Miracle-dz/UniFAR-FTUs huggingface dataset:
Delayed Acceptance ABC-SMC

Abstract Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a model that is specified in the form of a simulator, and approximates the likelihood at a parameter value θ by simulating auxiliary data sets x and evaluating the distance of x from the true data y. However, ABC is not computationally feasible in cases where using the simulator for each θ is very expensive. This article investigates this situation in cases where a cheap, but approximate, simulator is available. The approach is to employ delayed acceptance Markov chain Monte Carlo within an ABC sequential Monte Carlo sampler to, in a first stage of the kernel, use the cheap simulator to rule out parts of the parameter space that are not worth exploring, so that the “true” simulator is only run (in the second stage of the kernel) where there is a reasonable chance of accepting proposed values of θ. We show that this approach can be used quite automatically, with few tuning parameters. Applications to stochastic differential equation models and latent doubly intractable distributions are presented. Supplementary materials for this article are available online.
Uniform Asymptotics for Nonparametric Quantile Regression with an Application to Testing Monotonicity

In this paper, we establish a uniform error rate of a Bahadur representation for local polynomial estimators of quantile regression functions. The error rate is uniform over a range of quantiles, a range of evaluation points in the regressors, and over a wide class of probabilities for observed random variables. Most of the existing results on Bahadur representations for local polynomial quantile regression estimators apply to the fixed data generating process. In the context of testing monotonicity where the null hypothesis is of a complex composite hypothesis, it is particularly relevant to establish Bahadur expansions that hold uniformly over a large class of data generating processes. In addition, we establish the same error rate for bootstrap local polynomial estimators which can be useful for various bootstrap inference. As an illustration, we apply to testing monotonicity of quantile regression and present Monte Carlo experiments based on this example.
Extending the small-ball method

The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a uniform small-ball estimate, that is, $Pr(|f| \geq \kappa\|f\|_{L_2}) \geq \delta$ for given constants $\kappa$ and $\delta$. Here we extend the small-ball method and obtain a high probability, almost-isometric (rather than isomorphic) lower bound on the quadratic empirical process. The scope of the result is considerably wider than the small-ball method: there is no need for class members to satisfy a uniform small-ball condition, and moreover, motivated by the notion of tournament learning procedures, the result is stable under a `majority vote'. As applications, we study the performance of empirical risk minimization in learning problems involving bounded subsets of $L_p$ that satisfy a Bernstein condition, and of the tournament procedure in problems involving bounded subsets of $L_\infty$.
Bayesian Reconstruction of Past Land Cover From Pollen Data: Model Robustness and Sensitivity to Auxiliary Variables

Realistic depictions of past land cover are needed to investigate prehistoric environmental changes, effects of anthropogenic deforestation, and long‐term land cover‐climate feedbacks. Observation‐based reconstructions of past land cover are rare, and commonly used model‐based reconstructions exhibit considerable differences. Recently, Pirzamanbein et al. (2018, 10.1016/j.spasta.2018.03.005, Spatial Statistics, 24:14–31) developed a statistical interpolation method that produces spatially complete reconstructions of past land cover from pollen assemblage. These reconstructions incorporate a number of auxiliary data sets raising questions regarding the method's sensitivity to different auxiliary data sets. Here the sensitivity of the method is examined by performing spatial reconstructions for northern Europe during three time periods (1900 CE, 1725 CE, and 4000 BCE). The auxiliary data sets considered include the most commonly utilized sources of past land cover data—for example, estimates produced by a dynamic vegetation model and anthropogenic land cover change models. Five different auxiliary data sets were considered, including different climate data driving the dynamic vegetation model and different anthropogenic land cover change models. The resulting reconstructions were evaluated using cross validation for all the time periods. For the recent time period, 1900 CE, the different land cover reconstructions were also compared against a present day forest map. The validation confirms that the statistical model provides a robust spatial interpolation tool with low sensitivity to differences in auxiliary data and high capacity to capture information in the pollen‐based proxy data. Further auxiliary data with high spatial detail improves model performance for areas with complex topography or few observations.
Prediction of Daytime Hypoglycemic Events Using Continuous Glucose Monitoring Data and Classification Technique

