At my work we use kernel density estimation to estimate a density distribution from a set of measured points (we measure the size and refractive index of microparticles in liquid samples). I found a paper that relates kernel density estimation to Gaussian process based approaches. I haven't finished reading the paper yet, but it seems that kernel density estimation is a frequentist approach while Gaussian process techniques take a Bayesian perspective. https://arxiv.org/abs/2506.17366
#frequentist
#bayesian
#kernelDensityEstimation
3/3
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences between them are reviewed for fundamental topics such as regression, interpolation, numerical integration, distributional discrepancies, and statistical dependence, as well as for sample path properties of Gaussian processes. A unifying perspective for these equivalences is established, based on the equivalence between the Gaussian Hilbert space and the RKHS. The monograph serves as a basis to bridge many other methods based on Gaussian processes and reproducing kernels, which are developed in parallel by the two research communities.
#statstab #346 Jeffreys-Lindley paradox
Thoughts: I like this short explanation of the "paradox" of why frequentist and bayesian inference can differ.
#paradox #frequentist #bayesian #inference #bayesfactor #pvalue #explanation
https://michael-franke.github.io/intro-data-analysis/jeffreys-lindley-paradox.html
#statstab #337 Confidence intervals and tests are two sides of the same research question
Thoughts: Comment describing the connection between NHST p-values/test and Confidence Intervals (CI).
#NHST #ConfidenceIntervals #pvalues #frequentist #estimation
#statstab #335 Bayesian New Statistics
Thoughts: An influential paper with a great overview of different approaches to research.
#bayesian #nhst #nhbt #estimation #testing #frequentist
https://link.springer.com/content/pdf/10.3758/s13423-016-1221-4.pdf
#statstab #289 The meaning of significance in data testing
Thoughts: Fisherian significance testing =/= Neyman-Pearson statistical hypothesis testing. Many debates on p-values and frequentist stats are due to this confusion.
#statstab #287 Dance of the p Values
Thoughts: One of my go-to demonstrations for the variability of p-values, and why they say so little about a study.
#pvalues #NHST #education #estimation #frequentist #replication #error #visualization #teaching
#statstab #270 Seeing Theory: Frequentist Inference
Thoughts: Are you learning about NHST? Are you a visual learner? This might be for you.
#NHST #dataviz #visualisation #learning #education #teaching #frequentist
https://seeing-theory.brown.edu/frequentist-inference/index.html
I expect a Nobel Prize for Peace (!) will be awarded to that Mathematician who creates a statistical framework unifying frequentist and Bayesian statistics.
David Ruffner
Dr Mircea Zloteanu 🌺🌞🍃
Michael Misamore
Wilmar Igl, PhD