All Questions
Tagged with ordinary-differential-equations statistics
24
questions with no upvoted or accepted answers
23
votes
1
answer
774
views
Kähler Geodesics
Consider the Kähler manifold in coordinates $(a,b)$ given by the complex Riemannian metric
$$\begin{pmatrix} \frac{1}{1-|a|^2}&\frac{1}{1-a\bar{b}}\\\frac{1}{1-\bar{a}b}&\frac{1}{1-|b|^2}\end{...
- 3,838
6
votes
0
answers
121
views
The statistical average of a continuous value: $\overline{O} = \int O(x) \rho(x) dx$, but coordinate invariant
I am trying to solve a Lagrange multiplier problem for the following equation
$$
L= - \int_{-\infty}^\infty \rho(x) \ln \frac{\rho(x)}{q(x)} dx + \alpha \left( 1- \int_{-\infty}^\infty \rho(x) dx \...
- 2,589
5
votes
0
answers
153
views
Clarification in a paper
This is regarding a clarification in page 384 of a paper published in Annals of Statistics by Amari.
In page no. 384, he defines $$R_i(t)=\frac{\partial}{\partial \theta_i} D_{\alpha}\{q(x,t),p(x,\...
- 706
1
vote
0
answers
60
views
Literature on Principal differential analysis
I'm currently dealing with topics in Functional Data Analysis (FDA), specifically Principal Differential Analysis (PDA). By the corresponding R package description, this is related to estimating a ...
- 61
1
vote
0
answers
19
views
How to obtain the parameter update for the multiclass classification (general loss and activation function)?
Consider the feature space $\mathcal{X}=\mathbb R^{d}$ and $\mathcal{Y}=\{1,...,c\}$ such that $c > 2$. We consider some activation function $\alpha: \mathbb R^{c} \to \mathbb R^{c}$ and out weight ...
- 998
1
vote
0
answers
84
views
SIR epidemic model with vital dynamics
I am reading the Wikipedia article on the SIR model with vital dynamics.
I am wondering about the birth and death rate. The birth rate seems to be constant, ie, it seems like the population in all 3 ...
- 697
1
vote
0
answers
46
views
How to minimize the difference between datasets
How do I go about matching a real-world dataset to a differential equation that describes it? In this case I have a real, tracked set of pendulum angles over time and self-made python script to ...
1
vote
0
answers
56
views
Pearson Type III probability distribution in an old math paper
The paper I'm getting this from can be found here. It's William Gosset's original derivation of the t-distribution.
I'm interested in the author's use on page 4 of the Pearson Type III distribution ...
- 177
1
vote
0
answers
62
views
Is there a variational problem that can provide the following class of variational derivative?
Suppose I have the variational problem
$$
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'',
$$
Is there a ...
- 5,317
1
vote
0
answers
79
views
Epidemic threshold on activity driven network
I am trying to understand the equations used in a paper
(https://www.nature.com/articles/srep00469.pdf)
Mainly I'm trying to understand how the epidemic thershold was calculated using the ...
- 111
1
vote
0
answers
158
views
Stable distribution law related to the Dickman function
It is known that if $U$ is a random variable with uniform distribution on the interval $(0,1]$, then the random variable defined as
$$
X\stackrel{d}{=} U^{1/\alpha}(1+X)
$$
where $\alpha>0$ ...
- 765
1
vote
0
answers
318
views
How to find variance of a CIR process
CIR process is defined as follows:
http://en.wikipedia.org/wiki/CIR_process
I get an SDE form for d_Vt/dt, but can't proceed further.
- 157
0
votes
0
answers
57
views
Time Series Analysis and Recurrence Relations/Differential Equations
I am beginning to watch a video playlist on the subject of time series analysis, and it seems pretty clear both from notation and some of the terminology (such as "characteristic equation") ...
- 1,922
0
votes
0
answers
31
views
Determining correlations of derivatives of a function given only measurements of that function
Cross-posted from statistics stackexchange:
Say we have a permanent-magnet DC motor that roughly obeys the system equation $\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma$, where $x(t)$ is the ...
- 1,378
0
votes
0
answers
64
views
Solving for the $k$, given the survival function for a newborn as: $S(t) = \frac{\left(121 - t\right)^{1/2}}{k},\; t\in\left(0, 121\right]$
I'm doing an assignment and I can't seem to solve the following question:
Given the survival function for a newborn as:
$$S(t) = \frac{\left(121 - t\right)^{1/2}}{k},\; t\in\left(0, 121\right].$$
What ...
- 19