Related papers: The art of fitting p-mode spectra: Part I. Maximum…
In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using 'Maximum Likelihood…
We introduce a modified version of a standard power spectrum `peak-bagging' technique which is designed to gain some of the advantages that fitting the entire low-degree p-mode power spectrum simultaneously would bring, but without the…
Thanks to their high quality, new and upcoming asteroseismic observations - with CoRoT, Kepler, and from the ground... - can benefit from the experience gained with helioseismology. We focus in this paper on solar-like oscillations, for…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
Mode fitting or "peak-bagging" is an important procedure in helioseismology allowing one to determine the various mode parameters of solar oscillations. Here we describe a way of reducing the systematic bias in the fits of certain mode…
We present a novel technique to parametrize experimental data, based on the construction of a probability measure in the space of functions, which retains the full experimental information on errors and correlations. This measure is…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…
Pixel-space full spectrum fitting exploiting non-linear $\chi^2$ minimization became a \emph{de facto} standard way of deriving internal kinematics from absorption line spectra of galaxies and star clusters. However, reliable estimation of…
We present a maximum likelihood method for fitting two-dimensional model distributions to stellar data in colour-magnitude space. This allows one to include (for example) binary stars in an isochronal population. The method also allows one…
Mode fitting or "peak-bagging" is an important procedure in helioseismology allowing one to determine the various mode parameters of solar oscillations. We have recently developed a new "pseudo-global" fitting algorithm as a way of reducing…
In this paper we consider the problem of parameter estimation in the $p$-spin Curie-Weiss model, for $p \geq 3$. We provide a complete description of the limiting properties of the maximum likelihood (ML) estimates of the inverse…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
The method of obtaining confidence intervals on a subset of the total number of parameters (p) of a model used for fitting X-ray spectra is to perturb the best-fitting model until, for each parameter, a range is found for which the change…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…