Daytime hypoglycemia should be accurately predicted to achieve normoglycemia and to avoid disastrous situations. Hypoglycemia, an abnormally low blood glucose level, is divided into daytime hypoglycemia and nocturnal hypoglycemia. Many studies of hypoglycemia prevention deal with nocturnal hypoglycemia. In this paper, we propose new predictor variables to predict daytime hypoglycemia using continuous glucose monitoring (CGM) data. We apply classification and regression tree (CART) as a prediction method. The independent variables of our prediction model are the rate of decrease from a peak and absolute level of the BG at the decision point. The evaluation results showed that our model was able to detect almost 80% of hypoglycemic events 15 min in advance, which was higher than the existing methods with similar conditions. The proposed method might achieve a real-time prediction as well as can be embedded into BG monitoring device.
Pearson information-based lower bound on Fisher information

The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either unknown or intractable. For this reason, it is of interest to develop useful lower bounds on the FIM. In this lecture note, we derive such a bound based on moment constraints. We call this bound the Pearson information matrix (PIM) and relate it to properties of a misspecified data distribution. Finally, we show that the inverse PIM coincides with the asymptotic covariance matrix of the optimally weighted generalized method of moments.
A class of multi-resolution approximations for large spatial datasets

Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple resolutions to achieve fast inference and that can (approximately) represent any covariance structure. We consider two special cases of this multi-resolution-approximation framework, a taper version and a domain-partitioning (block) version. We describe theoretical properties and inference procedures, and study the computational complexity of the methods. Numerical comparisons and an application to satellite data are also provided.
Semi-Parametric Causal Sufficient Dimension Reduction Of High Dimensional Treatments

Cause-effect relationships are typically evaluated by comparing the outcome responses to binary treatment values, representing cases and controls. However, in certain applications, treatments of interest are continuous and high dimensional. For example, understanding the causal relationship between severity of radiation therapy, represented by a high dimensional vector of radiation exposure values at different parts of the body, and post-treatment side effects is a problem of clinical interest in oncology. In such circumstances, a more appropriate strategy for making interpretable causal inferences is to reduce the dimension of the treatment. If individual elements of a high dimensional feature vector weakly affect the outcome, but the overall relationship between the feature vector and the outcome is strong, careless approaches to dimension reduction may not preserve this relationship. The literature on sufficient dimension reduction considers strategies that avoid this issue. Parametric approaches to sufficient dimension reduction in regression problems were recently generalized to semi-parametric models. Methods developed for regression problems do not transfer in a straightforward way to causal inference due to complications arising from confounding. In this paper, we use semi-parametric inference theory for structural models to give a general approach to causal sufficient dimension reduction of a high dimensional treatment.
Sparse Sliced Inverse Regression via Lasso

Abstract For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieves the optimal convergence rate under certain sparsity conditions when p is of order , where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples. Supplementary materials for this article are available online.
On the number of principal components in high dimensions

SUMMARYWe consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is shown to be consistent, performs well in high-dimensional simulation studies, and provides reasonable estimates in examples.
Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts

Conway–Maxwell–Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the mean of counts, making them not compatible with nor comparable to competing count regression models, such as the log-linear Poisson, negative-binomial or generalized Poisson regression models. This note illustrates how CMP distributions can be parametrized via the mean, so that simpler and more easily interpretable mean-models can be used, such as a log-linear model. Other link functions are also available, of course. In addition to establishing attractive theoretical and asymptotic properties of the proposed model, its good finite-sample performance is exhibited through various examples and a simulation study based on real datasets. Moreover, the MATLAB routine to fit the model to data is demonstrated to be up to an order of magnitude faster than the current software to fit standard CMP models, and over two orders of magnitude faster than the recently proposed hyper-Poisson model.
When is the first spurious variable selected by sequential regression procedures?

