Miracle-dz/UniFAR-FTUs huggingface dataset:
A model selection approach to genome wide association studies

For the vast majority of genome wide association studies (GWAS) published so far, statistical analysis was performed by testing markers individually. In this article we present some elementary statistical considerations which clearly show that in case of complex traits the approach based on multiple regression or generalized linear models is preferable to multiple testing. We introduce a model selection approach to GWAS based on modifications of Bayesian Information Criterion (BIC) and develop some simple search strategies to deal with the huge number of potential models. Comprehensive simulations based on real SNP data confirm that model selection has larger power than multiple testing to detect causal SNPs in complex models. On the other hand multiple testing has substantial problems with proper ranking of causal SNPs and tends to detect a certain number of false positive SNPs, which are not linked to any of the causal mutations. We show that this behavior is typical in GWAS for complex traits and can be explained by an aggregated influence of many small random sample correlations between genotypes of a SNP under investigation and other causal SNPs. We believe that our findings at least partially explain problems with low power and nonreplicability of results in many real data GWAS. Finally, we discuss the advantages of our model selection approach in the context of real data analysis, where we consider publicly available gene expression data as traits for individuals from the HapMap project.
Average Collapsibility of Some Association Measures

Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the covariate. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient conditions for the average collapsibility of the measures under consideration are obtained. Some difficult, but interesting, counter-examples are constructed. Applications to linear, Poisson, logistic and negative binomial regression models are addressed. An extension to the case of multivariate covariate W is also discussed.
Remembering Leo

I do not remember when was the first time that I met Leo, but I have a clear memory of going to Leo’s office on the 4th floor of Evans Hall to talk to him in my second year in Berkeley’s Ph.D. program in 1986. The details of the conversation are not retained but a visual image of his clean and orderly office remains, in a stark contrast to a high entropy state of the same office now being used by myself. In the 1980s, the Berkeley Statistics Department’s Statistical Computing Facility (SCF) managed mainframe computers named after musicians such as Bizet and Bach. Later I learned that Leo came back to Berkeley in 1980 as a professor from industrial consulting and soon established and directed SCF—a far-sighted move by any measure, and one that benefited the department for decades to come. Before his retirement in January 1993, Leo had not only been an energetic and effective director of SCF but also an energetic and effective teacher in his multivariate statistics graduate class, in addition to much original research. After his retirement, he remained a strong leader of statistical computing in the department by advising students and helping start the statistical machine learning group with many joint appointments with Computer Science and Electrical Engineering. Moreover, as he told me himself, this period after retirement was the best time for his research— he was producing seminal papers one after the other on statistical machine learning, for example, on analyzing boosting and developing now-popular algorithms such as bagging and random forests. After I returned to Berkeley as a faculty member in 1993, I would frequently encounter Leo on the 4th floor of Evans Hall since my first office was also on the same floor. We would have hallway conversations and he would tell me what was on his mind at that time. During one of those conversations, Leo asked me to join a journal club on neural networks, one of the topics that attracted Leo’s attention at that time and the beginning of his work on understanding machine learning methods and developing many
Bayesian variable selection for spatially dependent generalized linear models

Despite the abundance of methods for variable selection and accommodating spatial structure in regression models, there is little precedent for incorporating spatial dependence in covariate inclusion probabilities for regionally varying regression models. The lone existing approach is limited by difficult computation and the requirement that the spatial dependence be represented on a lattice, making this method inappropriate for areal models with irregular structures that often arise in ecology, epidemiology, and the social sciences. Here we present a novel method for spatial variable selection in areal generalized linear models that can accommodate arbitrary spatial structures and works with a broad subset of GLM likelihoods. The method uses a latent probit model with a spatial dependence structure where the binary response is taken as a covariate inclusion indicator for area-specific GLMs. The covariate inclusion indicators arise via thresholding of latent standard normals on which we place a conditionally autoregressive prior. We propose an efficient MCMC algorithm for computation that is entirely conjugate in any model with a conditionally Gaussian representation of the likelihood, thereby encompassing logistic, probit, multinomial probit and logit, Gaussian, and negative binomial regressions through the use of existing data augmentation methods. We demonstrate superior parameter recovery and prediction in simulation studies as well as in applications to geographic voting patterns and population estimation. Though the method is very broadly applicable, we note in particular that prior to this work, spatial population estimation/capture-recapture models allowing for varying list dependence structures has not been possible.
Bounds smaller than the Fisher information for generalized linear models

