Related papers: A method to deconvolve stellar rotational velociti…
Knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. Because we measure the projected rotational speed vsini, we need to solve an ill-posed problem given by a Fredholm integral of…
Rotational speed is an important physical parameter of stars and knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. However, it cannot be measured directly but the convolution of…
Context. Kinematical data such as the mean velocities and velocity dispersions of stellar samples are useful tools to study galactic structure and evolution. However, observational data are often incomplete (e.g., lacking the radial…
We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…
We present a three-dimensional reconstruction of the velocity distribution of nearby stars (<~ 100 pc) using a maximum likelihood density estimation technique applied to the two-dimensional tangential velocities of stars. The underlying…
The random coefficients model $Y_i={\beta_0}_i+{\beta_1}_i {X_1}_i+{\beta_2}_i {X_2}_i+\ldots+{\beta_d}_i {X_d}_i$, with $\mathbf{X}_i$, $Y_i$, $\mathbf{\beta}_i$ i.i.d, and $\mathbf{\beta}_i$ independent of $X_i$ is often used to capture…
In this paper, a very accurate approximation method for the statistics of the sum of M\'{a}laga-$\mathcal{M}$ random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by…
Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…
A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…
The determination of galaxy merger fraction of field galaxies using automatic morphological indices and photometric redshifts is affected by several biases if observational errors are not properly treated. Here, we correct these biases…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
Determining the mass of stars is crucial both to improving stellar evolution theory and to characterising exoplanetary systems. Asteroseismology offers a promising way to estimate stellar mean density. When combined with accurate radii…