Related papers: Linearity of Data and Linear Probability Space
Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space…
Techniques for decision making with knowledge of linear constraints on condition probabilities are examined. These constraints arise naturally in many situations: upper and lower condition probabilities are known; an ordering among the…
Often the rows (cases, objects) of a dataset have weights. For instance, the weight of a case may reflect the number of times it has been observed, or its reliability. For analyzing such data many rowwise weighted techniques are available,…
When reading peer-reviewed scientific literature describing any analysis of empirical data, it is natural and correct to proceed with the underlying assumption that experiments have made good faith efforts to ensure that their analyses…
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be…
We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
We extend the correspondence between two-stage coding procedures in data compression and penalized likelihood procedures in statistical estimation. Traditionally, this had required restriction to countable parameter spaces. We show how to…
Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…
Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Forecasting with longitudinal data has been rarely studied. Most of the available studies are for continuous response and all of them are for univariate response. In this study, we consider forecasting multivariate longitudinal binary data.…