Sergio Peignier

Stochastic Processes & Probabilistic Modeling

Introduction to stochastic processes and probabilistic modeling, with applications to biological systems, neural activity, and dynamic data-driven systems.

Focus: Probability · Markov Processes · Stochastic Simulation · Dynamic Systems

Methods: Markov Models · Stochastic Simulation · Time-Series Analysis · Probabilistic Modeling

Applications: Neuroscience · Systems Biology · AI · Sequential Data Modeling

Level: Undergraduate / Graduate

Probability Foundations

Core principles of probability theory for modeling uncertainty in complex systems.

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Bernoulli & Poisson Processes

Modeling discrete events and arrival processes in time.

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Markov Chains & Moran Processes

Modeling state transitions in stochastic systems and population dynamics.

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Branching Processes

Stochastic modeling of growth, reproduction, and cascading processes.

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Gillespie Algorithm

Simulation of stochastic chemical and biological systems at the molecular level.

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Project: Neuronal Spike Train Analysis

Analysis of neural activity using stochastic modeling and time-series data.

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Project: Modeling Cancer Development

Analysis of cancer develpment using Moran process modeling.

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Project: Position Weight Matrices & Markov Chains

Application of Markov models to biological sequence analysis.

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Project: Hidden Markov Models

Modeling hidden states in sequential data using probabilistic graphical models.

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Project: Gillespie Simulation

Hands-on implementation of stochastic simulations for dynamic biological systems.

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