A novel two-stage parameter estimation framework integrating Approximate Bayesian Computation and Machine Learning: The ABC-RF-rejection algorithm arxiv.org/abs/2507.02072 .ME

BACTA-GPT: An AI-Based Bayesian Adaptive Clinical Trial Architect arxiv.org/abs/2507.02130 .AP .OT

BACTA-GPT: An AI-Based Bayesian Adaptive Clinical Trial Architect

Bayesian adaptive clinical trials offer a flexible and efficient alternative to traditional fixed-design trials, but their implementation is often hindered by the complexity of Bayesian computations and the need for advanced statistical programming expertise. The authors introduce a custom fine-tuned LLM designed to assist with this and lower barriers to adoption of Bayesian methods for adaptive clinical trials. This paper describes the development and fine-tuning of BACTA-GPT, a Large Language Model (LLM)-based tool designed to assist in the implementation of Bayesian Adaptive Clinical Trials. This engine uses GPT-3.5 as the underlying model and takes in Natural Language input from the Statistician or the Trialist. The fine-tuned model demonstrates a viable proof-of-concept in its objectives. Test case evaluations show that the model is capable of generating a fit-for-purpose Bayesian model for an adaptive trial and evaluate its operating characteristics via simulations using R and JAGS. The integration of AI code generation has significant potential to lower technical barriers for the design and implementation of Bayesian Adaptive trials. But they also require attention to important considerations regarding validation and quality control.

arXiv.org

A Variance Decomposition Approach to Inconclusives in Forensic Black Box Studies arxiv.org/abs/2507.02240 .AP

A Variance Decomposition Approach to Inconclusives in Forensic Black Box Studies

In the US, `black box' studies are increasingly being used to estimate the error rate of forensic disciplines. A sample of forensic examiner participants are asked to evaluate a set of items whose source is known to the researchers but not to the participants. Participants are asked to make a source determination (typically an identification, exclusion, or some kind of inconclusive). We study inconclusives in two black box studies, one on fingerprints and one on bullets. Rather than treating all inconclusive responses as functionally correct (as is the practice in reported error rates in the two studies we address), irrelevant to reported error rates (as some would do), or treating them all as potential errors (as others would do), we propose that the overall pattern of inconclusives in a particular black box study can shed light on the proportion of inconclusives that are due to examiner variability. Raw item and examiner variances are computed, and compared with the results of a logistic regression model that takes account of which items were addressed by which examiner. The error rates reported in black box studies are substantially smaller than ``failure rate" analyses that take inconclusives into account. The magnitude of this difference is highly dependent on the particular study at hand.

arXiv.org

Targeted tuning of random forests for quantile estimation and prediction intervals arxiv.org/abs/2507.01430 .ME .AP .ML

Root/Additional Metric (RoAM) framework: a guide for goal-centred metric construction arxiv.org/abs/2507.01526 .ME

Root/Additional Metric (RoAM) framework: a guide for goal-centred metric construction

The use of metrics underpins the quantification, communication and, ultimately, the functioning of a wide range of disciplines as diverse as labour recruitment, institutional management, economics and science. For application of metrics, customised scores are widely employed to optimise progress monitoring towards a goal, to contribute to decision-making, and to quantify situations under evaluation. However, the development of such metrics in complex and rigorous settings intrinsically relies on mathematical processes which are not always readily accessible. Here, we propose a framework for construction of metrics suitable for a wide range of disciplines, following a specified workflow that combines existing decision analysis and utility theory concepts to create a customisable performance metric (with corresponding uncertainty) that can be used to quantitatively evaluate goal achievement. It involves dividing criteria into two groups (root and additional) to utilise a newly proposed alternative form of utility function designed to build such customised metrics. Once the metrics are produced by this approach, these metrics can be used on a varied set of contexts, including their use in subsequent statistical analysis with the metric values as a response variable, or informing a decision-making process. The flexibility of the metric construction makes it suitable for a wide range of fields and applications, and could provide a valuable first step for monitoring and comparison in many different settings.

arXiv.org

A new algorithm for sampling parameters in a structured correlation matrix with application to estimating optimal combinations of muscles to quantify progression in Duchenne muscular dystrophy arxiv.org/abs/2506.21719 .ME

A new algorithm for sampling parameters in a structured correlation matrix with application to estimating optimal combinations of muscles to quantify progression in Duchenne muscular dystrophy

