Solving non-Markovian master equations with Libtorch
Author. Hardwick, Robert J Date. 2024-05-04 Concept. To compute direct numerical solutions for non-Markovian phenomena. We do this by revealing different orders of temporal correlation that are present in the full master equation of a generalised non-Markovian process. By relating higher-order correlations to a form of time dependence in the pairwise correlation, we then show how to numerically solve a discretised version of the system to obtain the time evolution of state probabilities. Since this computation can become very numerically intensive, we implement the basic algorithm in C++ using the Libtorch library.
Self-learning simulations
Author. Hardwick, Robert J Date. 2024-05-03 Concept. To develop a framework for online simulation inference which should work for any system that can be configured in practice. In order to achieve this generality, we show how concepts from Bayesian inference ultimately motivate the design of an 'embedded simulation' concept within the stochadex package. Leveraging this new software abstraction, we embed the inference computations for simulations within simulations themselves; giving rise to the idea of generalised 'self-learning simulations'.
A generalised probabilistic framework for simulation engines
Author. Hardwick, Robert J Date. 2024-05-03 Concept. To extend the mathematical formalism from a previous article to describe the time evolution of state probabilities in a simulation engine. Having introduced the basic concepts, we use this formalism to motivate a useful method for probabilistic estimation which is well-suited to the software abstractions provided by the stochadex package. In order to illustrate the point, we also demonstrate how to embed this algorithm within the computational graph of the simulation itself.
Building a generalised simulation engine
Author. Hardwick, Robert J Date. 2024-03-28 Concept. To lay out the fundamental mathematical foundations for simulating almost any system on a computer. Having provided these foundations, we then design and build a generalised simulation engine called the 'stochadex' which is able to generate samples from practically any real-world system that a researcher could encounter. With such a thing pre-built and self-contained as a highly-configurable simulation framework, it can become the basis upon which to build generalised software solutions for a lot of different problems.
Building Python simulations of limit order books
Author. Hardwick, Robert J Date. 2021-11-14 Concept. To illustrate the basic building blocks required to construct a full microsimulation of limit order book dynamics for financial markets. The simulation is a synchronous ensemble version of the well-studied epsilon-intelligence model. This is a short post on how the simulation was conceptualised, analysing some of its outputs and outlining prospects for potential future work on price emulation.
Some simple Gaussian graphical models in Python
Author. Hardwick, Robert J Date. 2021-06-15 Concept. To build some simple Bayesian graphical models for forecasting generic n-dimensional time series data. In one model we take the time series, compress it into autoregressive features using kernel convolutions and then couple the resulting variances in a Gaussian model. In the other, we try compressing with k-means clustering and dynamic time warping (using the tslearn package). In this short post we describe the models and outline the calculations required to compute their gradients for more efficient parameter optimisation.
Mean-field inference of multi-state models with a counting memory: applications to pneumococcus
Author. Hardwick, Robert J Date. 2021-05-25 Concept. To study a type of multi-state models (stochastic processes occupying one of a finite set of states at each moment in time) which exhibit a memory of past occurances through a counting variable. The statistical inference (or selection) of these models for real-world applications frequently involves data in the form of a sequence of individual state observations, which are often coupled with some diagnostic uncertainty (as is the case for pneumococcus). In this post, we are able to demonstrate an ODE mean-field description for these types of system is valid and can be used to accelerate the statistical inference from this type of data. The model case study we use is for systems which simulate the spread of pneumococcus in human populations.