"2010-03-09+01:00"^^ . . "doubly stochastic point process" . " Bayesian estimation" . . " loss function" . "The aim of the project was achieved in: modeling and statistics of space-time point processes on a curve and of discs, latency estimation in spike trains and their observation in a short window, statistical analysis of regression models for intensities."@en . "\u010Casoprostorov\u00E9 bodov\u00E9 procesy a jejich aplikace" . . . . . . "doubly stochastic point process, Cox process, Orstein-Uhlenbeck type processes, generating functional, moment measures, simulations, MCMC, admissibility, loss function, Bayesian estimation, neuronal models, spike trains, market microstructure"@en . "http://www.karlin.mff.cuni.cz/~benesv/casoprostor.html"^^ . "2006-01-01+01:00"^^ . " admissibility" . " moment measures" . . . "The project is devoted to basic research in mathematics, probability and statistics, with applications to neurophysiology and economics. A broad new class of random point processes in space and time will be developed and its properties investigated mainly analytically and also by means of simulations. Advanced probabilistic tools will be enhanced to solve complex modeling problems. Various statistical questions arise to achieve inference of these models. Parametric and semi-parametric methods will be developed to this purpose, the admissibility of estimators will be studied. Classical, Bayes and Monte Carlo techniques will be enhanced. Spike trains of animal's neurons will be modeled by spatial-temporal point processes, prediction and filtration problems will be solved. Various estimators of characteristics will be compared using real data in this situation. The project will be solved in four cooperating workplaces, by partly engaged researchers and PhD students within five years."@en . " spike trains" . "42"^^ . "42"^^ . "Projekt p\u0159edstavuje z\u00E1kladn\u00ED v\u00FDzkum v matematice, pravd\u011Bpodobnosti a statistice, s aplikacemi v neurofyziologii a ekonomii. Bude vyvinuta \u0161irok\u00E1 t\u0159\u00EDda nov\u00FDch model\u016F \u010Dasoprostorov\u00FDch bodov\u00FDch proces\u016F a jej\u00ED vlastnosti budou vy\u0161et\u0159ov\u00E1ny p\u0159edev\u0161\u00EDm analyticky a t\u00E9\u017E pomoc\u00ED simulac\u00ED. K \u0159e\u0161en\u00ED slo\u017Eit\u00FDch probl\u00E9m\u016F modelov\u00E1n\u00ED budou vytvo\u0159eny nov\u00E9 pokro\u010Dil\u00E9 pravd\u011Bpodobnostn\u00ED n\u00E1stroje. P\u0159i statistick\u00E9m usuzov\u00E1n\u00ED o t\u011Bchto modelech vzniknou r\u016Fzn\u00E9 statistick\u00E9 probl\u00E9my. K jejich \u0159e\u0161en\u00ED budou vyvinuty parametrick\u00E9 a neparametrick\u00E9 metody, bude posuzov\u00E1na t\u00E9\u017E p\u0159\u00EDpustnost odhad\u016F. Budou rozvinuty klasick\u00E9, Bayesovsk\u00E9 i Monte Carlo postupy. Posloupnosti neuron\u00E1ln\u00EDch impuls\u016F z mozku pokusn\u00E9ho zv\u00ED\u0159ete budou modelov\u00E1ny \u010Dasoprostorov\u00FDmi bodov\u00FDmi procesy, budeme se zab\u00FDvat ot\u00E1zkami predikce a filtrace. U\u017Eit\u00ED re\u00E1ln\u00FDch dat v t\u00E9to situaci umo\u017En\u00ED srovn\u00E1n\u00ED r\u016Fzn\u00FDch odhad\u016F charakteristik. Projekt bude \u0159e\u0161en spolu na \u010Dty\u0159ech pracovi\u0161t\u00EDch, s \u010D\u00E1ste\u010Dn\u00FDmi \u00FAvazky v\u011Bdc\u016F a doktorand\u016F, v dob\u011B p\u011Bti let." . . . " Cox process" . "1"^^ . " generating functional" . "2013-06-28+02:00"^^ . . . "http://www.isvav.cz/projectDetail.do?rowId=IAA101120604"^^ . "4"^^ . " simulations" . " Orstein-Uhlenbeck type processes" . . "2010-12-31+01:00"^^ . "Byl spln\u011Bn c\u00EDl projektu v oblastech: modelov\u00E1n\u00ED a statistiky \u010Dasoprostorov\u00FDch bodov\u00FDch proces\u016F na k\u0159ivce resp. disk\u016F, odhadu latence bodov\u00E9ho procesu impuls\u016F v neuronu resp. pozorov\u00E1n\u00ED v kr\u00E1tk\u00E9m okn\u011B, statistick\u00E9 anal\u00FDzy regresn\u00EDch model\u016F pro intenzity."@cs . "0"^^ . . " MCMC" . . "IAA101120604" . . "Spatial-temporal point processes and their applications"@en . . " neuronal models" .