a finite family of similarities that, starting from certain initial conditions, evolve the system into the attractor. This set, characterized by its own complexity, measured in terms of the Hausdorff dimension, represents the unconscious of the therapist-patient system and it is characterized by symmetry and self-similarity.

Keywords: Coherent upper conditional probability, Hausdorff outer measures, fractal sets, therapeutic alliance, unconscious, emotions.

Pages: 14 – 28 | Full PDF Paper