Genomic Prediction Using Bayesian Regression Models With Global–Local Prior

Bayesian regression models are widely used in genomic prediction for various species. By introducing the global parameter τ, which can shrink marker effects to zero, and the local parameter λk, which can allow markers with large effects to escape from the shrinkage, we developed two novel Bayesian models, named BayesHP and BayesHE. The BayesHP model uses Horseshoe+ prior, whereas the BayesHE model assumes local parameter λk, after a half-t distribution with an unknown degree of freedom. The performances of BayesHP and BayesHE models were compared with three classical prediction models, including GBLUP, BayesA, and BayesB, and BayesU, which also applied global–local prior (Horseshoe prior). To assess model performances for traits with various genetic architectures, simulated data and real data in cattle (milk production, health, and type traits) and mice (type and growth traits) were analyzed. The results of simulation data analysis indicated that models based on global–local priors, including BayesU, BayesHP, and BayesHE, performed better in traits with higher heritability and fewer quantitative trait locus. The results of real data analysis showed that BayesHE was optimal or suboptimal for all traits, whereas BayesHP was not superior to other classical models. For BayesHE, its flexibility to estimate hyperparameter automatically allows the model to be more adaptable to a wider range of traits. The BayesHP model, however, tended to be suitable for traits having major/large quantitative trait locus, given its nature of the “U” type-like shrinkage pattern. Our results suggested that auto-estimate the degree of freedom (e.g., BayesHE) would be a better choice other than increasing the local parameter layers (e.g., BayesHP). In this study, we introduced the global–local prior with unknown hyperparameter to Bayesian regression models for genomic prediction, which can trigger further investigations on model development.

State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics

<div>In a recent methodological paper, we have shown how a (local) ensemble Kalman filter can be used to learn both the state and the dynamics of a system in an online framework. The surrogate model is fully parametrised (for example, this could be a neural network) and the update is a two-step process: (i) a state update, possibly localised, and (ii) a parameter update consistent with the state update. In this framework, the parameters of the surrogate model are assumed to be global. <br><br>In this presentation, we show how to extend the method to the case where the surrogate model, still fully parametrised, admits both global and local parameters (typically forcing parameters). In this case, localisation can be applied not only to the state update, but also to the local parameters update. This results in a collection of new algorithms, depending on the localisation method (covariance localisation or domain localisation) and on whether localisation is applied to the state update, or to both the state and local parameter update. The algorithms are implemented and tested with success on the 40-variable Lorenz model. Finally, we show a two-dimensional illustration of the method using a multi-layer Lorenz model with radiance-like non-local observations.</div>

A Projection Framework for Testing Shape Restrictions That Form Convex Cones

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in nonstandard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density‐related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data‐driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.

Secondary Household Covid-19 Transmission Modelling of Students Returning Home from University

We estimate the number of secondary Covid-19 infections caused by potentially infectious students returning from university to private homes with other occupants. Using a Monte-Carlo method and data derived from UK sources, we predict that an infectious student would, on average, infect 0.94 other household members. Or, as a rule of thumb, each infected student would generate (just less than) one secondary within-household infection. The total number of secondary cases for all returning students is dependent on the virus prevalence within the student population at the time of their departure from campus back home. Correspondingly, we provide results for prevalence ranging from 0.5% to 15%, which is based on observed minimum and maximum estimates from Cardiff University’s asymptomatic testing service. Although the proposed estimation method is general and robust, the results are sensitive to the input data. We therefore provide Matlab code and a helpful online app (http://bit.ly/Secondary_infections_app) that can be used to estimate numbers of secondary infections based on local parameter values.

On the Measurement of Bias in Geographically Weighted Regression Models

Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated data set with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.