Posted in 2025
Modeling spatial point patterns with a marked log-Gaussian Cox process
- 31 December 2025
The log-Gaussian Cox process (LGCP) is a probabilistic model of point patterns typically observed in space or time. It has two main components. First, an underlying intensity field \(\lambda(s)\) of positive real values is modeled over the entire domain \(X\) using an exponentially-transformed Gaussian process which constrains \(\lambda\) to be positive. Then, this intensity field is used to parameterize a Poisson point process which represents a stochastic mechanism for placing points in space. Some phenomena amenable to this representation include the incidence of cancer cases across a county, or the spatiotemporal locations of crime events in a city. Both spatial and temporal dimensions can be handled equivalently within this framework, though this tutorial only addresses data in two spatial dimensions.
Bayesian Workflow with SEMs
- 12 September 2025
This case study extends the themes of contemporary Bayesian workflow and Structural Equation Modelling. While both topics are well represented in the PyMC examples library, our goal here is to show how the principles of the Bayesian workflow can be applied concretely to structural equation models (SEMs). The iterative and expansionary strategies of model development for SEMs provide an independent motivation for the recommendations of [Gelman et al., 2020] stemming from the SEM literature broadly. But [Kline, 2023] in particular highlights the utility of a staggered approach to model development as a diagnostic for model mis-specification.
The Bayesian Workflow: COVID-19 Outbreak Modeling
- 16 June 2025
Bayesian modeling is a robust approach for drawing conclusions from data. Successful modeling involves an interplay among statistical models, subject matter knowledge, and computational techniques. In building Bayesian models, it is easy to get carried away with complex models from the outset, often leading to an unsatisfactory final result (or a dead end). To avoid common model development pitfalls, a structured approach is helpful. The Bayesian workflow (Gelman et al.) is a systematic approach to building, validating, and refining probabilistic models, ensuring that the models are robust, interpretable, and useful for decision-making. The workflow’s iterative nature ensures that modeling assumptions are tested and refined as the model grows, leading to more reliable results.
Forecasting Hurricane Trajectories with State Space Models
- 15 June 2025
Duplicate implicit target name: “forecasting hurricane trajectories with state space models”.
Time Series Models Derived From a Generative Graph
- 12 January 2025
In this notebook, we show how to model and fit a time series model starting from a generative graph. In particular, we explain how to use scan to loop efficiently inside a PyMC model.