Statistics for the Life Sciences.
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1. Introduction. Statistics and the Life Sciences. Examples and Overview. 2. Description of Populations and Samples. Introduction. Frequency Distributions: Techniques for Data. Frequency Distributions: Shapes and Examples. Descriptive Statistics: Measures of Center. Boxplots. Measures of Dispersion. Effect of Transformation of Variables (Optional). Samples and Populations: Statistical Inference. Perspective. 3. Random Sampling, Probability, and the Binomial Distribution. Probability and the Life Sciences. Random Sampling. Introduction to Probability. Probability Trees. Probability Rules (Optional). Density Curves. Random Variables. The Binomial Distribution. Fitting a Binomial Distribution to Data (Optional). 4. The Normal Distribution. Introduction. The Normal Curves. Areas Under a Normal Curve. Assessing Normality. The Continuity Correction (Optional). Perspective. 5. Sampling Distributions. Basic Ideas. Dichotomous Observations. Quantitative Observations. Illustration of the Central Limit Theorem (Optional). The Normal Approximation to the Binomial Distribution (Optional). Perspective. 6. Confidence Intervals. Statistical Estimation. Standard Error of the Mean. Confidence Interval. Planning a Study to Estimate. Conditions for Validity of Estimation Methods. Confidence Interval for a Population Proportion. Perspective and Summary. 7. Comparison of Two Independent Samples. Introduction. Standard Error of (y1 - y2). Confidence Interval. Hypothesis Testing: The t-test. Further Discussion of the t-test. One-Tailed Tests. More on Interpretation of Statistical Significance. Planning for Adequate Power (Optional). Student's t: Conditions and Summary. More on Principles of Testing Hypotheses. The Wilcoxon-Mann-Whitney Test. Perspective. 8. Statistical Principles of Design. Introduction. Observational Studies. Experiments. Restricted Randomization: Blocking and Stratification. Levels of Replication. Sampling Concerns (Optional). Perspective. 9. Comparison of Paired Samples. Introduction. The Paired-Sample t-Test and Confidence Interval. The Paired Design. The Sign Test. The Wilcoxon Signed-Rank Test. Further Considerations in Paired Experiments. Perspective. 10. Analysis of Categorical Data. Inference for Proportions: The Chi-Squared Goodness-of-Fit Test. The Chi-Squared Test for a 2 X 2 Contingency Table. Independence and Association in a 2 X 2 Contingency Table. Fisher's Exact Test (Optional). The r x k Contingency Table. Applicability of Methods. Confidence Interval for a Difference Between Proportions. Paired Data and 2 X 2 Tables (Optional). Relative Risk and the Odds Ratio (Optional). Summary of Chi-Squared Tests. 11. Comparing the Means of Many Independent Samples. Introduction. The Basic Analysis of Variance. The Analysis of Variance Model (Optional). The Global F-Test. Applicability of Methods. Two-Way ANOVA (Optional). Linear Combinations of Means (Optional). Multiple Comparisons (Optional). Perspective. 12. Linear Regression and Correlation. Introduction. The Fitted Regression Line. Parametric Interpretation of Regression: The Linear Model. Statistical Inference Concerning B1. The Correlation Coefficient. Guidelines for Interpreting Regression and Correlation. Perspective. Summary of Formulas. 13. A Summary of Inference Methods. Introduction. Data Analysis Samples. Appendices. Chapter Notes. Statistical Tables. Answers to Selected Exercises. Index. Index of Examples.
We study inference for continuous linear functionals of solutions to ill-posed inverse problems, including Euclidean parameters arising in nonparametric instrumental variables, proximal causal inference, and shadow-variable models. Although pointwise root-$n$ inference is possible under standard conditions, we show that this need not translate into locally reliable inference. Under a model imposing only minimal regularity conditions, the target is Hellinger discontinuous…
高维线性回归的统一谱分析:去偏与阈值化
We use spectral analysis to establish a unified theory of debiasing, thresholding, and simultaneous inference for high-dimensional linear regression with ill-conditioned designs. The methods include Ridge regression, spectral cut-off, and iterative and dynamical regression procedures. A common debiasing procedure uses two applications of the original linear algorithm with fixed parameters. Spectral analysis shows that debiasing squares the residual, while implementations…
Uniform confidence bands are widely used in empirical analysis for uncertainty qualification of nonparametric inference of unknown functions. A variety of simple implementation methods, including multiplier bootstrap, have been proposed and theoretically justified. However, an implementation over a literally continuous index set is generally computationally infeasible, and practitioners therefore compute the critical value by evaluating the statistic on a finite evaluation…
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自删失模型下信息性缺失的纵向因果推断
Longitudinal observational data are often subject to informative missingness. For example, in healthcare research using electronic health records, covariates and outcomes are measured only when patients interact with the healthcare system. Whether these data are observed usually depends on the unobserved variable values themselves, introducing a common form of data missing not at random. We develop identification and estimation methods for the effects of longitudinal…
通过正交化自适应估计发现存在混杂的时间序列因果滞后结构
Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal…