Recent Posts – Hirofumi Shiba

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Implementation Details of `PDMPFlux.jl`

Simulating PDMPs with Automatic Differentiation

composites / constructs such as BoundBox, PDMPState, PDMPHistory are defined.

Likelihood of Hierarchical Models

We examine how to find & formally determine the likelihood function of hierarchical models. As a real-world example, we consider the ideal point model, also known as the 2-parameter logistic item response model.

On the Identifiability of the Bafumi et. al. Ideal Point Model

Rethinking of the Hierarchical Model of Bafumi et. al. (2005)

Ideal point models are 2-parameter item response model, tailored to the purpose of visualizing / measuring the ideological positions of the legislators / judges. (Bafumi et al., 2005) introduced a hierarchical structure to the model to deal with the problem of identifiability. In this article, we re-examine the model and show that the posterior distribution of the parameters (ideal points) is still bimodal, indicating its weak identifiability.

A Recent Development of Particle Methods

Inquiry towards a Continuous Time Limit and Scalability

Recently developments in continuous-time MCMC algorithms have emerged as a promising direction for scalable Bayesian computation. This poster explores their SMC counterparts. A new finding about a continuous-time limit of particle filter is discussed.

Measurability of the Minkowski Sum of Two Sets

For two Borel sets \(A,B\in\mathcal{B}(\mathbb{R}^n)\), we cannot expect \(A+B\) to be always Borel. We give sufficient conditions for the Minkowski sum \(A+B\) to be Borel, and also give a concrete counterexample for the case \(n\ge3\).

Influential Books Which Paved My Path into Mathematics

Book Recommendations

I will explore how a few books inspired me and paved my way into Mathematics.

References

Bafumi, J., Gelman, A., Park, D. K., and Kaplan, N. (2005). Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation. Political Analysis, 13(2), 171–187.