Miracle-dz/UniFAR-FTUs huggingface dataset:
Two-step wavelet-based estimation for mixed Gaussian fractional processes

A mixed Gaussian fractional process {Y (t)}t∈R = {PX(t)}t∈R is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries X by a nonsingular matrix P . It is interpreted that Y is observable, while X is a hidden process occurring in an (unknown) system of coordinates P . Mixed processes naturally arise as approximations to solutions of physically relevant classes of multivariate fractional SDEs under aggregation. We propose a semiparametric two-step wavelet-based method for estimating both the demixing matrix P−1 and the memory parameters of X. The asymptotic normality of the estimators is established both in continuous and discrete time. Monte Carlo experiments show that the finite sample estimation performance is comparable to that of parametric methods, while being very computationally efficient. As applications, we model a bivariate time series of annual tree ring width measurements, and establish the asymptotic normality of the eigenstructure of sample wavelet matrices.
An empirical evaluation of alternative methods of estimation for Permutation Entropy in time series with tied values

Bandt and Pompe introduced Permutation Entropy in 2002 for Time Series where equal values, xt1 = xt2, t1 = t2, were neglected and only inequalities between the xt were considered. Since then, this measure has been modified and extended, in particular in cases when the amount of equal values in the series can not be neglected, (i.e. heart rate variability (HRV) time series). We review the different existing methodologies that treats this subject by classifying them according to their different strategies. In addition, a novel Bayesian Missing Data Imputation is presented that proves to outperform the existing methodologies that deals with type of time series. All this facts are illustrated by simulations and also by distinguishing patients suffering from Congestive Heart Failure from a (healthy) control group using HRV time series
BPEC: An R Package for Bayesian Phylogeographic and Ecological Clustering

BPEC is an R package for Bayesian Phylogeographic and Ecological Clustering which allows geographical, environmental and phenotypic measurements to be combined with DNA sequences in order to reveal clustered structure resulting from migration events. DNA sequences are modelled using a collapsed version of a simplified coalescent model projected onto haplotype trees, which subsequently give rise to constrained clusterings as migrations occur. Within each cluster, a multivariate Gaussian distribution of the covariates (geographical, environmental, phenotypic) is used. Inference follows tailored Reversible Jump Markov chain Monte Carlo sampling so that the number of clusters (i.e., migrations) does not need to be pre-specified. A number of output plots and visualizations are provided which reflect the posterior distribution of the parameters of interest. BPEC also includes functions that create output files which can be loaded into Google Earth. The package commands are illustrated through an example dataset of the polytypic Near Eastern brown frog Rana macrocnemis analysed using BPEC.
Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models

ABSTRACT Topic models, and more specifically the class of latent Dirichlet allocation (LDA), are widely used for probabilistic modeling of text. Markov chain Monte Carlo (MCMC) sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler. Supplementary materials for this article are available online.
Characterization of multivariate Bernoulli distributions with given margins

We express each Fr\'echet class of multivariate Bernoulli distributions with given margins as the convex hull of a set of densities, which belong to the same Fr\'echet class. This characterisation allows us to establish whether a given correlation matrix is compatible with the assigned margins and, if it is, to easily construct one of the corresponding joint densities. % Such %representation is based on a polynomial expression of the distributions of a Fr\'echet class. We reduce the problem of finding a density belonging to a Fr\'echet class and with given correlation matrix to the solution of a linear system of equations. Our methodology also provides the bounds that each correlation must satisfy to be compatible with the assigned margins. An algorithm and its use in some examples is shown.
Which Findings from the Functional Neuromaging Literature Can We Trust

In their recent "Cluster Failure" paper, Eklund and colleagues cast doubt on the accuracy of a widely used statistical test in functional neuroimaging. Here, we leverage nonparametric methods that control the false discovery rate to offer more nuanced, quantitative guidance about which findings in the existing literature can be trusted. We show that, in the task studies examined by Eklund et al., most clusters originally reported to be significant are indeed trustworthy by the false discovery rate benchmark.
Why Condorcet Consistency is Essential

