Recent Posts

Masked diffusion models are conceptually based upon an absorbing forward process and its reverse denoising process. However, their roles are intricately intertwined, in that all three aspects of training, sampling, and modeling are involved. To develop our understanding, we give two toy examples, 1d and 2d, without training a neural network, to showcase how absorbing processes behave. We identify core questions which should be investigated to expand our understanding.

Sep 15, 2025

Hirofumi Shiba

A Function that is Continuous on a Closed Subset

The set of all continuity points of a function is a \(G_\delta\) set. Conversely, every \(G_\delta\) set is the set of all continuity points of some function. We construct an example of a function \(f:\mathbb{R}\to\mathbb{R}\) that is continuous on \((-\infty,0]\) but discontinuous on \((0,\infty)\).

Apr 17, 2025

Hirofumi Shiba

Implementation Details of `PDMPFlux.jl`

Simulating PDMPs with Automatic Differentiation

In this introduction, we quickly give an overview of how the PDMPFlux.jl package works, through a standard example.

Dec 31, 2024

Hirofumi Shiba

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.

Dec 23, 2024

Hirofumi Shiba

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.

Dec 22, 2024

Hirofumi Shiba

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.

Mar 8, 2024

Hirofumi Shiba

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 \(n\ge3\).

Jan 5, 2024

Hirofumi Shiba