Applied statisticians use sequential regression procedures to produce a ranking of explanatory variables and, in settings of low correlations between variables and strong true effect sizes, expect that variables at the very top of this ranking are truly relevant to the response. In a regime of certain sparsity levels, however, three examples of sequential procedures--forward stepwise, the lasso, and least angle regression--are shown to include the first spurious variable unexpectedly early. We derive a rigorous, sharp prediction of the rank of the first spurious variable for these three procedures, demonstrating that the first spurious variable occurs earlier and earlier as the regression coefficients become denser. This counterintuitive phenomenon persists for statistically independent Gaussian random designs and an arbitrarily large magnitude of the true effects. We gain a better understanding of the phenomenon by identifying the underlying cause and then leverage the insights to introduce a simple visualization tool termed the double-ranking diagram to improve on sequential methods. As a byproduct of these findings, we obtain the first provable result certifying the exact equivalence between the lasso and least angle regression in the early stages of solution paths beyond orthogonal designs. This equivalence can seamlessly carry over many important model selection results concerning the lasso to least angle regression.
Quasi-Bayes properties of a recursive procedure for mixtures

Bayesian methods are attractive and often optimal, yet nowadays pressure for fast computations, especially with streaming data and online learning, brings renewed interest in faster, although possibly sub-optimal, solutions. To what extent these algorithms may approximate a Bayesian solution is a problem of interest, not always solved. On this background, in this paper we revisit a sequential procedure proposed by Smith and Makov (1978) for unsupervised learning and classification in finite mixtures, and developed by M. Newton and Zhang (1999), for nonparametric mixtures. Newton's algorithm is simple and fast, and theoretically intriguing. Although originally proposed as an approximation of the Bayesian solution, its quasi-Bayes properties remain unclear. We propose a novel methodological approach. We regard the algorithm as a probabilistic learning rule, that implicitly defines an underlying probabilistic model; and we find this model. We can then prove that it is, asymptotically, a Bayesian, exchangeable mixture model. Moreover, while the algorithm only offers a point estimate, our approach allows us to obtain an asymptotic posterior distribution and asymptotic credible intervals for the mixing distribution. Our results also provide practical hints for tuning the algorithm and obtaining desirable properties, as we illustrate in a simulation study. Beyond mixture models, our study suggests a theoretical framework that may be of interest for recursive quasi-Bayes methods in other settings.
Bayesian Nonparametric Differential Analysis for Dependent Multigroup Data with Application to Colorectal Cancer DNA Methylation

With recent advances in array-based and next-generation sequencing technologies, cancer datasets involve widely varying sizes and scales, measurement variables, and correlation structures. An overarching scientific goal in cancer research is the invention of general statistical techniques that can cleanly sift the signal from the noise in identifying genomic signatures of the disease across a set of experimental or biological conditions. We propose BayesDiff, a nonparametric Bayesian approach based on a novel class of first order mixture models, called the Sticky Poisson-Dirichlet process or multicuisine restaurant franchise. The BayesDiff methodology flexibly utilizes information from all the measurements and adaptively accommodates any serial dependence in the data to perform simultaneous inferences on the variables. The technique is applied to analyze the motivating DNA methylation colorectal cancer dataset, which displays both serial correlations and complex interaction patterns. In simulation studies, we demonstrate the effectiveness of the BayesDiff procedure relative to existing techniques for differential DNA methylation. Returning to the motivating dataset, we detect the genomic signature for four subtypes of colorectal cancer.
Principal components analysis of regularly varying functions

The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not require this assumption. Instead, we assume that the observed functions are regularly varying. We derive the asymptotic distribution of the sample covariance operator and of the sample functional principal components. We obtain a number of results on the convergence of moments and almost sure convergence. We apply the new theory to establish the consistency of the regression operator in a functional linear model.
Consistency of the maximum likelihood and variational estimators in a dynamic stochastic block model

We consider a dynamic version of the stochastic block model, in which the nodes are partitioned into latent classes and the connection between two nodes is drawn from a Bernoulli distribution depending on the classes of these two nodes. The temporal evolution is modeled through a hidden Markov chain on the nodes memberships. We prove the consistency (as the number of nodes and time steps increase) of the maximum likelihood and variational estimators of the model parameters, and obtain upper bounds on the rates of convergence of these estimators. We also explore the particular case where the number of time steps is fixed and connectivity parameters are allowed to vary.
A stochastic approximation method for chance-constrained nonlinear programs

