Based on geometric invariance properties, we derive an explicit prior distribution for the parameters of multivariate linear regression problems in the absence of further prior information. The problem is formulated as a rotationally-invariant distribution of L-dimensional hyperplanes inN dimensions, and the associated system of partial differential equations is solved. The derived prior distri...

We investigate a general characteristic of the trade-off in learning problems between goodness-of-fit and model complexity. Specifically we characterize a general class of learning problems where the goodness-of-fit function can be shown to be convex within firstorder as a function of model complexity. This general property of "diminishing returns" is illustrated on a number of real data sets a...

12 We review the use of artificial neural networks, particularly the feedforward multilayer 13 perceptron with back-propagation for training (MLP), in ecological modelling. In MLP 14 modeling, there are no assumptions about the underlying form of the data that must be met as 15 in standard statistical techniques. Instead the researchers should make clear the process of 16 modelling, because thi...

BACKGROUND Hu County is a serious hemorrhagic fever with renal syndrome (HFRS) epidemic area, with notable fluctuation of the HFRS epidemic in recent years. This study aimed to explore the optimal model for HFRS epidemic prediction in Hu. METHODS Three models were constructed and compared, including a generalized linear model (GLM), a generalized additive model (GAM), and a principal componen...

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This paper extends existing research on firm heterogeneity by exploring whether differences in firm performance characteristics may in part be related to the gender of the proprietor of the firm. Using a data set of Irish manufacturing firms covering the period 1993 to 2002, we estimate multivariate regression models comparing the performance of female-owned and male-female joint ownership firm...

This paper develops a new framework and statistical tools to analyze stock returns using high frequency data. We consider a continuous-time multi-factor model via a continuous-time multivariate regression incorporating realistic empirical features, such as persistent stochastic volatilities with leverage effects. We find that conventional regression approach often leads to misleading and incons...

In the last decade, fNIRS has provided a non-invasive method to investigate neural activation in developmental populations. Despite its increasing use cognitive neuroscience, there is little consistency or consensus on how pre-process and analyse infant data. With this registered report, we investigated feasibility of applying more advanced statistical analyses data compared most commonly used ...