All Questions
Tagged with estimators bayesian
34
questions
1
vote
0
answers
58
views
Is there a good review on complete class theorems?
I'm trying to get an overview of the various results called "complete class theorems" and their relatives, especially the ones that say things along the lines of "every admissible ...
- 425
1
vote
0
answers
42
views
Showing that the estimator of the log posterior used in stochastic gradient MCMC is unbiased
In the SGLD paper as well as in this paper it is claimed (paraphrasing) that
the following estimator:
$$\widetilde{U}(\theta) = -\dfrac{|\mathcal{S}|}{|\widetilde{\mathcal{S}}|} \sum_{{x}\in \...
- 33
1
vote
0
answers
33
views
Large samples property of bayes procedures
I was reading through Wasserman's All of Statistics and I came across this property in the Bayesian statistics chapter:
I think I don't really get what is supposed to be the intuition behind it, and ...
- 41
3
votes
1
answer
78
views
Best estimate of conditional probability P(C|A and B) from P(C|A) and P(C|B)?
Assume I have three events A, B, and C, and I know the following probabilities:
Scenario 1:
$P(A)$ and $P(B)$
$P(C|A)$ and $P(C|B)$
Scenario 2:
I additionally know $P(C)$.
I am looking for $P(C|A\...
- 131
1
vote
2
answers
207
views
Bayesian Learning: Finding the variance of noise
Suppose $x_i \sim N(10,4)$ - ie, the distribution is known.
There is a noisy signal $s_i \sim N(x_i, \sigma_e^2)$ and I want to estimate $\sigma_e$.
I see some pairs ($s_i, x_i$) but they are not '...
- 23
1
vote
0
answers
29
views
Reduce Variance of monte carlo estimator using guess of mean
Suppose you have a random variable $X$ and black-box function $f$. Suppose you also have prior estimates $m$ and $s$ of the mean and standard deviation of $f(X)$.
How can we use this prior information ...
- 111
7
votes
1
answer
197
views
Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Which estimator is better?
Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Compare the risks of the squared loss of two estimators of $p$:
$$
\hat{p}_1=\bar{X}, \, \hat{p}_2=\frac{n\bar{X}+\alpha}{\alpha+\beta+n}
$$...
- 747
6
votes
2
answers
107
views
Are bias and variance used as metrics to evaluate estimators in Bayesian inference?
Consider the parameter $\theta$, which is a deterministic unknown in the frequentist paradigm. Given a random variable $X \sim p_X(x ; \theta)$, consider the estimator $\Theta(X)$ of $\theta$, and the ...
- 5,120
9
votes
1
answer
421
views
Minimax estimator for geometric distribution
I'm trying to solve this problem:
Let $X$ be a single sample from Geo($p$) where $p ∈ (0, 1)$. Find a minimax estimator for $p$ under the loss $L(p, δ(x)) = (p−δ(x))^2/
p(1−p)$ .
I'm trying to put ...
- 231
5
votes
2
answers
350
views
What is Bayes estimator of $\theta$ when loss function is $L(\theta,a)=I(|\theta -a|>\delta)$?
Suppose $X$ given $\theta$ has pdf $f(x\mid \theta)=e^{-(x-\theta)}I(x>\theta)$ and there is a standard Cauchy prior on $\theta$. As part of an exercise, I am trying to find a Bayes estimator of $\...
- 11.5k
2
votes
1
answer
156
views
Find posterior distribution and Bayes estimator [duplicate]
Suppose that an observation $x \in (-1,1)$ comes from a sample model with a parameter $\theta$, with density function:
$$
f(x\mid\theta) = \begin{cases}
\theta\ &\text{if }\ -1 < x < 0\\
...
- 21
1
vote
1
answer
233
views
MMSE estimator with dirac delta prior pdf
The question is as follows, it's mainly part 3 that I was having problem with.
A discrete-valued parameter with the prior pdf $$p(x) =
> \sum_{i=1}^2p_i\delta(x-i)$$ is measured with the additive ...
- 131
5
votes
1
answer
67
views
Estimating the $\chi^2$-divergence with Monte Carlo: which distribution to sample from?
Notation: let the $\chi^2$-divergence between $p, q$ be defined as
$$\chi^2 (p||q) := \int \left ( \frac{p(x)}{q(x)} \right )^2 q(x)\mathrm{d}x -1 = \int \frac{p(x)}{q(x)} p(x)\mathrm{d}x - 1. $$
...
- 2,480
0
votes
0
answers
107
views
Find Bayesian estimator for $e^{\theta}$
Given $\{Y_i\}_n\sim U(\theta-1,\theta+1)$ and prior distribution $\theta\sim U(a,b),1\leq a<b$
is the posterior distribution conjugate? Find the absolute error estimator for $e^{\theta}$ and ...
- 109
2
votes
3
answers
112
views
Robustness of MAP estimate
In Bayesian inference, we have a dataset $x$ and assumed to come from a known parameterized distribution with unknown parameters $\theta$. We then seek to maximize the posterior $P(\theta|x)$ in order ...
- 399