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A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as $theta(widehat{F}_n)=sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and $theta_U(widehat{F}_n)=sum_{i eq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/sum_{i eq j}W_iW_j$, where $widehat{F}_n$
The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without consistency che
Velocity measurements of wind blowing near the North Sea border of Northern Germany and velocity measurements under local isotropic conditions of a turbulent wake behind a cylinder are compared. It is shown that wind gusts - measured by means of velo
Random divisions of an interval arise in various context, including statistics, physics, and geometric analysis. For testing the uniformity of a random partition of the unit interval $[0,1]$ into $k$ disjoint subintervals of size $(S_k[1],ldots,S_k[k
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional data and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse graphs