In a single winner election with several candidates and ranked choice or rating scale ballots, a Condorcet winner is one who wins all their two way races by majority rule or MR. A voting system has Condorcet consistency or CC if it names any Condorcet winner the winner. Many voting systems lack CC, but a three step line of reasoning is used here to show why it is necessary. In step 1 we show that we can dismiss all the electoral criteria which conflict with CC. In step 2 we point out that CC follows almost automatically if we can agree that MR is the only acceptable system for elections with two candidates. In step 3 we make that argument for MR. This argument itself has three parts. First, in races with two candidates, the only well known alternatives to MR can sometimes name as winner a candidate who is preferred over their opponent by only one voter, with all others preferring the opponent. That is unacceptable. Second, those same systems are also extremely susceptible to strategic insincere voting. Third, in simulation studies using spatial models with two candidates, the best known alternative to MR picks the best or most centrist candidate significantly less often than MR does.
Efficient model-based clustering with coalescents: Application to multiple outcomes using medical records data

We present a sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. The model is appropriate for multivariate non-\iid data and our approach offers a substantial reduction in computational cost when compared to the original sampler. We also propose a quadratic complexity approximation that in practice shows almost no loss in performance compared to its counterpart. Our formulation leads to a greedy algorithm that exhibits performance improvement over other greedy algorithms, particularly in small data sets. We incorporate the Coalescent into a hierarchical regression model that allows joint modeling of multiple correlated outcomes. The approach does not require {\em a priori} knowledge of either the degree or structure of the correlation and, as a byproduct, generates additional models for a subset of the composite outcomes. We demonstrate the utility of the approach by predicting multiple different types of outcomes using medical records data from a cohort of diabetic patients.
On the physical interpretation of a meta-analysis in the presence of heterogeneity and bias: from clinical trials to Mendelian randomization

The funnel plot is a graphical visualisation of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modelling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the centre of mass of a physical system. We used this analogy, with some success, to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulae. In this paper we aim to formalise this analogy at a more technical level using the estimating equation framework: firstly, to help elucidate some of the basic statistical models employed in a meta-analysis and secondly, to forge new connections between bias adjustment in the evidence synthesis and causal inference literatures.
Estimating HIV epidemics for subnational areas

As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national levels. Currently, the epidemic models have been applied independently to the sub-national areas within countries. However, the availability and quality of the data vary widely, which leads to biased and unreliable estimates for areas with very few data. We propose to overcome this issue by introducing the dependence of the parameters across areas in a mixture model. The joint distribution of the parameters in multiple areas can be approximated directly from the results of independent fits without needing to refit the data or unpack the software. As a result, the mixture model has better predictive ability than the independent model as shown in examples of multiple countries in Sub-Saharan Africa.
Fitting Prediction Rule Ensembles with R Package pre

Prediction rule ensembles (PREs) are sparse collections of rules, offering highly interpretable regression and classification models. This paper shows how they can be fitted using function pre from R package pre, which derives PREs largely through the methodology of Friedman and Popescu (2008). The implementation and functionality of pre is described and illustrated through application on a dataset on the prediction of depression. Furthermore, accuracy and sparsity of pre is compared with that of single trees, random forests, lasso regression and the original RuleFit implementation of Friedman and Popescu (2008) in four benchmark datasets. Results indicate that pre derives ensembles with predictive accuracy similar to that of random forests, while using a smaller number of variables for prediction. Furthermore, pre provided better accuracy and sparsity than the original RuleFit implementation.
Combining empirical likelihood and robust estimation methods for linear regression models

Abstract Ordinary least square (OLS) and robust methods are used for estimating the parameters of a linear regression model. These methods perform well under some distributional assumptions which may not be appropriate for some data sets. Therefore, nonparametric methods like Empirical likelihood (EL) may be considered. The EL method maximizes an EL function under some constraints. We consider the EL method with robustified constraints using M estimation method. We provide a small simulation study and a real data example to demonstrate the capability of robust EL method and results reveal that robust constraints are needed when outliers are resent in data.
Regression Analysis of Doubly Truncated Data

