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This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
We study the statistical properties of return intervals $r$ between successive energy dissipation rates above a certain threshold $Q$ in three-dimensional fully developed turbulence. We find that the distribution function $P_Q(r)$ scales…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that the convex hull of $n$ independent copies of $X$ contains a given point $\theta$. We provide several sharp inequalities regarding $p_{n, X}(\theta)$ and…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
In cosmological $N$-body simulations of warm dark matter, thermal velocities of dark-matter particles are sometimes taken into account by adding random initial velocities to the particles of simulation. However, a particle in the $N$-body…
In this work we tackle the problem of estimating the density $ f_X $ of a random variable $ X $ by successive smoothing, such that the smoothed random variable $ Y $ fulfills the diffusion partial differential equation $ (\partial_t -…
We investigate properties of the probability distribution of the net quark number near the chiral crossover transition in the quark-meson model. The calculations are performed within the functional renormalization group approach, as well as…
We calculate reduced moments $\overline \xi_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law…
Melott has made pioneering studies of the effects of particle discreteness in N-body simulations, a fundamental point that needs careful thought and analysis since all such simulations suffer from numerical noise arising from the use of…
Longitudinal biomarkers are frequently collected in clinical studies due to their strong association with time-to-event outcomes. While considerable progress has been made in methods for jointly modeling longitudinal and survival data,…
We combine the ideas of scaling theory and universal conductance fluctuations with density-functional theory to analyze the conductance properties of doped silicon nanowires. Specifically, we study the cross-over from ballistic to diffusive…
We compute the joint probability density function (jpdf) P_N(M, \tau_M) of the maximum M and its position \tau_M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N \to \infty, this jpdf is…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
The effect of space distribution of randomly-placed particles in a representative composite volume on the thermoelastic effective properties and local stress and strain distribution is analyzed. Quantitative assessment is performed using…