statistics

An especially strong motivating case for the usage of spatial probability models comes from the mining industry. During exploration for mineral resources, prospectors will take geologic samples by drilling holes and examining the resulting material for presence or concentration of valuable ores. These data typically show strong spatial correlation, but constructing a fully-detailed geophysical mo…

This paper formalises two memoryless arithmetic processes—the Prime Gap State Machine and the Collatz odd backbone—as exact Markov chains on the six vortex residues {1,2,4,5,7,8} (mod 9) defined by the Prime Lattice Coherence Theorem (PLCT). The chains arise directly from the PLCT’s zone structure and its core theorems. For the Collatz process, the transition matrix is derived analytically from t…

This record contains a preprint manuscript presenting a calibrated Bourdieu-inspired agent-based model of scientific fields and co-authorship networks. The model investigates how symbolic capital, legitimacy, bounded collaboration, and institutional inertia can generate discipline-like collaboration regimes resembling the canonical co-authorship profiles reported by Newman.

VC Dimension and the Fundamental Theorem of Statistical Learning — from Scratch May 2026 This post answers a single question: when does learning from data actually work? You train a model on samples, it performs well on those samples, and you hope it performs well on new data. When is that hope justified? The answer turns out to be a clean equivalence: a hypothesis class is learnable if and only …

Optimal Resolution in Histograms: A Rigorous Bayesian Approach to Density Fitting The post How to Mathematically Choose the Optimal Bins for Your Histogram appeared first on Towards Data Science .

Traditional investigations into the Collatz $(3x+1)$ problem primarily target forward path trajectories or long-term statistical graph densities, which frequently behave like pseudo-random systems. This paper introduces an exact arithmetic invariant operating within the inverse Collatz map, demonstrating that the global value-sum ratio of distinct structural subtrees converges monotonically to th…

Friends, despite all problems I am working, and I have checked the main algorithm to work fine, and I hope that I would be able to produce a basic program for optimization of correlation coefficients  sometime over this weekend that will at least work with the basic algorithm. But this might just be an intermediate program with more improvements to follow for the program for calculation of correl…

Liu regression, originally developed in the context of classical (crisp) statistics as a biased estimation method to mitigate multicollinearity, has not been previously extended to fuzzy regression frameworks. In this study, we propose a novel fuzzy adaptation of Liu regression, implemented within an [Formula: see text]-cut-based estimation structure. This approach provides a systematic methodolo…

We report two randomized evaluations of educational interventions targeting children in low-income neighborhoods of Delhi, India. Four math games, played in social groups, associated early emerging and universally intuitive concepts of number and geometry with the mathematical language, symbols, and operations taught in Delhi government schools. The first experiment, conducted in 231 NGO-run pres…

Statistical modelling and machine learning offer a vast toolbox of inference methods with which to model the world, discover patterns and reach beyond the data to make predictions when the truth is not certain. This concise book provides a clear introduction to those tools and to the core ideas – probabilistic model, likelihood, prior, posterior, overfitting, underfitting, cross-validation – that…

This study addressed the absence of a comprehensive bibliometric analysis of mental arithmetic research in educational psychology by systematically mapping its evolutionary trajectory over 83 years (1942–2024). Using Scopus database searches, 1,749 unique deduplicated records were retrieved, with 626 "arithmetic skills" records serving as the core dataset for descriptive bibliometric analyses of …

Abstract The free positive multiplicative Brownian motion $$(h_t)_{t\ge 0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> is the large N limit in non…

Meta-analysts frequently encounter missing covariate values, which can complicate valid estimation of meta-regression models. In practice, missing data are managed often through ad hoc deletion approaches, which can reduce the validity of statistical inferences. More advanced missing data handling approaches such as multiple imputation (MI) remain underutilized, particularly in meta-analyses with…