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraints violation. In order to be able to apply a projected stochastic subgradient algorithm to solve our reformulation with the probabilistic objective, we adapt existing smoothing-based approaches for chance-constrained problems to derive a convergent sequence of smooth approximations of our reformulated problem. In contrast with exterior sampling-based approaches (such as sample average approximation) that approximate the original chance-constrained program with one having finite support, our proposal converges to local solutions of a smooth approximation of the original problem, thereby avoiding poor local solutions that may be an artefact of a fixed sample. Computational results on three test problems from the literature indicate that our proposal is consistently able to determine better approximations of the efficient frontier than existing approaches in reasonable computation times. We also present a bisection approach for solving chance-constrained programs with a prespecified risk level.
Determinantal Point Process Mixtures Via Spectral Density Approach

We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead of using the rather restrictive case where analytical results are available, we adopt a spectral representation from which approximations to the DPP intensity functions can be readily computed. For the sake of concreteness the presentation focuses on a power exponential spectral density, but the proposed approach is in fact quite general. We later extend our model to incorporate covariate information in the likelihood and also in the assignment to mixture components, yielding a trade-off between repulsiveness of locations in the mixtures and attraction among subjects with similar covariates. We develop full Bayesian inference, and explore model properties and posterior behavior using several simulation scenarios and data illustrations.
Unbiased Markov chain Monte Carlo for intractable target distributions

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov chain Monte Carlo (MCMC) algorithms have been proposed for this setting, such as the pseudo-marginal method for latent variable models and the exchange algorithm for a class of undirected graphical models. As with any MCMC algorithm, the resulting estimators are justified asymptotically in the limit of the number of iterations, but exhibit a bias for any fixed number of iterations due to the Markov chains starting outside of stationarity. This "burn-in" bias is known to complicate the use of parallel processors for MCMC computations. We show how to use coupling techniques to generate unbiased estimators in finite time, building on recent advances for generic MCMC algorithms. We establish the theoretical validity of some of these procedures by extending existing results to cover the case of polynomially ergodic Markov chains. The efficiency of the proposed estimators is compared with that of standard MCMC estimators, with theoretical arguments and numerical experiments including state space models and Ising models.
Bivariate modelling of precipitation and temperature using a non-homogeneous hidden Markov model

Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities between the hidden states, and time-dependent emission distributions. This enables the model to account for the non-stationary behaviour of weather variables. By carefully choosing the emission distributions, it is also possible to model the dependance structure between the two variables. The model is applied to several weather stations in Europe with various climates, and we show that it is able to simulate realistic bivariate time series.
A Sheet of Maple to Compute Second-Order Edgeworth Expansions and Related Quantities of any Function of the Mean of an iid Sample of an Absolutely Continuous Distribution.

We designed a completely automated Maple ($\geqslant 15$) worksheet for deriving Edgeworth and Cornish-Fisher expansions as well as the acceleration constant of the bootstrap bias-corrected and accelerated technique. It is valid for non-parametric or parametric bootstrap, of any (studentized) statistics that is -a regular enough- function of the mean of an iid sample of an absolutely continuous distribution. This worksheet allowed us to point out one error in the second-order Cornish-Fisher expansion of the studentized mean stated in Theorem 13.5 by Das Gupta in [8, p. 194] as well as lay the stress on the influence of the slight change of the normalizing constant when computing the second-order Edgeworth and Cornish-Fisher expansions of the t-distribution as stated in Theorem 11.4. 2 by Lehman and Romano in [14, p. 460]. In addition, we successfully applied the worksheet to a complex maximum likelihood estimator as a first step to derive more accurate confidence intervals in order to enhance quality controls. The worksheet also features export of Maple results into R code. In addition, we provide R code to plot these expansions as well as their increasing rearrangements. All these supplemental materials are available upon request.