Messing around with Bayesian statistics

Notes and Analyses, examples, methods, and implementation details

π(θ | y) ∝ π(y | θ) π(θ)

q^*_B(θ) = argmin_{q ∈ P(Θ)} { E_q[Σ_i=1ⁿ l(θ, x_i)] + KLD(q || π) }

f(x) ∼ GP(m(x), k(x, x’))

Cov(f(x), f(x’)) = k_Matérn(x, x’)

k_Matérn(r) = σ² 2^1-ν/Γ(ν) (√(2ν) r / ρ)^ν K_ν(√(2ν) r / ρ)

β_t - β_t-1 ∼ N(0, τ^-1)

γ_t - 2γ_t-1 + γ_t-2 ∼ N(0, τ^-1)

dX_t = θ(μ - X_t) dt + σ dW_t

ρ(k) = 1/2 (|k + 1|^2H - 2|k|^2H + |k - 1|^2H)

Q_st = Q_t ⊗ Q_s

(κ² - Δ)^α/2(τu(s)) = W(s)

u(s) ≈ ∑_i=1ⁿ w_iφ_i(s), w ∼ N(0, Q^-1)

Bayesian analysis for structured data

Messing around with Bayesian statistics

Notes and Analyses, examples, methods, and implementation details

Browse all posts

What This Site Covers

Applied Bayesian modelling

Detailed statistical analyses in economics, finance, political science, or epidemiology, through the Bayesian lens.

Statistical methods

Posts that isolate one statistical practice and work through it carefully to explore potential loopholes.

INLA implementation notes

Short write-ups for R-INLA and inlabru modeling details that are easy to forget and difficult to find.

Latest R-INLA Updates

Source: hrue/r-inla rinla/NEWS.md.

Learn more about R-INLA and R-INLA-verse on their dedicated website.

INLA 26.04.26

• Merge PR #120 fixing a regression

INLA 26.04.25

• Updated family ‘gammacountmean’
• SIMDE cleanup and fixes

INLA 26.04.21-1

• Fix issues with ‘seed != 0’ in sampling functions
• Minor code cleanup

INLA 26.04.21

• New likelihood: ‘gammacountmean’
• Code cleanup and improvements

Methods

Fitting Bayesian Distributed Lag Non-Linear Models with inlabru

2026-04-26

Distributed lag non-linear models (DLNMs) are useful when an exposure can affect the response both non-linearly and with a delay. A common example is environmental epidemiology: t…

MMD estimator

2026-04-18

Download inla_mmd_cloglike.c

Censored binomial likelihood in R-INLA

2026-04-12

Download cloglike-censored-binomial.c

Univariate P-splines in R-INLA and inlabru

2026-04-12

P-splines combine a flexible B-spline basis with a roughness penalty on the coefficients. Their main practical objective is to make model specification more robust to the number a…

See all methods

News and Highlights

Bayesian Workflow book

2026-04-24

The Bayesian Workflow book by Andrew Gelman, Aki Vehtari, Richard McElreath, and coauthors is now announced and available for pre-order on Amazon.

Interesting blogs and packages

2026-04-18

Here is a short list of blogs and packages that I keep coming back to when working on Bayesian models, R-INLA workflows, and applied statistics.

Welcome!

2026-04-12

Welcome to my brand-new blog. If you would like to know more about my academic and professional background, you can visit my LinkedIn or read my CV. I hope you will find the posts…

See all news

Applications

Quarterly GDP Forecasting with Latent Components and Flexible Observation Laws

2026-04-15

A recent GDP nowcasting article from the French macroeconomic lab OFCE motivated the following exercise. The aim is deliberately narrow: assess how far a quarterly Bayesian foreca…

Daily joint prediction of CAC40 opening and closing levels

2026-04-12

This application studies a joint forecasting problem for the CAC 40 opening and closing levels. Rather than treating the intraday move as a single response, the specification uses…

See all applications

Hardware

No posts yet.

See all hardware posts