亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Consider the sum $Y=B+B(H)$ of a Brownian motion $B$ and an independent fractional Brownian motion $B(H)$ with Hurst parameter $H\in(0,1)$. Surprisingly, even though $B(H)$ is not a semimartingale, Cheridito proved in [Bernoulli 7 (2001) 913--934] that $Y$ is a semimartingale if $H>3/4$. Moreover, $Y$ is locally equivalent to $B$ in this case, so $H$ cannot be consistently estimated from local observations of $Y$. This paper pivots on a second surprise in this model: if $B$ and $B(H)$ become correlated, then $Y$ will never be a semimartingale, and $H$ can be identified, regardless of its value. This and other results will follow from a detailed statistical analysis of a more general class of processes called mixed semimartingales, which are semiparametric extensions of $Y$ with stochastic volatility in both the martingale and the fractional component. In particular, we derive consistent estimators and feasible central limit theorems for all parameters and processes that can be identified from high-frequency observations. We further show that our estimators achieve optimal rates in a minimax sense. The estimation of mixed semimartingales with correlation is motivated by applications to high-frequency financial data contaminated by rough noise.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.

We examine acoustic Doppler current profiler (ADCP) measurements from underwater gliders to determine glider position, glider velocity, and subsurface current. ADCPs, however, do not directly observe the quantities of interest; instead, they measure the relative motion of the vehicle and the water column. We examine the lineage of mathematical innovations that have previously been applied to this problem, discovering an unstated but incorrect assumption of independence. We reframe a recent method to form a joint probability model of current and vehicle navigation, which allows us to correct this assumption and extend the classic Kalman smoothing method. Detailed simulations affirm the efficacy of our approach for computing estimates and their uncertainty. The joint model developed here sets the stage for future work to incorporate constraints, range measurements, and robust statistical modeling.

The COVID-19 pandemic has brought forth the importance of epidemic forecasting for decision makers in multiple domains, ranging from public health to the economy as a whole. While forecasting epidemic progression is frequently conceptualized as being analogous to weather forecasting, however it has some key differences and remains a non-trivial task. The spread of diseases is subject to multiple confounding factors spanning human behavior, pathogen dynamics, weather and environmental conditions. Research interest has been fueled by the increased availability of rich data sources capturing previously unobservable facets and also due to initiatives from government public health and funding agencies. This has resulted, in particular, in a spate of work on 'data-centered' solutions which have shown potential in enhancing our forecasting capabilities by leveraging non-traditional data sources as well as recent innovations in AI and machine learning. This survey delves into various data-driven methodological and practical advancements and introduces a conceptual framework to navigate through them. First, we enumerate the large number of epidemiological datasets and novel data streams that are relevant to epidemic forecasting, capturing various factors like symptomatic online surveys, retail and commerce, mobility, genomics data and more. Next, we discuss methods and modeling paradigms focusing on the recent data-driven statistical and deep-learning based methods as well as on the novel class of hybrid models that combine domain knowledge of mechanistic models with the effectiveness and flexibility of statistical approaches. We also discuss experiences and challenges that arise in real-world deployment of these forecasting systems including decision-making informed by forecasts. Finally, we highlight some challenges and open problems found across the forecasting pipeline.

The fundamental challenge of drawing causal inference is that counterfactual outcomes are not fully observed for any unit. Furthermore, in observational studies, treatment assignment is likely to be confounded. Many statistical methods have emerged for causal inference under unconfoundedness conditions given pre-treatment covariates, including propensity score-based methods, prognostic score-based methods, and doubly robust methods. Unfortunately for applied researchers, there is no `one-size-fits-all' causal method that can perform optimally universally. In practice, causal methods are primarily evaluated quantitatively on handcrafted simulated data. Such data-generative procedures can be of limited value because they are typically stylized models of reality. They are simplified for tractability and lack the complexities of real-world data. For applied researchers, it is critical to understand how well a method performs for the data at hand. Our work introduces a deep generative model-based framework, Credence, to validate causal inference methods. The framework's novelty stems from its ability to generate synthetic data anchored at the empirical distribution for the observed sample, and therefore virtually indistinguishable from the latter. The approach allows the user to specify ground truth for the form and magnitude of causal effects and confounding bias as functions of covariates. Thus simulated data sets are used to evaluate the potential performance of various causal estimation methods when applied to data similar to the observed sample. We demonstrate Credence's ability to accurately assess the relative performance of causal estimation techniques in an extensive simulation study and two real-world data applications from Lalonde and Project STAR studies.

Since the average treatment effect (ATE) measures the change in social welfare, even if positive, there is a risk of negative effect on, say, some 10% of the population. Assessing such risk is difficult, however, because any one individual treatment effect (ITE) is never observed, so the 10% worst-affected cannot be identified, while distributional treatment effects only compare the first deciles within each treatment group, which does not correspond to any 10%-subpopulation. In this paper we consider how to nonetheless assess this important risk measure, formalized as the conditional value at risk (CVaR) of the ITE-distribution. We leverage the availability of pre-treatment covariates and characterize the tightest-possible upper and lower bounds on ITE-CVaR given by the covariate-conditional average treatment effect (CATE) function. We then proceed to study how to estimate these bounds efficiently from data and construct confidence intervals. This is challenging even in randomized experiments as it requires understanding the distribution of the unknown CATE function, which can be very complex if we use rich covariates so as to best control for heterogeneity. We develop a debiasing method that overcomes this and prove it enjoys favorable statistical properties even when CATE and other nuisances are estimated by black-box machine learning or even inconsistently. Studying a hypothetical change to French job-search counseling services, our bounds and inference demonstrate a small social benefit entails a negative impact on a substantial subpopulation.

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for and a suspected instrument. Under a causal structure commonly found in empirical applications, the testable conditional independence of the suspected instrument and the outcome given the treatment and the covariates has two implications. First, the instrument is valid, i.e. it does not directly affect the outcome (other than through the treatment) and is unconfounded conditional on the covariates. Second, the treatment is unconfounded conditional on the covariates such that the treatment effect is identified. We suggest tests of this conditional independence based on machine learning methods that account for covariates in a data-driven way and investigate their asymptotic behavior and finite sample performance in a simulation study. We also apply our testing approach to evaluating the impact of fertility on female labor supply when using the sibling sex ratio of the first two children as supposed instrument, which by and large points to a violation of our testable implication for the moderate set of socio-economic covariates considered.

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.