The Architecture of Chance: An Introduction to the Logic and Arithmetic of Probability.
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Introduction Common sense reduced to calculation The logic and arithmetic of compound probabilities Probability pathways and a first glance at the logic of probability assessment Binomial probabilities and the concept of sampling distributions The normal distribution-remarkable crossroad of fact and theory Some complex probability assessments based on the normal distribution A brief climb to one of the next higher levels: Student's t-distributions and the logic of estimation Appendix A: Table of the unit normal distribution Appendix B: Table of critical values of student's t-distributions.
Background: Generalized Odds (Gen Odds) provide summaries for ordinal outcomes without requiring the proportional odds assumption. However, conventional Gen Odds compares independently drawn treatment and control outcomes and targets a population-level contrast rather than an individual-level contrast. We developed an individual-level causal formulation of Gen Odds and examined its identification. Methods: We defined the Causal Gen Odds using the joint distribution of…
We develop a semiparametric continuous time inferential framework for testing cumulative treatment effects, including both immediate and carryover effects. The latent state process is modeled by an ordinary differential equation (ODE) whose drift depends on state and treatment, while the observed data are noisy measurements of this latent state at irregular, multi resolution time points. We define the average treatment effect (ATE) as the difference of expected cumulative…
Joint-event forecasts combine an estimated dependence model with current marginal forecasts. Retaining historical transforms at the marginal fits available when each outcome arrived creates overlapping estimation errors. We derive their joint influence with the terminal estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical…
当处理发生溢出:时空因果效应估计的神经网络框架
Real-world public health policies are often enacted by local jurisdictions, but their effects can ripple through connected populations. For causal evaluation, this creates a difficult spatiotemporal problem: intermittent policy updates create path-level treatments, and because spillover depends on neighboring treatment paths along with the focal-unit's own history, controlling time-varying confounding requires high-dimensional, multimodal information from both sources. To…
时空干扰下用于实验的聚类切换设计
We consider experimentation in the presence of non-stationarity, inter-unit (spatial) interference, and carry-over effects (temporal interference), where we wish to estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control. We suppose spatial interference is described by a graph, where a unit's outcome depends on its neighborhood's treatments, and that temporal interference is…
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…