Related papers: Bounded Statistics
This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to…
Statistical moments of the intensity distributions are used as molecular descriptors. They are used as a basis for defining similarity distances between two model spectra. Parameters which carry the information derived from the comparison…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
We consider big spatial data, which is typically produced in scientific areas such as geological or seismic interpretation. The spatial data can be produced by observation (e.g. using sensors or soil instrument) or numerical simulation…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
We present a discussion on the methods for extracting a given parameter from measurements of hadronic data, with particular focus on determinations of the strong coupling constant. We show that when the PDF dependency on the determination…
When dealing with document similarity many methods exist today, like cosine similarity. More complex methods are also available based on the semantic analysis of textual information, which are computationally expensive and rarely used in…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
It is often not possible to construct a probability density function that describes the data. This can happen if there is no analytic description, and the number of parameters is too large so that it is impossible to simulate and tabulate…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We say that two probabilities are similar at level $\alpha$ if they are contaminated versions (up to an $\alpha$ fraction) of the same common probability. We show how this model is related to minimal distances between sets of trimmed…
This paper investigates the probability density function ($pdf$) of the $(2n-1)$-vector $(n\geq 1)$ of both lower and upper record values for a sequence of independent random variables with common $pdf f$ defined on the same probability…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result…