Useful state partitions for real-world simulations
Author. Hardwick, Robert J Date. 2024-08-30 Concept. To provide some practical examples of the real-world simulation types which are supported in the stochadex engine by describing a group of widely-applicable state partitions. In particular, we discuss how these partitions can be useful in simulating everything from sports matches and spatial disease spread to traffic networks and supply chain logistics. With these examples (and many others) in mind, we also consider the realistic types of observation and interaction which are possible in each case.
Creating a toy rugby match simulator
Author. Hardwick, Robert J Date. 2024-05-05 Concept. To outline the basic design of an event-based rugby match simulator which uses the stochadex simulation engine to evolve its state forward in time. We also develop an alternative visualisation app for the stochadex which displays a 2D view of the rugby pitch and ball location. Given this extended functionality, we also discuss how this toy model could be developed into a full game with user interaction in future.
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 stochastic process 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'.
Probabilistic learning methods embedded within a simulation engine
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. Having introduced the basic concepts, we use this formalism to motivate some important methods for probabilistic learning that are well-suited to the software abstractions provided by the stochadex package. In order to illustrate the point, we demonstrate how to embed these learning algorithms within the computation 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 describing practically any stochastic simulation 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 stochastic processes that a researcher could encounter. With such a thing pre-built and self-contained as a highly-configurable simulation binary, 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.