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A central focus of data science is the transformation of empirical evidence into knowledge. As such, the key insights and scientific attitudes of deep thinkers like Fisher, Popper, and Tukey are expected to inspire exciting new advances in machine learning and artificial intelligence in years to come. Along these lines, the present paper advances a novel {\em typicality principle} which states, roughly, that if the observed data is sufficiently ``atypical'' in a certain sense relative to a posited theory, then that theory is unwarranted. This emphasis on typicality brings familiar but often overlooked background notions like model-checking to the inferential foreground. One instantiation of the typicality principle is in the context of parameter estimation, where we propose a new typicality-based regularization strategy that leans heavily on goodness-of-fit testing. The effectiveness of this new regularization strategy is illustrated in three non-trivial examples where ordinary maximum likelihood estimation fails miserably. We also demonstrate how the typicality principle fits within a bigger picture of reliable and efficient uncertainty quantification. 

Strong artificial intelligence (AI) is envisioned to possess general cognitive abilities and scientific creativity comparable to human intelligence, encompassing both knowledge acquisition and problem-solving. While remarkable progress has been made in weak AI, the realization of strong AI remains a topic of intense debate and critical examination. In this paper, we explore pivotal innovations in the history of astronomy and physics, focusing on the discovery of Neptune and the concept of scientific revolutions as perceived by philosophers of science. Building on these insights, we introduce a simple theoretical and statistical framework of weak beliefs, termed the Transformational Belief (TB) framework, designed as a foundation for modeling scientific creativity. Through selected illustrative examples in statistical science, we demonstrate the TB framework's potential as a promising foundation for understanding, analyzing, and even fostering creativity -- paving the way toward the development of strong AI. We conclude with reflections on future research directions and potential advancements. 

While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed calibrated bootstrap, designed to generate finite sample-valid parametric inference from a sample of size n. The central idea is to calibrate an m-out-of-n resampling scheme, where the calibration parameter m is determined against inferential pivotal quantities derived from the cumulative distribution functions of loss functions in parameter estimation. The method comprises two algorithms. The first, named resampling approximation (RA), employs a stochastic approximation algorithm to find the value of the calibration parameter m=mα for a given α in a manner that ensures the resulting m-out-of-n bootstrapped 1−α confidence set is valid. The second algorithm, termed distributional resampling (DR), is developed to further select samples of bootstrapped estimates from the RA step when constructing 1−α confidence sets for a range of α values is of interest. The proposed method is illustrated and compared to existing methods using linear regression with and without L1 penalty, within the context of a high-dimensional setting and a real-world data application. The paper concludes with remarks on a few open problems worthy of consideration.