Questions tagged [beta-distribution]
A two-parameter family of univariate distributions defined on the interval $[0,1]$.
406
questions
0
votes
0answers
9 views
Tuning the “strength” of updates to a posterior distribution for conjugates
I'm asking this question as a sanity check- I am not a statistician or research scientist, and just am doing a gut check on a model I am building. I want to quantify uncertainty of a specific metric ...
0
votes
0answers
39 views
Multi-armed bandit where you must pull N pulls in T timesteps
Multi-armed bandit where you must pull N pulls in T timesteps
Consider the beta-Bernoulli multi-armed bandit, with the following wrinkle:
We have a total of $T$ time steps.
We must pull $N$ pulls ...
1
vote
1answer
66 views
Fitting Beta Distributions to Data
I am trying to reproduce some beta distribution parameters found in this published paper. I have two data sets, y1 and y2, that ...
1
vote
0answers
10 views
rate of convergence acceptance-rejection vs inverse transform sampling
Does the acceptance-rejection method or inverse transform sampling converge to the mean quicker say for beta distribution, assuming acceptance-rejection has suitable envelope function? is there a way ...
0
votes
1answer
75 views
Bayesian A/B testing with parameters other than success rate
If I have certain number of clicks and conversions for a group of ads, I can do Bayesian A/B testing following this method http://ucanalytics.com/blogs/bayesian-statistics-to-improve-ab-testing-...
0
votes
0answers
16 views
LDA: weight distributions of inferred documents
I have trained a two-topic Latent Dirichlet Allocation (LDA) model on a corpus and I am now inferring on a test corpus (the nature of the corpus is irrelevant). During inference, for each new document ...
4
votes
1answer
69 views
Distribution Reference $\gamma x^{\gamma-1}$
I have been unable to find resources regarding the family of distributions with pdf
$$ f_\gamma(x) = \begin{cases}
\gamma x^{\gamma-1}, & \text{if } 0 \leq x \leq 1 \\
0, & \text{...
2
votes
1answer
52 views
From beta distribution to Dirichlet: Estimation of the concentrantion parameters
Searching at least 3 hours about the connection between beta distribution and dirichlet. My problem is:
I have a collection of random variables $X_i \sim Beta(a_i, b_i)$. The parameters $a_i$ and $...
0
votes
0answers
24 views
How to transform Beta distribution of second kind into Beta distribution of first kind?
!
I tried to solve it in a way but I can't complete in as I don't get any idea how to integrate the Beta kind two integrand within a finite boundary.
0
votes
0answers
23 views
Uniform conjugate prior for a Beta distribution
Given
$$
\pi \sim \text{Beta}(\alpha, \beta)
$$
I'd like to place a prior on $\alpha$ and $\beta$. The "trick" mentioned in this post and this post seems to be to recognize that since
$$
\begin{...
1
vote
0answers
66 views
Evaluating model fit for glmmTMB with beta distribution
I am looking for a way to evaluate model fit (e.g. R2, %deviance explained) for the following model:
m1<-glmmTMB(AUC_indep~woody+dispersal+log_densitys+log_seedwts+I(log_seedwts^2)+(1|modeltype), ...
4
votes
3answers
183 views
Proving transformations of two independent chi-squared random variables is equivalent to a Beta distribution
I came across the following in some old class notes of mine:
if $\chi_{v_{1}}^{2}$ is independent of $\chi_{v_{2}}^{2}$ then
$\frac{\chi_{v_{1}}^{2}}{\chi_{v_{1}}^{2}+\chi_{v_{2}}^{2}}\backsim
...
2
votes
1answer
55 views
Moment Generating Function of Beta ( Taylor series)
Suppose X is a random variable with a Beta ( a =$\frac{1}{2}$ , b=1) distribution and
x in (0,1)
Then the moment generating function is calculated as below
$ M_X(t) $ = $\mathbb{E}[e^{tX}]$ =$ \...
0
votes
0answers
41 views
Logistic regression - binary to continuous - how to interpret?
Given data with a binary outcome, i.e.: $0$ = no event, $1$ = event
which can be modeled with logistic regression, how then do we understand the following logic:
...
0
votes
0answers
52 views
R package for meta-analysis of beta-distributed data
I am conducting a meta-analysis, and my effect sizes are proportions, with a credible interval for weighing. I think I should assume a beta-distribution, but I do not know which package to use. This ...