Abstract Doubly truncated data are found in astronomy, econometrics, and survival analysis literature. They arise when each observation is confined to an interval, that is, only those which fall within their respective intervals are observed along with the intervals. Unlike the one-sided truncation that can be handled by counting process-based approach, doubly truncated data are much more difficult to handle. In their analysis of an astronomical dataset, Efron and Petrosian proposed some nonparametric methods for doubly truncated data. Motivated by their approach, as well as by the work of Bhattacharya et al. for right truncated data, we propose a general method for estimating the regression parameter when the dependent variable is subject to the double truncation. It extends the Mann–Whitney-type rank estimator and can be computed easily by existing software packages. Weighted rank estimation is also considered for improving estimation efficiency. We show that the resulting estimators are consistent and asymptotically normal. Resampling schemes are proposed with large sample justification for approximating the limiting distributions. The quasar data in Efron and Petrosian and an AIDS incubation data are analyzed by the new method. Simulation results show that the proposed method works well.
Bayesian Spectral Modeling of Microscale Spatial Distributions in a Multivariate Soil Matrix

Recent technological advances have enabled researchers in a variety of fields to collect accurately geocoded data for several variables simultaneously. In many cases it may be most appropriate to jointly model these multivariate spatial processes without constraints on their conditional relationships. When data have been collected on a regular lattice, the multivariate conditionally autoregressive (MCAR) models are a common choice. However, inference from these MCAR models relies heavily on the pre-specified neighborhood structure and often assumes a separable covariance structure. Here, we present a multivariate spatial model using a spectral analysis approach that enables inference on the conditional relationships between the variables that does not rely on a pre-specified neighborhood structure, is non-separable, and is computationally efficient. Covariance and cross-covariance functions are defined in the spectral domain to obtain computational efficiency. Posterior inference on the correlation matrix allows for quantification of the conditional dependencies. The approach is illustrated for the toxic element arsenic and four other soil elements whose relative concentrations were measured on a spatial lattice. Understanding conditional relationships between arsenic and other soil elements provides insights for mitigating poisoning in southern Asia and elsewhere.
An Adaptive Resample-Move Algorithm for Estimating Normalizing Constants

The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard choice of using a fixed number of particles at each iteration is suboptimal because some steps will contribute disproportionately to the variance of the estimate. We introduce an adaptive version of the Resample-Move algorithm, in which the particle set is adaptively expanded whenever a better approximation of an intermediate distribution is needed. The algorithm builds on the expression for the optimal number of particles and the corresponding minimum variance found under ideal conditions. Benchmark results on challenging Gaussian Process Classification and Restricted Boltzmann Machine applications show that Adaptive Resample-Move (ARM) estimates the normalizing constant with a smaller variance, using less computational resources, than either Resample-Move with a fixed number of particles or Annealed Importance Sampling. A further advantage over Annealed Importance Sampling is that ARM is easier to tune.
Efficient Functional ANOVA Through Wavelet-Domain Markov Groves

ABSTRACT We introduce a wavelet-domain method for functional analysis of variance (fANOVA). It is based on a Bayesian hierarchical model that employs a graphical hyperprior in the form of a Markov grove (MG)—that is, a collection of Markov trees—for linking the presence/absence of factor effects at all location-scale combinations, thereby incorporating the natural clustering of factor effects in the wavelet-domain across locations and scales. Inference under the model enjoys both analytical simplicity and computational efficiency. Specifically, the posterior of the full hierarchical model is available in closed form through a pyramid algorithm operationally similar to Mallat’s pyramid algorithm for discrete wavelet transform (DWT), achieving for exact Bayesian inference the same computational efficiency—linear in both the number of observations and the number of locations—as for carrying out the DWT. In particular, posterior probabilities of the presence of factor contributions to functional variation are directly available from the pyramid algorithm, while posterior samples for the factor effects can be drawn directly from the exact posterior through standard (not Markov chain) Monte Carlo. We investigate the performance of our method through extensive simulation and show that it substantially outperforms existing wavelet-domain fANOVA methods in a variety of common settings. We illustrate the method through analyzing the orthosis data. Supplementary materials for this article are available online.
Adaptive posterior contraction rates for the horseshoe

