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- W2912493849 abstract "Single particle tracking (SPT) is a class of experimental techniques and mathematical algorithms for following the motion of very small particles moving inside living cells, including viruses, proteins, and strands of RNA, to mention a few. There are several models in the literature to describe the motion of such small particles. Amongst the most common ones is the so-called simple diffusion model, which corresponds to a random walk with noisy observations. Maximum Likelihood (ML) is an estimation method to determine the value of parameters in a model. It has been utilised in previous works in the context of SPT to estimate key parameters in motion models. However, these works pose the limitation that the parameters are considered time-invariant. An early attempt to include time-varying parameters (TVP) is SPT considers a probability of change in a jump Markov model, however, it does not allow to continuously track TVP, requiring the inclusion of probabilities that might have no physical meaning. Here, the estimation problem of TVP is posed as a local time-invariant likelihood function, which is optimised (locally) to obtain parameters within a window of nominated span. This local likelihood function is centred at time t. To develop the idea, we introduce a weight K((u(i) - t)/h), where u(i) is the data inside the window, h is the window size. and t is a chosen point inside the window. The estimation algorithm continues when the time points are increased by one unit and terminates when the last data point is included in the window. Results of the estimation considering time-varying diffusion have been carried out with different window lengths. Our estimation algorithm is capable of producing a TVP for this simple motion model, having, as expected, less variance when considering longer windows." @default.
- W2912493849 created "2019-02-21" @default.
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- W2912493849 date "2019-02-01" @default.
- W2912493849 modified "2023-09-30" @default.
- W2912493849 title "Estimation of Time-Varying Single Particle Tracking Models using Local Likelihood" @default.
- W2912493849 doi "https://doi.org/10.1016/j.bpj.2018.11.3059" @default.
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