1
vote
1answer
44 views
Expectation of Sufficient Statistic for Beta Distribution
I am looking at question 1b of the following notes: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1/asst1.pdf
In 1a, I have shown that the Beta distribution has a density that can be written in the ...
0
votes
0answers
16 views
0
votes
1answer
66 views
Uber's Pyro less accurate than expected on toy example
Trying to understand the pyro example here:
https://pyro.ai/examples/svi_part_i.html
which starts with a Beta(10,10) prior, adds 10 Bernoulli likelihood datapoints with a 6,4 split. The analytic ...
1
vote
0answers
98 views
MLE for Beta distribution, with $\beta$ = 3
I'm trying to calculate the Maximum-Likelihood Estimator for $\alpha$, using the beta distribution with $\beta = 3$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
1
vote
1answer
77 views
If $X\sim\text{Beta}(\theta,1)$, obtain the confidence interval of $100(1-\alpha)\%$ based on the asymptotic distribution of the score function
Let $X_{1},X_{2},\ldots,X_{n}$ be a random sample whose distribution is given by $\text{Beta}(\theta,1)$. Obtain the approximate confidence interval of $100(1-\alpha)\%$ based on the asymptotic ...
0
votes
0answers
32 views
Is fair to compare Dirichlet to a Multivariate Beta regression?
I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions.
I am trying to investigate the effect of a categorical variable (cl) to ...
1
vote
1answer
27 views
Valid highly informative prior for proportion
I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a ...
2
votes
1answer
54 views
Squared internally studentized residual over $n-p$ is Beta distributed
Assume a regression model $y = X \beta + \varepsilon$ with $n$ observations and $p$ parameters. Let $r_i$ be the $i$-th internally studentized residual:
$$r_i = \frac{e_i}{\sqrt{\hat{\sigma} (1 -h_{ii}...
0
votes
0answers
21 views
Model reputation with beta distribution
I am trying to develop a reputation score in which the reputation is calculated by the ratings that buyers give to sellers. What i am trying is to replicate a paper very well known http://faculty.neu....
2
votes
1answer
63 views
Efficiently Computing The Beta CDF [duplicate]
I am using numba to JIT compile some looped python functions as part of a larger application. Ideally, everything will run in numba's "no python" mode, such that the loop can be parallelised.
One of ...
1
vote
1answer
49 views
Understanding the Bayesian question [closed]
I have a Bayesian question here:
In a drug experiment, patients with a chronic condition are asked to choose between two drugs, C (control), and T (new treatment). (You may assume for the purpose ...
0
votes
0answers
39 views
What is support of beta distribution? [duplicate]
I do know that the probability density function of beta distribution is
$$
\frac{x^{\alpha-1}(1-x)^{\beta-1}} {\displaystyle \mathrm {B}(\alpha,\beta)}\!
$$
where
$$
{\displaystyle \mathrm {B} (\...
1
vote
0answers
53 views
Can't understand the Beta distribution as described in this paper
I'm reading through the following paper (1). On page 2, section 2.1, there's a description of the selection of a beta distribution used:
Since both the choice of s and the strategy for handling the
...
1
vote
0answers
73 views
Distribution of dot products of two random independent unit vectors in $D$ dimensions
Duplicate of the stats stack exchange question here; however, I need some help with some of the steps in the accepted answer.
A uniform distribution on the unit sphere $\mathbb{S}^{D-1}$ is
...
0
votes
1answer
48 views
Proportion/Rate data and zero-inflation (two counts)
I have an experimental dataset which makes use of two counts. Using vague terms, we are studying animals as they become behaviourally inactive and then apply a stimulus once an hour. One of the counts ...
1
vote
0answers
15 views
How to relate beta CDF to student-t CDF? [duplicate]
We can relate the student-t and beta distributions as such:
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution:
$$\frac{\nu}{\nu + X^2} \...
2
votes
2answers
35 views
Interpretation very small standardized coefficient beta
In one of my studies I have results similar to the below:
β=-0.0007 (95% CI: -0.0009, -0.0002), p=0.01
Since β is so small (but also the Confidence Interval (CI)), is this result still meaningful?
...
0
votes
0answers
19 views
In a manuscript, is an incomplete beta function a useful simplification of a sum, if the argument ends up negative?
I'm working on a manuscript which I intend to submit to a statistics journal. I have a sum which I "simplify" to the regularized incomplete beta function $I_{-t}(a,b)$, where $t$ is a positive real ...