We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of signals, was known. We drop this assumption and characterize the behavior of the maximum marginal likelihood estimator (MMLE) of a key parameter of the horseshoe prior. We prove that the MMLE is an effective estimator of the sparsity level, in the sense that it leads to (near) minimax optimal estimation of the underlying mean vector generating the data. Besides this empirical Bayes procedure, we consider the hierarchical Bayes method of putting a prior on the unknown sparsity level as well. We show that both Bayesian techniques lead to rate-adaptive optimal posterior contraction, which implies that the horseshoe posterior is a good candidate for generating rate-adaptive credible sets.
Cramer-Rao bound for source estimation using a network of binary sensors

The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the context of a source of a continuous release in the atmosphere of hazardous gas or aerosol. Numerical results show a good agreement with the empirical errors, obtained using an MCMC parameter estimation technique.
The Contemporary State of Fundamental Physical Research and the Future Path to Scientific Knowledge

Classical physics has enabled the acquisition of significant knowledge of the physical properties of nature on a standard macroscopic scale. These achievements were driven by use of the causal ontological approach (proposed originally by Aristotle) to formulate models of physical reality. At the beginning of the 20th century, however, the physics community began to prefer models based on a fundamentally different approach to human knowledge. Copenhagen quantum mechanics (CQM) was used to describe the micro-world. The special theory of relativity was used to describe the kinematics of objects moving at high velocity values in both the macroscopic and microscopic regions. This phenomenological approach to knowledge has been more focused on how things appear - instead of their actual properties and causal sequence. In the middle of the 20th century, the causal ontological approach was used to develop a significant scientific advance: the systematization of fundamental strongly interacting particles on the basis of unified algebra in three-dimensional isotopic spin space for spin values 1, 1/2, and 0. However, it was later strongly deformed under the influence of the phenomenological approach and the quark model. This paper will show that practically all contemporary theoretical models of physical reality contain mistakes or unresolved problems. Further scientific progress can be obtained if (and only if) scientists return to the successful causal ontological approach and falsification. Classical physics may be slightly generalized to enable the description of inertia mass increase in dependence on velocity, replacing the relativity theory and CQM. New assumptions may then be employed using generalized classical physics (GCP) to formulate new descriptions of observed phenomena that were previously inaccurately interpreted and used to promote fundamentally inadequate theories.
Selective inference after cross-validation

This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply the inference framework in Loftus et al. (2015) for models determined by quadratic constraints to the model that minimizes CV test error. Our only requirement on the model training pro- cedure is that its selection events are regions satisfying linear or quadratic constraints. This includes both Lasso and forward stepwise, which serve as our main examples throughout. We do not require knowledge of the error variance $\sigma^2$. The procedures described here are computationally intensive methods of selecting models adaptively and performing inference for the selected model. Implementations are available in an R package.
Noise contrastive estimation: asymptotics, comparison with MC-MLE

A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation), and NCE (noise contrastive estimation); both methods rely on simulating artificial data-points to approximate the normalising constant. While the asymptotics of MC-MLE have been established under general hypotheses (Geyer, 1994), this is not so for NCE. We establish consistency and asymptotic normality of NCE estimators under mild assumptions. We compare NCE and MC-MLE under several asymptotic regimes. In particular, we show that, when m goes to infinity while n is fixed (m and n being respectively the number of artificial data-points, and actual data-points), the two estimators are asymptotically equivalent. Conversely, we prove that, when the artificial data-points are IID, and when n goes to infinity while m/n converges to a positive constant, the asymptotic variance of a NCE estimator is always smaller than the asymptotic variance of the corresponding MC-MLE estimator. We illustrate the variance reduction brought by NCE through a numerical study.
Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes ( ) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this article, it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time‐discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.