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On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data
Papáček, Š. ; Jablonský, J. ; Matonoha, Ctirad
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model parameter estimation and then we focus on how the different methods of data pre- processing influence the confidence interval of the estimated parameters, namely the diffusion constant $p$. Finally, we present a preliminary study of two methods for the computation of a least-squares estimate $\hat{p}$ and its confidence interval.
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A note on weighted combination methods for probability estimation
Sečkárová, Vladimíra
To successfully learn from the information provided by avail- able information sources, the choice of automatic method combining them into one aggregate result plays an important role. To respect the reliability in the source’s performance each of them is assigned a weight, often subjectively influenced. To overcome this issue, we briefly describe the method based on Bayesian decision theory and elements of infor- mation theory. In particular we consider discrete-type information, rep- resented by probability mass functions (pmfs) and obtain an aggregate result, which has also form of pmf. This result of decision making pro- cess is found to be a weighted linear combination of available information. Besides the brief description of the novel method, the paper focuses on its comparison with other combination methods. Since we consider the available information and unknown aggregate as pmfs, we mainly focus on the case when the parameter of binomial distribution is of interest and the sources provide appropriate pmfs.
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Impact of forgetting on models of rolling mills
Dedecius, Kamil ; Jirsa, Ladislav
The research report deals with an analysis of various models for modelling of the cold sheet rolling process. It comprises a thorough analysis of a mass-flow model and its weaknesses, brief analysis of normalization impact on modelling and exhaustive analysis of 4 defined models with exponential and partial forgetting and their comparison to models without forgetting. The report ends with a computer-intensive search for new blackbox models.
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Bayesian vector auto-regression model with Laplace errors applied to financial market data
Šindelář, Jan
The article presents alternative version of Bayesian vector auto-regression model with Laplace distributed innovations. Bayesian estimation in such model is more computationally demanding than estimation in a model with normally distributed innovations, but because of the heavier tails of Laplace distribution, it is more robust. In the article I try to present the way of proceeding with the estimation, obtaining a full posterior distribution of the parameters as a result. At the end an efficient algorithm is sketched, but this part of the research is still unfinished.
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Asimilace časoprostorového rozložení radionuklidů v časné fázi radiační nehody
Hofman, Radek ; Šmídl, Václav
Exploitation of the data assimilation methodology in the early phase of radiation accident is studied. When radioactive pollutants are released into the atmosphere, a radioactive plume is passing over the terrain. The released radioactive material causes pathway-specific irradiation which has detrimental effects on population health. In order to ensure efficiency of introduced countermeasures, it is necessary to predict spatial and temporal distribution of the aerial pollution and material already deposited on the ground. The predictions are made by the means of a numerical dispersion model with many inputs. Output of such a model is a prediction of radiation situation given in terms of radiological quantities. Exact values of the inputs are uncertain due to the stochastic nature of the dispersion, lack of accurate information, etc. Their subjective choice can introduce significant errors into the predictions and thus decrease the positive impact of the countermeasures.
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Parciální zapomínání. Nová metoda sledování časově proměnných parametrů
Dedecius, Kamil ; Nagy, Ivan ; Kárný, Miroslav ; Pavelková, Lenka
Tracking of slowly varying parameters is an important task in the theory of adaptive systems. Majority of prediction and control algorithms, employing regression models like autoregression model (AR), autoregression model with exogenous inputs (ARX), autoregression model with moving average (ARMA) etc., assume a carefully defined model structure and correctly estimated parameters. Problems arise, when the model parameters vary in time. The problems of slowly time-varying model parameters were given a thorough attention. The proposed partial forgetting method tries to solve this issue by a new approach.
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