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Among various mathematical frameworks, multidimensional continuous-time Markov jump processes $(Z_t)$ on $\N^d$ form a natural set-up for modeling $SIR$-like epidemics. In this study we extend the res...
Models for complex systems are often built with more parameters than can be uniquely identified by available data. Because of the variety of causes, identifying a lack of parameter identifiability typ...
Statistical Inference For Persistent Homology     persistent homology  topology  density estimation       font style='font-size:12px;'> 2013/4/28
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features as one varies a tuning parame...
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variabilit...
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to cal...
We consider a general nonparametric regression model called the compound model. It includes,as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates b...
Polyploidy is an important speciation mechanism, particularly in land plants. Allopolyploid species are formed after hybridization betweenother-wise intersterile parental species. Recent theoretical p...
Rob Kass presents a fascinating vision of a “post”-Bayes/frequentist-controversy world in which prac-tical utility of statistical models is the guiding prin-ciple for statistical inference.
Kass states (page 5) that Figure 3 is not a good general description of statistical inference and that Figure 1 is more accurate. I completely agree. Kass states (page 5) that It is important for stu...
In this piece, Rob Kass brings to bear his insights from a long career in both theoretical and applied statistics to reflect on the disconnect between what we teach and what we do.
Statistical Inference: The Big Picture     Bayesian  confidence  frequentist  statistical education       font style='font-size:12px;'> 2011/7/5
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results?
Statistical inference across time scales     Discretely observed random process  LAN property       font style='font-size:12px;'> 2011/7/5
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps.
The Dempster–Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence.DS theory has been widely used in computer science and engineering appl...
In this article we study the problem of a semi-parametric inference on the parameters of a multidimensional L´evy process Lt based on the low-frequency observations of the corresponding time-c...
Statistical inference from set-valued observations      Statistical inference  set-valued observations        font style='font-size:12px;'> 2009/9/22
Consider a random experiment whose true (unknown) outcome is modelled by a certain random element X and the available imprecise observations are modelled by some random set A such that XE A almost ...

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