Fabio Nakano

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes.

Hierarchical Forecasting with Polynomial Nets

This article presents a two level hierarchical forecasting model developed in a consulting project for a Brazilian magazine publishing company. The first level uses a VARMA model and considers econometric variables. The second level takes into account qualitative aspects of each publication issue, and is based on polynomial networks generated by Genetic Programming (GP).

Optimization Models for Reaction Networks: Information Divergence, Quadratic Programming and Kirchhoff’s Laws

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Intentional Sampling by Goal Optimization with Decoupling by Stochastic Perturbation

Intentional sampling methods are non-probabilistic procedures that select a group of individuals for a sample with the purpose of meeting specific prescribed criteria. Intentional sampling methods are intended for exploratory research or pilot studies where tight budget constraints preclude the use of traditional randomized representative sampling. The possibility of subsequently generalize statistically from such deterministic samples to the general population has been the issue of long standing arguments and debates. Nevertheless, the intentional sampling techniques developed in this paper explore pragmatic strategies for overcoming some of the real or perceived shortcomings and limitations of intentional sampling in practical applications.

Hierarchical Forecasting with Functional Trees

This paper presents the use of polynomial networks, synthesized as optimal functional trees by genetic algorithms, in a hierarchical forecasting model.