Filippo Monti

Modeling Evolution

Research

My research develops Bayesian statistical methods for modeling stochastic processes in biological and epidemiological systems. By integrating computational statistics, applied probability, and evolutionary biology, I work to understand how complex systems evolve and change over time.

Methodology

  • Bayesian StatisticsHierarchical and nonparametric modeling
  • Computational StatisticsScalable gradient-based inference.
  • Continuous-time Markov processesContinuous-time Markov chains (CTMCs), Poisson processes, diffusion processes.

PhD Thesis

Scalable Inference for Continuous-Time Markov Processes

Estimated publication: November 2026.

  1. Introduction
  2. Part I: Discrete Processes
    1. Research Chapter: Nonparametric Modeling of Continuous-Time Markov Chains with Scalable Exact and Approximate Gradients
    2. Research Chapter: Scalable Nonparametric Modeling of Random Integrals with Squared Basis Expansions
  3. Part II: Continuous Processes
    1. Research Chapter: Stable Matrix Parametrization and Structured Adjoints for Ornstein-Uhlenbeck Processes
  4. Part III: Dependencies between Continuous-Time Markov Processes
    1. Research Chapter: Investigating the Drivers of Time-Varying Rates of Evolution
    2. Research Chapter: Substitution Rate Heterogeneity Driven by the Threshold-Occupation Time of a Latent Brownian Motion