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We propose a multi-resolution scanning approach to identifying two-sample differences. Windows of multiple scales are constructed through nested dyadic partitioning on the sample space and a hypothesis regarding the two-sample difference is defined on each window. Instead of testing the hypotheses on different windows independently, we adopt a joint graphical model, namely a Markov tree, on the null or alternative states of these hypotheses to incorporate spatial correlation across windows. The induced dependence allows borrowing strength across nearby and nested windows, which we show is critical for detecting high resolution local differences. We evaluate the performance of the method through simulation and show that it substantially outperforms other state of the art two-sample tests when the two-sample difference is local, involving only a small subset of the data. We then apply it to a flow cytometry data set from immunology, in which it successfully identifies highly local differences. In addition, we show how to control properly for multiple testing in a decision theoretic approach as well as how to summarize and report the inferred two-sample difference. We also construct hierarchical extensions of the framework to incorporate adaptivity into the construction of the scanning windows to improve inference further.

The paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametric prior for the latent structure. A commonly used model for such a problem is the mixture of Dirichlet process model. Here, we replace the Dirichlet process with a more general non-parametric prior obtained from a generalized gamma process. The basic feature of this model is that it yields a partition structure for the latent variables which is of Gibbs type. This relates to the well-known (exchangeable) product partition models. If compared with the usual mixture of Dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter σ belonging to the interval (0,1): it is shown that such a parameter greatly influences the clustering behaviour of the model. A value of σ that is close to 1 generates a large number of clusters, most of which are of small size. Then, a reinforcement mechanism which is driven by σ acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements. These features turn out to be very useful in the context of mixture modelling. Since it is difficult to specify a priori the reinforcement rate, it is reasonable to specify a prior for σ. Hence, the strength of the reinforcement mechanism is controlled by the data.

In the large literature on the stock return–inflation puzzle, existing works have used constant coefficient linear regression models or change point analysis with abrupt change points. Motivated by the time varying stock return–inflation relationship and the drawbacks of change point analysis, we propose to use the recently emerged locally stationary models to model stock return and inflation. Although the model exhibits non-parametric time varying dependence structure over a long time span, it has local stationarity within each small time interval. Detailed empirical analysis is conducted and comparisons are made between various approaches. We find that the stock return–inflation correlation is negative during early sample periods and turns positive during late sample periods, but the turning time point is different for the total inflation rate and core inflation rate.

Bayesian analysis results require a choice of prior distribution. In long-baseline neutrino oscillation physics, the usual parameterisation of the mixing matrix induces a prior that privileges certain neutrino mass and flavour state symmetries. Here we study the effect of privileging alternate symmetries on the results of the T2K experiment. We find that constraints on the level of CP violation (as given by the Jarlskog invariant) are robust under the choices of prior considered in the analysis. On the other hand, the degree of octant preference for the atmospheric angle depends on which symmetry has been privileged.

Inferring underlying cooperative and competitive strategies from human behaviour in repeated games is important for accurately characterizing human behaviour and understanding how people reason strategically. Finite automata, a bounded model of computation, have been extensively used to compactly represent strategies for these games and are a standard tool in game theoretic analyses. However, inference over these strategies in repeated games is challenging since the number of possible strategies grows exponentially with the number of repetitions yet behavioural data are often sparse and noisy. As a result, previous approaches start by specifying a finite hypothesis space of automata that does not allow for flexibility. This limitation hinders the discovery of novel strategies that may be used by humans but are not anticipated a priori by current theory. Here we present a new probabilistic model for strategy inference in repeated games by exploiting non-parametric Bayesian modelling. With simulated data, we show that the model is effective at inferring the true strategy rapidly and from limited data, which leads to accurate predictions of future behaviour. When applied to experimental data of human behaviour in a repeated prisoner's dilemma, we uncover strategies of varying complexity and diversity.

Credit rating or credit scoring systems are important tools for estimating the obligor’s creditworthiness and for providing an indication of the obligor’s future status. The discriminatory power of a credit rating or credit scoring system refers to its ex ante ability to distinguish between two or more classes of borrowers. One of the most popular tools for the validation of the power of credit rating or credit scoring models to distinguish between two (or more) classes of borrowers is the receiver operating characteristic (ROC) curve (hypersurface) and its widely used overall summary, the area (hypervolume) under the curve (hypersurface). As the end goal of building such models is to predict and quantify uncertainty about future loans, prediction methods are especially valuable in this context. For this, non-parametric predictive inference is a promising candidate for such inference as it is a frequentist statistical method that is explicitly aimed at using few modelling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. The aim of the paper is to introduce non-parametric predictive inference for ROC analysis within a banking context, for which novel results on ROC hypersurfaces for more than three groups are presented. Examples are provided to illustrate the method.

The Central Limit Theorem (CLT) for extrinsic and intrinsic means on manifolds is extended to a generalization of Fréchet means. Examples are the Procrustes mean for 3D Kendall shapes as well as a mean introduced by Ziezold. This allows for one-sample tests previously not possible, and to numerically assess the 'inconsistency of the Procrustes mean' for a perturbation model and 'inconsistency' within a model recently proposed for diffusion tensor imaging. Also it is shown that the CLT can be extended to mildly rank deficient diffusion tensors. An application to forestry gives the temporal evolution of Douglas fir tree stems tending strongly towards cylinders at early ages and tending away with increased competition.

It is well-known that minimally repaired systems are characterized by non-homogeneous Poisson processes. When the underlying lifetime distribution function or its associated intensity function is completely known, the statistical inference of the cumulative number of failures/repairs is made through some standard techniques. On the other hand, when the parametric form of the lifetime distribution or the intensity function is not known, non-parametric inference techniques such as non-parametric maximum likelihood estimate (NPMLE) and kernel-based estimates are employed. Since these techniques are based on the underlying lifetime data, the resulting estimates of the cumulative number of failures/repairs with respect to the system operation time are discontinuous and troublesome in assessing the reliability measures such as reliability function and mean time to failure, etc. In this paper, we propose a novel lifetime analysis of the repairable systems via Daubechies wavelets. More specifically, we generalize the seminal Daubechies wavelet estimate by Kuhl and Bhairgond (Winter Simul Conf Proc 1:562–571, 2000) by combining the ideas on NPMLE and KMBs. In both simulation experiments and real data analyses, we investigate applicability of our Daubechies wavelet-based approaches and compare them with the conventional non-parametric methods.

IntroductionThis study is a comprehensive investigation of the relationship between food security, environmental performance, and their interaction with change in population.MethodsIt adopts a data-driven non-parametric approach, including ANOVA-inspired statistics and a randomized sample space, to make a preliminary investigation of the relationship between these variables. Data from 2014 to 2022 are utilized to generate temporal, regional, and economic results.Results and DiscussionThis shows that there is no relationship between any of the independent variables and change in population in developed countries, indicating that food and the environment no longer play key roles in deciding trends in human populations. Even in some developing countries, the relationship is still not very noticeable. The research does show, however, that for African and Middle Eastern countries there is an obvious relationship between these independent variables and the population growth rate. This analysis also provides a reference for policymakers in these countries: securing food abundance and environmental safety are the paramount issues for their population policy. The policymakers of countries outside these regions should focus more on matters such as tax incentives, housing, and education policies.

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. We demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.