Related papers: Exchangeability, the 'Histogram Theorem', and popu…

We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be…

The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called…

Experimental work regularly finds that individual choices are not deterministically rationalized by well-defined preferences. Nonetheless, recent work shows that data collected from many individuals can be stochastically rationalized by a…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…

We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…

Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…

Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units.…

A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are…

Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…

Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…

Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially…

In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential…