Bias-corrected maximum-likelihood estimation of multiplicity of infection and lineage frequencies

Background The UN’s Sustainable Development Goals are devoted to eradicate a range of infectious diseases to achieve global well-being. These efforts require monitoring disease transmission at a level that differentiates between pathogen variants at the genetic/molecular level. In fact, the advantages of genetic (molecular) measures like multiplicity of infection (MOI) over traditional metrics, e.g., R0, are being increasingly recognized. MOI refers to the presence of multiple pathogen variants within an infection due to multiple infective contacts. Maximum-likelihood (ML) methods have been proposed to derive MOI and pathogen-lineage frequencies from molecular data. However, these methods are biased. Methods and findings Based on a single molecular marker, we derive a bias-corrected ML estimator for MOI and pathogen-lineage frequencies. We further improve these estimators by heuristical adjustments that compensate shortcomings in the derivation of the bias correction, which implicitly assumes that data lies in the interior of the observational space. The finite sample properties of the different variants of the bias-corrected estimators are investigated by a systematic simulation study. In particular, we investigate the performance of the estimator in terms of bias, variance, and robustness against model violations. The corrections successfully remove bias except for extreme parameters that likely yield uninformative data, which cannot sustain accurate parameter estimation. Heuristic adjustments further improve the bias correction, particularly for small sample sizes. The bias corrections also reduce the estimators’ variances, which coincide with the Cramér-Rao lower bound. The estimators are reasonably robust against model violations. Conclusions Applying bias corrections can substantially improve the quality of MOI estimates, particularly in areas of low as well as areas of high transmission—in both cases estimates tend to be biased. The bias-corrected estimators are (almost) unbiased and their variance coincides with the Cramér-Rao lower bound, suggesting that no further improvements are possible unless additional information is provided. Additional information can be obtained by combining data from several molecular markers, or by including information that allows stratifying the data into heterogeneous groups.

Comparison of Bayesian Methods for Recovering Sinusoids

In this paper, we study a problem of estimating parameters of sinusoids from noisy data within Bayesian inferential framework. In this context, three different computational schemes such as, Bretthorst’s integral method (BRETTHORST), Gibbs sampling (GIBBS) and parallel tempering (PT) are studied and modifications of their algorithms were tested on data generated from synthetic signals. In addition, our emphasis is given to a comparison of their performances with respect to Cramér-Rao lower bound (CRLB).

Maximum Likelihood Estimation of Power-law Degree Distributions via Friendship Paradox-based Sampling

This article considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g., linear regression on double-logarithmic axes and maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution. As a solution, we present a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution. We analytically show that the proposed method results in a smaller bias, variance and a Cramèr–Rao lower bound compared to the vanilla maximum likelihood estimate obtained with uniformly sampled nodes (which is the most commonly used method in literature). Detailed numerical and empirical results are presented to illustrate the performance of the proposed method under different conditions and how it compares with alternative methods. We also show that the proposed method and its desirable properties (i.e., smaller bias, variance, and Cramèr–Rao lower bound compared to vanilla method based on uniform samples) extend to parametric degree distributions other than the power-law such as exponential degree distributions as well. All the numerical and empirical results are reproducible and the code is publicly available on Github.