Tagged Questions
0
votes
0answers
11 views
Bayesian Parameter Estimation Doubt
I was going through a pattern recognition book and in the chapter of Bayesian Parameter Estimation I came across this formula. I cannot understand how the 2nd line is derived from the first line. ...
0
votes
0answers
15 views
Naive Bayesian Classifier for Object with Variable attributes
Let say our objects are connected graphs. They are to be classified into two categories, say A and B. However, for our purpose attributes for each graph is equal to the number of vertex of the graph ...
1
vote
0answers
50 views
Kolmogorov's paper defining Bayesian sufficiency
I'm looking for a translation to either English, French or German of Kolmogorov's Russian paper
Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi de Gauss. Bull. Acad. Sci. ...
0
votes
0answers
20 views
Dynamic Linear Model - Joint distribution of observations and states
In my DLM, observations are denoted by $Y_t $ and the state vector by $ \theta_t$.
We assume we're in a closed system so that we can only learn about the future through past observations.
Our first ...
1
vote
1answer
38 views
Bayes theorem for calculation with personal probabilities
I'm completely stuck on some homework I have and can't figure it out.
The task is to calculate the probability of a bus being late conditional on the weather being snowy and bus driver being ...
1
vote
0answers
29 views
Posterior density and posterior moments
I would be very grateful to get some help with the following problem.
Let $X_1, ..., X_n$ be independent and uniformly distributed on the interval $(0,\theta)$ with $\theta>0$.
Let the prior ...
1
vote
1answer
34 views
Bayesian learning
Imagine we assume there are two different types of coins:
Coin A: a fair coin, p(heads) = 0.5.
Coin B: biased to heads at p(heads)=0.7.
We then want to learn from samples which coin we are ...
0
votes
0answers
30 views
Hypothesis Testing Bayesian Way
I'm having trouble with the following problem:
Suppose a machine is composed of 2 components (1 and 2, independent from each other). Each component has a exponential failure probability distribution ...
0
votes
2answers
81 views
Find the posterior distribution of $\theta$
I'm having trouble solving the following problem:
Find the posterior distribution of $\theta | x$. Suppose $x$ is a random variable with distribution $f(x) = \theta x^{\theta - 1}$, you observe a ...
1
vote
0answers
13 views
Find posterior mean
I have this problem,
Let $X\sim U(0,\theta)$ with $\theta>0$. Assume a signal random sample $X$, the squared error loss, and the prior $\pi(\theta) = \exp(1)$ i.e.
$\pi(\theta) = \theta ...
1
vote
1answer
16 views
Find the posterior distribution and posterior risk
I have this problem,
Let $X\sim U(0,\theta)$ with $\theta>0$. Assume a signal random sample $X$, the squared error loss, and the prior $\pi(\theta) = \exp(1)$ i.e.
$\pi(\theta) = \theta ...
0
votes
0answers
12 views
Constant DLM - Showing stationarity
Consider the CDLM
$ Y_t =\theta_t + v_t $
$\theta_t =g\theta_{t-1} + \omega_t$
Where $v_t $ and $\omega_t $ are all independent of each other and $v_t$ ~ $N (0,V)$ and $\omega_t $~$ N(0,W)$
(a) ...
1
vote
0answers
5 views
Conditional distribution for a label given a scalar feature
I am trying to create a simple simulation setup for classifiers on toy data. Each data point can has a scalar feature $X$, which is uniformly distributed between -1 and 1. Depending on the feature, ...
2
votes
1answer
45 views
Is there a formal explanation of the concept of “improper prior” in Bayesian statistics?
The Bayesian concept of "improper prior" seems to be surrounded with magic. Even formal, Bayesian-oriented books, such as Schervish's "Theory of Statistics", treat it with the heuristic hand waving ...
1
vote
0answers
82 views
Bayesian posterior with integrals over normal densities
Realizations from normal distributions with known precision are used to estimate the mean, but the realizations are not always precisely observed. Instead, only a range of the realization is observed. ...
1
vote
1answer
31 views
Independent random variables considering expression
Having $x, y, z, c \in \mathbb{R}$, is it valid to say:
$c \propto g(x, z) h(y, z)$
The context here is to say whether or not the random variables $X$ and $Y$ are independent given the value of $Z$.
...
0
votes
0answers
45 views
Does $\hat{x}$ always mean normalized version of a vector $x$?
From this article:
"...a maximum-a-posteriori
$(MAP_{x,k}^{\,\,\,\,\,1})$ estimation, seeking a pair $(\hat{x}, \hat{k})$ maximizing:
$$p(x, k\mid y) \propto p(y|x, k)p(x)p(k).$$
Are ...
0
votes
0answers
90 views
bayesian estimation on the poisson distribution
Suppose X~Poisson($\lambda$) and $\lambda$~Gamma($\alpha,\beta$). Find the posterior distribution and the Bayesian estimator of $\lambda$.
Thus the prior distribution is: ...
2
votes
1answer
38 views
Bayesian Problem… I think
Let X be the number of coin tosses until heads is obtained. Without knowing that the coin is fair, I assume that the probability of heads is uniformly distributed.
How would I find the distribution ...
