arXiv subjects

Nicolás Kuschinski

Publications and source records attributed to Nicolás Kuschinski.

4 recordsLinked to original sources

arXiv2024

Bayesian Copula Density Estimation Using Bernstein Yett-Uniform Priors

Probability density estimation is a central task in statistics. Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. Choosing a class of copula models is not a trivial task and its misspecification can lead to wrong conclusions. We introduce a novel class of random Bernstein copula functions, and studied its support and the behavior of its posterior distribution. The proposal is based on a particular class of random grid-uniform copulas, referred to as yett-uniform copulas. Alternative Markov chain Monte Carlo algorithms for exploring the posterior distribution under the proposed model are also studied. The methodology is illustrated by means of simulated and real data.

stat.ME↗

arXiv2023

Bayesian statistical models to explore the use glucometer measurements of capillary blood sugar for OGTT Tests

A common test for the diagnosis of type 2 diabetes is the Oral Glucose Tolerance Test (OGTT). Recent developments in the study of OGTT tests have framed it as a Bayesian inverse problem. These data analysis advances promise great improvements in the descriptive power of OGTTs. OGTT tests are typically done with invasive, bothersome, and somewhat expensive venous blood tests. A natural question is whether improved data analysis techniques would allow for less invasive and cheaper glucometer measurements to be used. In this paper we explore this question. Using one dynamic model, we develop an error model for glucometer capillary blood sugar measurements and compare results of venous blood sugar tests for 65 patients, finding a match in over 90% of observed cases. Our conclusion suggests that this model (or one much like it) may permit capillary glucose to be used with reasonable accuracy in performing OGTTs.

stat.AP↗

arXiv2021

Grid-Uniform Copulas and Rectangle Exchanges: Bayesian Model and Inference for a Rich Class of Copula Functions

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. Choosing a class of copula models is not a trivial task and its misspecification can lead to wrong conclusions. We introduce a novel class of grid-uniform copula functions, which is dense in the space of all continuous copula functions in a Hellinger sense. We propose a Bayesian model based on this class and develop an automatic Markov chain Monte Carlo algorithm for exploring the corresponding posterior distribution. The methodology is illustrated by means of simulated data and compared to the main existing approach.

stat.ME↗

arXiv2019

Modeling Oral Glucose Tolerance Test (OGTT) data and its Bayesian Inverse Problem

One common way to test for diabetes is the Oral Glucose Tolerance Test or OGTT. Most common methods for the analysis of the data on this test are wasteful of much of the information contained therein. We propose to model blood glucose during an OGTT using a compartmental dynamic model with a system of ODEs. Our model works well in describing most scenarios that occur during an OGTT considering only 4 parameters. Fitting the model to data is an inverse problem, which is suitable for Bayesian inference. Priors are specified and posterior inference results are shown using real data.

stat.AP↗