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Questions tagged [nonlinear-dynamical-system]

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Representation of Hessian in Augmented State-Space Filtering Problems

Question Let $z_t := (x_t, x_{t-1}, x_t^2, x_{t-1}x_t,x_{t-1}x_t,x_{t-1}^2)$, and $R(x_t) := \sum_{(i,j) \in \{\{0,1,2,3,4\} \otimes \{0,1,2,3,4\} : i+j \le 4\}} w_{i,j} x_t^i x_{t-1}^j$, so $R(\cdot)$...
hipHopMetropolisHastings's user avatar
1 vote
1 answer
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Research field of timeseries with unpaired measurements?

I have measurements of cells' gene expression at different time points (t0, t1, t2, ...). Cells die when measured and therefore all measurements are from different samples, i.e. I do not observe any ...
N8_Coder's user avatar
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1 vote
1 answer
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Parameterization of Negative Binomial for Dynamical System Model Calibration/Fitting

I'm studying about the applications of bayesian inference to fitting dynamical systems to observations. So the model itself is a deterministic SIR model: $$ f(R_0,D_{inf})=\begin{cases} \frac{dS}{t}&...
Derf's user avatar
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Efficiently sample from a limit set given a differential equation?

Given a dynamical system of many variables, described by an ordinary differential equation, is there some way to use machine learning to efficiently sample from the limit set (or maybe more accurately ...
HelloGoodbye's user avatar
3 votes
1 answer
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Autocorrelation function of the logistic map $x_{n+1}=4x_n(1-x_n)$

Is there a proof that for the sequence $x_{n+1}=4x_n(1-x_n)$, the lag-$m$ autocorrelation for $m=1,2$ and so on, is zero if you start with a random seed $x_0$, or say $x_0=\frac{1}{3}$? It is defined ...
Vincent Granville's user avatar
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Parameters in mlemodel in statsmodel

I am trying to run a TVP-VAR on statsmodel for a big data, but seems to run in a problem when I am trying to validate the vector matrix and the vector shape. Particularly, in the start and the update ...
HelenA's user avatar
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2 votes
1 answer
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What is the difference between these two observational update models in an information filter?

The Information Filter is defined as the mathematical inverse of the Kalman filter. As defined in this Wikipedia article, the observation update of the Information Matrix is defined as $$y_{k|k} = y_{...
Prometheus2508's user avatar
1 vote
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TVP-VAR fails statespace.MLEModel

I am trying to run a TVP-VAR for a panel in python using statsmodels. I am using the site example, trying to adopt it in my model. Data are from 1945-2020 for 50 countries Furthermore, I am getting ...
David K's user avatar
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Meaning of a scaling constant in a well-calibrated model

I'm reading this paper on safe model-based reinforcement learning. Assumption 2 in this paper states: Let $\mu_n(\cdot)$ and $\Sigma_n(\cdot)$ denote the posterior mean and covariance matrix ...
alexanderd5398's user avatar
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Do stochastic chaotic systems decorrelate with time?

Assume I have a dynamical system with additive process noise of the form $$\mathbf{x}_{t} = \mathbf{F}\left(\mathbf{x_{t-1}}\right) + \mathbf{\epsilon}$$ where $\mathbf{x}_{t}$ is the state at time $t$...
J.Galt's user avatar
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1 answer
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Time Varying Coefficients vs Rolling Estimation

What are the practical differences for forecasting from fitting a model with time varying coefficients vs. estimating a model with fixed parameters over rolling windows? Intuitively it seems that ...
mgilbert's user avatar
  • 600
1 vote
1 answer
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Kalman Filter and Monte Carlo

What is the consequence on the uncertainty of our estimate when applying the standard kalman filter to nonlinear systems? If we are unaware of the functional form of these non linear systems how do ...
Kaykhusraw's user avatar
3 votes
1 answer
257 views

Chaos theory, equation-free modeling and non-parametric statistics

Being interested in complex systems and trying to get a beginner's understanding of the field, today I ran across this interesting article in Quanta Magazine on chaos theory and equation-free modeling....
Aleksandr Blekh's user avatar