Cadeias estocásticas de memória ilimitada com aplicação na neurociência

• Ano de defesa: 2019
• Autor(a) principal: Ferreira, Ricardo Felipe
• Orientador(a): Gallo, Alexsandro Giacomo Grimbert
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
• Palavras-chave em Português: Cadeias estocásticas de memória ilimitada; Medida invariante; Inferência em processos estocásticos; Limites da concentração; Neurociência
• Palavras-chave em Inglês: Stochastic chains with unbounded memory; Invariant measure; Inference in stochastic processes; Concentration bounds; Neuroscience
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA EM PROCESSOS ESTOCASTICOS; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOS
• Link de acesso: https://repositorio.ufscar.br/handle/ufscar/11229

Stochastic chains with unbounded memory are a natural generalization of Markov chains, in the sense that the transition probabilities may depend on the whole past. These process, introduced independently by Onicescu and Mihoc in 1935 and Doeblin and Fortet in 1937, have been receiving increasing attention in the probabilistic literature, because they form a class richer than the Markov chains and have practical capabilities modelling of scientific data in several areas, from biology to linguistics. In this work, we use them to model interactions between spike trains. Our main goal is to develop new mathematical results about stochastic chains with unbounded memory. First, we study conditions that guarantee the existence and uniqueness of stationary chains compatible with a discontinuous family of transition probabilities. Then, we address the understanding of the phenomenology of spike trains and we propose to use directed information to quantify the information flow from one neuron to another. In this occasion, we fix concentration bounds for directed information estimation.