All Questions
7 questions
2
votes
0
answers
87
views
A complex problem involving densities (likelihood functions) and optimization
Consider the following autoregressive process with normal errors:
\begin{equation}\label{7YlUV4i8nuO}\tag{I}
y_t = \phi y_{t-1}+ u_t, \quad u_t \overset{iid}{\sim} N(0,\sigma^2)
\end{equation}
We ...
- 13
4
votes
1
answer
287
views
Local maxima of the sum of Gaussian functions in *multiple dimensions* are always strict local maxima - prove/disprove/prove conditionally?
This is a follow up of the question in one dimension, that asked to show that the all the maxima of the sum of Gaussian
$$f_n(x):= \sum_{i=1}^{n}e^{-(x-x_i)^2}, x_1 < x_2 < \dots < x_n$$
are ...
- 1,467
1
vote
0
answers
73
views
Reduce the asymptotic variance for a class of Metropolis-Hasting estimates
I'm running the Metropolis-Hastings algorithm with state space $E$, target distribution $\mu=p\lambda$ and proposal kernel $Q$ to estimate $\mu(hf)$ for a fixed function $f:E\to[0,\infty)^3$ and a ...
- 167
2
votes
0
answers
101
views
Best describing a stochastic process in terms of others
Intuitive Question
Suppose I'm given a set of $k$ time-series $\{X_t^1,\dots X_t^k\}$. Is there a way to determine how much of each series is dependent on the others.
Formal Question
More ...
- 5,405
1
vote
0
answers
64
views
Posterior consistency of non linear model
This is possibly a reference request. Let $G$ : $\mathbb{R}^p \to \mathbb{R}^q$ be a continuous injective/bijective function. Let $\mu$(we may also assume this to be a non degenerate Gaussian) be ...
- 157
0
votes
0
answers
444
views
How to decide a value of learning rate for Stochastic Gradient Descent?
I'd like to know how to decide a value of learning rate for Stochastic Gradient Descent (SGD), such as $\eta$ on the following parameter update iteration equation,
$w_{i+1} = w_i + -\eta \nabla E_n(...
4
votes
0
answers
213
views
Optimization problem involving Multivariate Normal
I use $\phi(t)$ to describe the standard normal distribution density and $\Phi(t)$ as the normal distribution CDF and would like to prove that for all
$n\geq3$, the function:
$$h(\mu_{1},\ldots,\...
- 41