All Questions
Tagged with ordinary-differential-equations statistics
50
questions
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71
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Estimating parameters of SIR model and problem with real-life data
I tried to make an SIR model based on real-world data. But, I ran into a snag when I'm trying to estimate the parameters of $\beta$ and $\gamma$. With equations:
$$
\begin{cases}
\frac{dS(t)}...
0
votes
0
answers
34
views
How to distinguish chaos from inaccurate?
If you have a system of ODE that gives rise to a chaotic system, you can easily find that the solutions either explicit or implicit are drastically different from real-world results. Yet, this does ...
1
vote
0
answers
84
views
SIR epidemic model with vital dynamics
I am reading the Wikipedia article on the SIR model with vital dynamics.
I am wondering about the birth and death rate. The birth rate seems to be constant, ie, it seems like the population in all 3 ...
- 697
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votes
1
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312
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Write down the backward equations for $P_{12}$ and $P_{21}$ and use the symmetry of Q to solve these equations.
Hint: Whenever confronted with an ordinary differential equation of the form x′(t) = ax(t)+b(t), it might be beneficial to consider the function y(t) = $e^{−at}x(t)$.
$$Q = \left[ \begin{matrix}
...
- 253
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votes
1
answer
22
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Standard Theory of Linear Difference Equations, Power Function
I'm reading this paper and have a question about the math done on page 4.
We go from having
$$\lambda^{T_0} = p \lambda^{T_{0 + 1}} + q\lambda^{T_{0 - 1}}$$ to
$$p \lambda^2 - \lambda + q = 0$$
...
- 37
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0
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94
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Validity of Coronavirus Curves - Are we using the correct baseline?
For most analysis (models), are we inaccurately assuming that the newly reported cases are the number of actual new cases? Could this exponentially growing number just be a function of the way testing ...
- 17
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votes
1
answer
41
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Logit regression change in $x$
I've been reviewing the logit regression equation to predict the probability of a response variable given $X=x$ as per below and I can't understand how a per unit change in the predictor is equal to $...
- 478
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117
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Understanding the stochastic SIR model
I am learning about what it means for a model to be Stochastic. To do this, I am examining the stochastic SIR model found here: https://en.wikipedia.org/wiki/Gillespie_algorithm (scroll down to the ...
1
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0
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46
views
How to minimize the difference between datasets
How do I go about matching a real-world dataset to a differential equation that describes it? In this case I have a real, tracked set of pendulum angles over time and self-made python script to ...
1
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0
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56
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Pearson Type III probability distribution in an old math paper
The paper I'm getting this from can be found here. It's William Gosset's original derivation of the t-distribution.
I'm interested in the author's use on page 4 of the Pearson Type III distribution ...
- 177
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72
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Manifold assumption when visualizing high dimensional dynamical systems
I come from a background in statistics, where we often visualize high dimensional data sets by projecting them onto lower dimensional subspaces. The most common example of this approach is Principal ...
- 2,531
1
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62
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Is there a variational problem that can provide the following class of variational derivative?
Suppose I have the variational problem
$$
E(y) = \frac{1}{2}\int_{a}^{b} y^2 + \alpha y'^2dx
$$
Variational derivative will provide
$$
\frac{\delta E}{ \delta y} = y -\alpha y'',
$$
Is there a ...
- 5,317
1
vote
0
answers
79
views
Epidemic threshold on activity driven network
I am trying to understand the equations used in a paper
(https://www.nature.com/articles/srep00469.pdf)
Mainly I'm trying to understand how the epidemic thershold was calculated using the ...
- 111
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0
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119
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Branching annihilating random walks and mean field theory
I am attempting a project on modelling branching morphogenesis, but am getting very confused looking at the literature.
On the one hand, the structure formation itself is clearly best described by a ...
- 3,197
2
votes
1
answer
763
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Linear regression with 2 unknown intercepts
The linear equation $y=2.2+0.6(x+1.2)$ has the slope $0.6$, the given y-intercept $2.2$ and x-intercept $-1.2$. The table is
$$
\begin{array}{c|lcr}
x & y \\
\hline
1 & 3.52 \\
2 & 4.12 ...
- 131