In this paper, we propose a parameter space augmentation approach that is based on "intentionally" introducing a pseudo-nuisance parameter into generalized linear models for the purpose of variance reduction. We first consider the parameter whose norm is equal to one. By introducing a pseudo-nuisance parameter into models to be estimated, an extra estimation is asymptotically normal and is, more importantly, non-positively correlated to the estimation that asymptotically achieves the Fisher/quasi Fisher information. As such, the resulting estimation is asymptotically with smaller variance-covariance matrices than the Fisher/quasi Fisher information. For general cases where the norm of the parameter is not necessarily equal to one, two-stage quasi-likelihood procedures separately estimating the scalar and direction of the parameter are proposed. The traces of the limiting variance-covariance matrices are in general smaller than or equal to that of the Fisher/quasi-Fisher information. We also discuss the pros and cons of the new methodology, and possible extensions. As this methodology of parameter space augmentation is general, and then may be readily extended to handle, say, cluster data and correlated data, and other models.
The Wang-Landau algorithm reaches the Flat Histogram criterion in finite time

The Wang-Landau algorithm aims at sampling from a probability distribution, while penalizing some regions of the state space and favouring others. It is widely used, but its convergence properties are still unknown. We show that for some variations of the algorithm, the Wang-Landau algorithm reaches the so-called Flat Histogram criterion in finite time, and that this criterion can be never reached for other variations. The arguments are shown on an simple context -- compact spaces, density functions bounded from both sides-- for the sake of clarity, and could be extended to more general contexts.
Vertices of the Least Concave Majorant of Brownian Motion with Parabolic Drift

It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result in Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size $n$ from the uniform distribution on $[0,1]$ is asymptotically normal, with an asymptotic expectation and variance which are both of order $\log(n)$. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices in such an interval is about half the size of the expectation, if the length of the interval tends to infinity. We prove an asymptotic normality result for the number of vertices in an increasing interval, which translates into a corresponding result for the least concave majorant of an empirical distribution function of a sample of size $n$, generated by a strictly concave distribution function. In this case the number of vertices is of order cube root $n$ and the variance is again about half the size of the asymptotic expectation. As a side result we obtain some interesting relations between the first moments of the number of vertices, the square of the location of the maximum of Brownian motion minus a parabola, the value of the maximum itself, the squared slope of the least concave majorant at zero, and the value of the least concave majorant at zero. An erratum is available in EJP volume 18 paper 46 .
Desentrañando la historia y evolución en el principal «hotspot» de biodiversidad vegetal ibérica. Una aproximación multiescalar en el Parque Nacional de Sierra Nevada

Given current threats of global change on biodiversity, it is of outstanding importance to unravel the mechanisms that allowed the evolutionary construction of biodiversity hotspots. Sierra Nevada is a hotspot within the Mediterranean basin, where a complex geological and climatic history have promoted a high diversity of habitats, moulding different plant communities and assemblages. In this context, the evolutionary history of species is critical to understand the current composition of communities. In this project, we have developed a phylogenetic approach using the woody flora of Sierra Nevada, which is nested within the Baetic-Rifan hotspot. We use floristic data for the whole Baetic-Rifan hotspot, the Baetic sierras and woody plant communities at different elevations and substrates in Sierra Nevada, as well as regional megaphylogenies for the whole hotspot and phylogenies specifically developed for Sierra Nevada. We specifically address the following key questions: (i) How is alpha and beta phylogenetic diversity distributed in the Baetic-Rifan hotspot and what is the position of Sierra Nevada within this context? (ii) What is the phylogenetic and functional structure of woody plant communities, and how does community structure vary along elevation gradients Desentrañando la historia y evolución en el principal «hotspot» de biodiversidad vegetal ibérica. 153 and different substrates? (iii) What are the biological correlates of these adaptive and differentiation processes? Besides, in order to get a better understanding of the mechanisms driving adaptive change and originating diversity and endemism, we study (iv) the phylogenetic and genetic relationships of a key genus of high diversity in Sierra Nevada, Helianthemum (Cistaceae). Thus, we jointly address the macroand microevolutionary mechanisms determining the high plant biodiversity of Sierra Nevada and surrounding regions.
Snore-GANs: Improving Automatic Snore Sound Classification With Synthesized Data

One of the frontier issues that severely hamper the development of automatic snore sound classification (ASSC) associates to the lack of sufficient supervised training data. To cope with this problem, we propose a novel data augmentation approach based on semi-supervised conditional generative adversarial networks (scGANs), which aims to automatically learn a mapping strategy from a random noise space to original data distribution. The proposed approach has the capability of well synthesizing “realistic” high-dimensional data, while requiring no additional annotation process. To handle the mode collapse problem of GANs, we further introduce an ensemble strategy to enhance the diversity of the generated data. The systematic experiments conducted on a widely used Munich–Passau snore sound corpus demonstrate that the scGANs-based systems can remarkably outperform other classic data augmentation systems, and are also competitive to other recently reported systems for ASSC.
Exact and Efficient Parallel Inference for Nonparametric Mixture Models

Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize inference in such models have relied on introducing approximations, which can lead to inaccuracies in the posterior estimate. In this paper, we describe auxiliary variable representations for the Dirichlet process and the hierarchical Dirichlet process that allow us to sample from the true posterior in a distributed manner. We show that our approach allows scalable inference without the deterioration in estimate quality that accompanies existing methods.
Forward Smoothing using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an online or “forward-only” implementation of a forward filtering backward smoothing SMC algorithm proposed in [18]. Compared to the standard path space SMC estimator whose asymptotic variance increases quadratically with time even under favourable mixing assumptions, the asymptotic variance of the proposed SMC estimator only increases linearly with time. This forward smoothing procedure allows us to implement on-line maximum likelihood parameter estimation algorithms which do not suffer from the particle path degeneracy problem. Some key words : Expectation-Maximization, Forward Filtering Backward Smoothing, Recursive Maximum Likelihood, Sequential Monte Carlo, Smoothing, State-Space Models.
Dense Signals, Linear Estimators, and Out-of-Sample Prediction for High-Dimensional Linear Models

Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional linear models: ridge regression estimators, scalar multiples of the ordinary least squares (OLS) estimator (referred to as James-Stein shrinkage estimators), and marginal regression estimators. The results in this paper require no assumptions about sparsity and imply: (i) if prior information about the population predictor covariance is available, then the ridge estimator outperforms the OLS, James-Stein, and marginal estimators; (ii) if little is known about the population predictor covariance, then the James-Stein estimator may be an effective alternative to the ridge estimator; and (iii) the marginal estimator has serious deficiencies for out-of-sample prediction. Both finite sample and asymptotic properties of the estimators are studied in this paper. Though various asymptotic regimes are considered, we focus on the setting where the number of predictors is roughly proportional to the number of observations. Ultimately, the results presented here provide new and detailed practical guidance regarding several well-known non-sparse methods for high-dimensional linear models.
Change Detection in INAR(p) Processes Against Various Alternative Hypotheses

Change in the coefficients or the mean of the innovation of an INAR(p) process is a sign of disturbance that is important to detect. The proposed methods can test for change in any one of these quantities separately, or in any collection of them. They make both one-sided and two-sided tests possible, furthermore, they can be used to test against the “epidemic” alternative. The tests are based on a CUSUM process using CLS estimators of the parameters. Under the one-sided and two-sided alternatives, consistency of the tests is proved and the properties of the change-point estimator are also explored.
Variance Decomposition and Replication In Scrabble: When You Can Blame Your Tiles?

In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match against a superior player, and more difficult to determine the true ability of a player in a tournament or contest. I propose a new format for drawing tiles in a two-player game that allows for the same tile pattern (though not the same board) to be replicated over multiple matches, so that a player's result can be better compared against others, yet is indistinguishable from the bag-based draw within a game. A large number of simulations conducted with Scrabble software shows that the variance from the tile order in this scheme accounts for as much variance as the different patterns of letters on the board as the game progresses. I use these simulations as well as the experimental design to show how much various tiles are able to affect player scores depending on their placement in the tile seeding.
SMC2: an efficient algorithm for sequential analysis of state space models

Summary. We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ‐dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments and rejuvenates the θ‐particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x‐dimension, for any fixed θ. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the θ‐dimension, which propagates and resamples many particle filters in the x‐dimension. The filters in the x‐dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the θ‐particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non‐sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x‐particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.
Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.
Censored quantile regression processes under dependence and penalization

We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile regression model is large. It is demonstrated that traditional penalized estimators such as the adaptive lasso yield sub-optimal rates if the coecients of the quantile regression cross zero. New penalization techniques are introduced which are able to deal with specic problems of censored data and yield estimates with an optimal rate. In contrast to most of the literature, the asymptotic analysis does not require the assumption of independent observations, but is based on rather weak assumptions, which are satised for many
A Bernstein–von Mises theorem in the nonparametric right-censoring model

In the recent Bayesian nonparametric literature, many examples have been reported in which Bayesian estimators and posterior distributions do not achieve the optimal convergence rate, indicating that the Bernstein-von Mises theorem does not hold. In this article, we give a positive result in this direction by showing that the Bernstein-von Mises theorem holds in survival models for a large class of prior processes neutral to the right. We also show that, for an arbitrarily given convergence rate n -α with 0 < α ≤ 1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n -α .