Integrating Inference with Stochastic Process Algebra Models - Jane Hillston, Edinburgh

Explore a comprehensive lecture on integrating inference with stochastic process algebra models, delivered by Jane Hillston from Edinburgh at the Alan Turing Institute. Delve into the ProPPA probabilistic programming language, an extension of Bio-PEPA, designed for continuous-time dynamical systems with unknown parameters. Learn about the framework's ability to automate parameter inference algorithms, including a novel MCMC scheme for systems with infinite state-spaces. Discover the application of these techniques in diverse fields such as biology, ecology, and urban transport. Examine the combination of logic and learning in formal methods, and understand the benefits of integrating stochastic process algebra with machine learning and Bayesian statistics. Follow the lecture's progression through topics like molecular processes as concurrent computations, Bio-PEPA modeling, probabilistic programming workflow, and constraint Markov chains. Gain insights into simulating probabilistic constraint Markov chains, calculating transient probabilities, and performing inference for infinite state spaces. Conclude with an exploration of challenges and future directions in this field of study.

Intro
Stochastic Process Algebra
Integrated analysis
Benefits of integration
Outline
Modelling in a Data Rich World
Molecular processes as concurrent computations
Formal modelling in systems biology
Bio-PEPA modelling
The semantics
Optimizing models
Alternative perspective
Machine Learning Bayesian statistics
Comparing the techniques
Developing a probabilistic programming approach
Probabilistic programming workflow
A Probabilistic Programming Process Algebra: ProPPA
Example Revisited
Constraint Markov Chains
Probabilistic CMCS
Semantics of ProPPA
Simulating Probabilistic Constraint Markoy Chains
Calculating the transient probabilities
Basic Inference
Inference for infinite state spaces
Expanding the likelihood
Example model
Results: ABC
Genetic Toggle Switch
Toggle switch model: species
Experiment
Genes (unobserved)
Proteins
Summary
Challenges and Future Directions