The goal of this paper is to estimate an optimal combination of biomarkers for individuals with Duchenne muscular dystrophy (DMD), which provides the most sensitive combinations of biomarkers to assess disease progression (in this case, optimal with respect to standardized response mean (SRM) for 4 muscle biomarkers). The biomarker data is an incomplete (missing and irregular) multivariate longitudinal data. We propose a normal model with structured covariance designed for our setting. To sample from the posterior distribution of parameters, we develop a Markov Chain Monte Carlo (MCMC) algorithm to address the positive definiteness constraint on the structured correlation matrix. In particular, we propose a novel approach to compute the support of the parameters in the structured correlation matrix; we modify the approach from \cite{Barnard} on the set of largest possible submatrices of the correlation matrix, where the correlation parameter is a unique element. For each posterior sample, we compute the optimal weights of our construct. We conduct data analysis and simulation studies to evaluate the algorithm and the frequentist properties of the posteriors of correlations and weights. We found that the lower extremities are the most responsive muscles at the early and late ambulatory disease stages and the biceps brachii is the most responsive at the non-ambulatory disease stage.

arXiv.org

Monte Carlo and quasi-Monte Carlo integration for likelihood functions arxiv.org/abs/2506.21733 .ST .ME .ML .TH

Monte Carlo and quasi-Monte Carlo integration for likelihood functions

We compare the integration error of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods for approximating the normalizing constant of posterior distributions and certain marginal likelihoods. In doing so, we characterize the dependency of the relative and absolute integration errors on the number of data points ($n$), the number of grid points ($m$) and the dimension of the integral ($p$). We find that if the dimension of the integral remains fixed as $n$ and $m$ tend to infinity, the scaling rate of the relative error of MC integration includes an additional $n^{1/2}\log(n)^{p/2}$ data-dependent factor, while for QMC this factor is $\log(n)^{p/2}$. In this scenario, QMC will outperform MC if $\log(m)^{p - 1/2}/\sqrt{mn\log(n)} < 1$, which differs from the usual result that QMC will outperform MC if $\log(m)^p/m^{1/2} < 1$.The accuracies of MC and QMC methods are also examined in the high-dimensional setting as $p \rightarrow \infty$, where MC gives more optimistic results as the scaling in dimension is slower than that of QMC when the Halton sequence is used to construct the low discrepancy grid; however both methods display poor dimensional scaling as expected. An additional contribution of this work is a bound on the high-dimensional scaling of the star discrepancy for the Halton sequence.

arXiv.org

Modification of a Numerical Method Using FIR Filters in a Time-dependent SIR Model for COVID-19 arxiv.org/abs/2506.21739 .ML .OC .LG

Modification of a Numerical Method Using FIR Filters in a Time-dependent SIR Model for COVID-19

Authors Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, and Tzu-Hsuan Liu use the Finite Impulse Response (FIR) linear system filtering method to track and predict the number of people infected and recovered from COVID-19, in a pandemic context in which there was still no vaccine and the only way to avoid contagion was isolation. To estimate the coefficients of these FIR filters, Chen et al. used machine learning methods through a classical optimization problem with regularization (ridge regression). These estimated coefficients are called ridge coefficients. The epidemic mathematical model adopted by these researchers to formulate the FIR filters is the time-dependent discrete SIR. In this paper, we propose a small modification to the algorithm of Chen et al. to obtain the ridge coefficients. We then used this modified algorithm to track and predict the number of people infected and recovered from COVID-19 in the state of Minas Gerais/Brazil, within a prediction window, during the initial period of the pandemic. We also compare the predicted data with the respective real data to check how good the approximation is. In the modified algorithm, we set values for the FIR filter orders and for the regularization parameters, both different from the respective values defined by Chen et al. in their algorithm. In this context, the numerical results obtained by the modified algorithm in some simulations present better approximation errors compared to the respective approximation errors presented by the algorithm of Chen et al.

arXiv.org

TADA: Improved Diffusion Sampling with Training-free Augmented Dynamics arxiv.org/abs/2506.21757 .ML .LG

TADA: Improved Diffusion Sampling with Training-free Augmented Dynamics

Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images but typically suffer from inefficient sampling. Many solver designs and noise scheduling strategies have been proposed to dramatically improve sampling speeds. In this paper, we introduce a new sampling method that is up to $186\%$ faster than the current state of the art solver for comparative FID on ImageNet512. This new sampling method is training-free and uses an ordinary differential equation (ODE) solver. The key to our method resides in using higher-dimensional initial noise, allowing to produce more detailed samples with less function evaluations from existing pretrained diffusion models. In addition, by design our solver allows to control the level of detail through a simple hyper-parameter at no extra computational cost. We present how our approach leverages momentum dynamics by establishing a fundamental equivalence between momentum diffusion models and conventional diffusion models with respect to their training paradigms. Moreover, we observe the use of higher-dimensional noise naturally exhibits characteristics similar to stochastic differential equations (SDEs). Finally, we demonstrate strong performances on a set of representative pretrained diffusion models, including EDM, EDM2, and Stable-Diffusion 3, which cover models in both pixel and latent spaces, as well as class and text conditional settings. The code is available at https://github.com/apple/ml-tada.

arXiv.org
Show older
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.