2
votes
2answers
134 views
Statistics: Finding posterior distribution given prior distribution & R.Vs distribution
I'm now learning Bayesian inference.This is one of the questions I'm doing.
Suppose we have R.V.s $X_1,X_2,\ldots,X_n$ each have an Exponential distribution with parameter $\theta$.
and prior for ...
1
vote
1answer
93 views
How would you approach this problem on the Bayes theorem?
I've been reading a book on Statistics and I could COMPLETELY understand all of its text. It basically explained the bayes theorem and what priors were, what posteriors were etc. But then in the ...
1
vote
1answer
82 views
Bayes Estimator
Let $X_{1},...,X_{n}$ be a random sample of size n from the continuous distribution with pdf:
$f_{X}(x|\alpha,\beta) = ...
1
vote
1answer
97 views
Bayes' Rules: The probability of at least one event occurring?
There is a 60 percent chance that the event $A$ will occur. If $A$ does not occur, then
there is a 10 percent chance that $B$ will occur.
(a) What is the probability that at least one of the ...
0
votes
1answer
44 views
$u$~$N(0,A)$ and z$|u$~$N(u,1)$ how to show that $u|z$~$N(Bz,B)$ where $B=A/(A+1)$?
$u$~$N(0,A)$ and $z|u$~$N(u,1)$ how to show that $u|z$~$N(Bz,B)$ where $B=A/(A+1)$ ?
4
votes
1answer
59 views
Bayesian inference
I'm a bit confused with arranging the Bayes equation to update probability. Say, I have the following data:
$P(\text{blue birds in the whole study area}) = 0.16$;
$P(\text{all except blue colored ...
0
votes
0answers
71 views
What does the notation O(A1:A2) mean in statistic? [closed]
I am reading this wiki, but I forget what does the notation means.
It has been a while since I read math related stuff :P
1
vote
2answers
85 views
Conjugate prior for noisy Bernoulli
It is well known that the Beta distribution serves as a conjugate prior for the Bernoulli distribution, and that when you observe a Bernouilli random variable, you need only increment the appropriate ...
0
votes
1answer
23 views
How to re-parametrize posterior function?
How can I write the unnormalized posterior
$ f(p_1, p_2 | Y) = (z_1-1)*log(p_1) + (n_1-z_1-1)*log(1-p_1) + (z_2-1)*log(p_2) + (n_2-z_2-1)*log(1-p_2) $
in terms of the log odds-ratio $\alpha$ and the ...
2
votes
1answer
52 views
Questions on Bayesian analysis of an opinion poll (an example in a book)
I'm sorry in advance for rather long questions. This is an example in "Bayesian logical data analysis for physical sciences" by P. C. Gregory and I have some questions about the example.
In a poll ...
0
votes
0answers
20 views
Theory of Bayesian Estimation
I'm starting with Bayesian analysis, and I've been trying to understand how to write down a Bayesian model. Let's suppose a one-way random effects ANOVA model:
$y_{ij}|\mu_i, \sigma^2 \sim N(\mu_i, ...
0
votes
0answers
33 views
Conditional probabilities given certain values
suppose that the chance that someone is happy after visiting the bathroom is 0.05.
If he has not visited the bathroom the chance that he is happy is 0.01.
If he goes to the bathroom there is a 0.7 ...
0
votes
0answers
37 views
Random Sampling around a Random Sample
Imagine I want to randomly sample how fast a driver is going on a highway. And for this purpose, let's assume that the distribution is normal with the mean as the speed limit. Now if I take a sample, ...
2
votes
1answer
111 views
A confusing excersice about Bayes' rule
The following is from a textbook one bayesian stats. that I can't understand some deduction. It is relevant about multiple parameters to be estimated.
The jth observation in the ith group is denoted ...
1
vote
1answer
67 views
trump cards question from Bayesian stats book
I'm looking at this problem in a bayesian stats book:
A card game is played with 52 cards divided equally between 4 players, North, South, East and West, all arrangements equally likely. 13 of the ...
2
votes
1answer
118 views
I am confused about Bayes' rule in MCMC
Bayes' rule appears to bevery simple at first sight, but when studied deeply I find it is difficult and confusing, especially in MCMC applications when multiple parameters need to be estimated.
For ...
2
votes
1answer
276 views
How do I calculate the aposteriori probability distribution for someone's answer to a poll being an approval?
Imagine I'm polling a random sample from the population and it asks them if they approve of the President or not. I also ask them some categorical demographic questions (age-bracket, race, gender, ...
3
votes
2answers
146 views
Differentiating the posterior distribution function
I am learning about Bayesian statistics and I'm currently doing loss functions. Let $f(\theta | \mathbf{x} ) $ be a posterior pdf . Let $F(\theta | \mathbf{x} ) $ be the associated distribution ...
0
votes
2answers
39 views
Vector Autoregression Algebra, $M_t$, $L$
In the paper here
http://www.ems.bbk.ac.uk/for_students/bsc_FinEcon/fin_economEMEC007U/VAR.pdf
It shows VAR(p) model as
$$
W_t = A_1W_{t-1} + A_2W_{t-2} + ... + A_pW_{t-p} + \epsilon_t
$$
But ...