0
votes
0answers
9 views
Can I improve an estimate of a coin-flip probability from a single trial using an imperfect oracle?
I have the following generative model:
I have a unknown random variable $S\in[0,1]$ and samples $s_i \sim S$. I do not observe $s_i$ directly, but instead an imperfect oracle $q_i$, which might or ...
0
votes
0answers
13 views
Appropriate statistical test for continuos bounded r.v
I have a number of continuous random variables bounded in the domain [0,b] and I need to perform a statistical test to check whether their average is different from ...
4
votes
0answers
40 views
Beta-binomial distribution for scaled and translated Beta
Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
3
votes
1answer
62 views
Why p-values are not significant even though AIC values improved a lot in model selection using GAM mix modelling and beta regression
Dear StatExchange community,
I am studying disease progression in plant leaves and I am trying to estimate differences between a wild-type and a mutant plant. To achieve this I am using the ...
2
votes
0answers
56 views
In a bivariate normal sample, why is the squared sample correlation Beta distributed?
If $(X_i,Y_i), i = 1, \dots, n$ are independently bivariate normal distributed, with mean $(\mu_x , \mu_y)$ and variances $(\sigma_x^2, \sigma^2_y)$ and correlation coefficient $\rho = 0$.
Denote $T =...
0
votes
1answer
123 views
Simulate from a mixture of two beta distribution [closed]
I have this distribution :
$X \sim 0.75\mathcal{B}e(\alpha_{X_1}=1,\beta_{X_1}=3)+0.25\mathcal{B}e(\alpha_{X_2}=5,\beta_{X_2}=1.75)$
where the density function is given from this function:
...
1
vote
1answer
115 views
Mean of a truncated non-standard beta distribution
I have a non-standard beta distribution in the interval [-0.02 , 0.005] (as opposed to [0,1]).
I know its mean and variance (and thus α and β).
I want to calculate the mean of its truncation to [0 , ...
0
votes
2answers
30 views
All positive Beta exponents in a binomial logistic regression
I'm running a regression in which the predictor is a categorical measure of living arrangement (1=two parent household, 2 = single parent, etc). There are 8 total categories in this variable. I'm ...
1
vote
0answers
30 views
Question regarding FamaMcBeth regression
I'm new here and hope you can help me with three questions I'm having in regard to the FamaMcBeth regression methodology.
What is the advantage of using firm specific returns instead of an aggregate ...
0
votes
0answers
118 views
Change point detection in beta distribution
If the outcomes of agent is modeled as a Bernoulli distribution with success probability θ ∈ [0, 1]. Where α is number of successful tasks that agent execute, and β is number of unsuccessful tasks ...
0
votes
0answers
27 views
Power Analysis with Noncentral F distribution
I'm looking to replicate a power analysis for binary data using an MRMC analysis (details found here). The data looks like this, where Score is a binary variable.
...
1
vote
1answer
58 views
Probability that one random variable using the Beta Distribution being greater than another, bounded intervals
I am doing some practice problems to prepare for my statistics exam, and I just want to know if my reasoning is correct on one problem, and if not, I want to know how I should reason through this. The ...
0
votes
2answers
96 views
Independence of Beta ratios of Gamma variates
If $X= x_1/(x_1+x_2+x_3)$ and $Y= x_2/(x_1+x_2+x_3)$ where $x_1, x_2, x_3$ are independent $\chi^2$-distributed random variables with d.f. $-n_1,n_2, n_3$ respectively. Are $X$ and $Y$ independent?
I ...
0
votes
1answer
50 views
How to justify using Beta distribution as a prior distribution in the following problem
Let $\theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes ...
0
votes
2answers
32 views
Beta distribution and normalization [duplicate]
Here in the 4 pictures in the last answer, is the vertical axe
the probability? I.e. it seems to me that it is somewhat unnormalized : it has the value 2 in the 2nd picture and 3 in the 3rd picture. ...
0
votes
0answers
42 views
Self Study - How does $\alpha$ and $\beta$ correspond to mean and variance of a beta distribution? [duplicate]
I am trying to figure out how to provide $\alpha$ and $\beta$ in terms of $\mu$ and $\sigma$ in a beta distribution.
$\mu$ is given as $\mu = \frac{\alpha}{\alpha + \beta} $
$\sigma$ is given as $\...
0
votes
1answer
12 views
Analysis in a beta simulation
I did a simulation where shape1=1 and shape2=2, for n=10, n=100 and n=1000, the following is:
...
