Questions tagged [bayesian]
Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.
8,144
questions
-3
votes
0
answers
111
views
Posterior Predictive Distibution [closed]
How do we actually calculate (what are the operations that need to be done) the posterior predictive given a vector of observations; can we do away with the assumption of independence?
Let's say we ...
0
votes
1
answer
19
views
Independence of processes vs independence of underlying parameters
I am interested in applying the approach in this paper by Laurent and Legrand:
A Bayesian Framework for the Ratio of Two Poisson Rates in the Context of Vaccine Efficacy Trials
The context of my ...
- 1,331
0
votes
0
answers
15
views
Importance Sampling covariance between numerator and denominator of the estimator
The (self-normalized) importance sampling estimator is
$$
\hat{H} = \frac{\displaystyle \frac{1}{N} \sum_{i=1}^N h(X_i) \frac{\tilde{p}(X_i)}{\tilde{q}(X_i)}}{\displaystyle \frac{1}{N}\sum_{i=1}^N \...
- 2,096
2
votes
1
answer
243
views
Relatively fast approximations to the marginal likelihood?
Let $\theta\in{\mathbb R}^d$ be a multidimensional parameters, where $d$ can be large (e.g. $d=100$ or more). What approximations can I use for the marginal likelihood:
$$\int f(x\mid \theta)\pi(\...
CommunityBot
- 1
0
votes
2
answers
42
views
Regarding samples gotten from MCMC
In one article explaining MCMC, I once read the following statement.
The idea of sampling methods is the following. Let’s assume first
that we have a way (MCMC) to draw samples from a probability
...
0
votes
0
answers
13
views
How can I compare model performance across datasets of varying sizes?
I have a person wearing 2 sensors. I create two models, one using Sensor-1 and other using Sensor-2 data
I have multiple people repeating the same experiment with varying numbers. How do I a ...
- 31
2
votes
1
answer
75
views
Bayesian stats and multiple tests
Are Bayesian models subject to the same problems as frequentist ones, where we cannot run a bunch of different models due to Type I error? For example, let's say I have a large data frame on airplanes,...
2
votes
0
answers
50
views
Rescaling matrix W in Random Fourier Features
I came across this beautiful idea of Random Fourier Features by Rahimi and Recht while working on optimising my GP model using Predictive Entropy Search.
I understand the overall idea of approximating ...
- 89.2k
33
votes
9
answers
3k
views
Why do we use hypothesis tests instead of just letting people do Bayesian updates?
Why do we need discretize our judgements using hypothesis tests?
Why can't we just have people report the data every time a study is done, and the p-values and effect size, and then report how the ...
- 111
0
votes
0
answers
12
views
Which model to use for predicting a categorical outcome based on human-annotated labeling?
I have a reddit dataset with thousands of online posts over the economy and inflation. We have used human-annotation on 60% of posts to determine whether users blame the following entities over the ...
- 193
2
votes
1
answer
382
views
Bayes Factor A/B Testing
I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one.
As far as I know we can ...
CommunityBot
- 1
1
vote
1
answer
27
views
How is R-squared calculated in the "Blavaan" R package and is it appropriate to use/report in bayesian analysis?
I am using the Blavaan R package to fit bayesian path analysis models. The output includes an R-squared value. It has come to my attention that there are problems with using R-squared for bayesian ...
- 141
1
vote
1
answer
288
views
How can I find the posterior distribution for gammadistributed data and prior?
I'm working on a project where I believe Bayesian statistics should be useful. However, my knowledge about bayesian statistics are very scarce. Suppose I got data following a Gammadistribution with a ...
CommunityBot
- 1
4
votes
1
answer
66
views
Bayes estimator of possion distribution with Pareto prior
Consider a random sample of size $n$ following the possion distribution with parameter $\ln \theta$, that is
$$
f(x|\theta)=\frac{(\ln\theta)^x}{\theta x!}, x=0,1,2,\cdots
$$
and the prior of the ...
- 118k
6
votes
3
answers
3k
views
Q: what book on Bayesian statistics, preferably with R? [duplicate]
I am frequentist by training and practice, but I'd like to learn more about Bayesian statistics. I know the basics, but I would be at a loss if I had to, for example, replace my normal ANOVA ...
- 31.8k
4
votes
1
answer
2k
views
Determining overdispersion of count variable in bayesian model (brms)
I am trying to determine whether my response count data are too overdispersed for a (brms) Bayesian poisson model. I constructed a poisson-generated response variable with low and high levels of noise/...
- 211
1
vote
2
answers
63
views
What are some good resources on Bayesian unconditional power analysis, besides John Uebersax's article?
I refer to the article "Bayesian Unconditional Power Analysis" by John S. Uebersax (2007).
I'd like to explore the subject further. I haven't checked yet the references that the Uebersax's ...
- 86.9k
3
votes
1
answer
42
views
Derivation of acceptance probability from Linero, Yang (2018)
I am wondering how this paper Bayesian Regression Tree Ensembles that Adapt to
Smoothness and Sparsity by Linero & Yang (2018) derived the acceptance probability for $\sigma$.
The authors give $\...
- 103k
0
votes
0
answers
13
views
Maximum likehood estimation and bayesian estimation [closed]
Lets consider $ X1, X2, X3 $ to be a sample of random variables distributed as follows: the first one with a marginal distribution $X_1 \backsim N(0,1)$ while $[X_2|X_1 = x_1] \backsim N(\theta x_1, 1)...
6
votes
3
answers
207
views
How to interpret the population parameters of a Bayesian Hierarchical model?
This is almost certainly a fatal misunderstanding of mine / knowledge gap but I am confused as to how to interpret the population parameters of a Bayesian Hierarchical model.
This is incredibly ...
0
votes
1
answer
272
views
pymc3: Updating the standard error prior
I am estimating a Bayesian multiple regression using continuous data on both the dependent variable and the regressors. My goal is to iteratively estimate the coefficient distributions as more data ...
- 955
0
votes
1
answer
831
views
Comparing top level group effects using a 3-level hierarchical regression
I would like to detect group effects (if any) along with statistical confidences. I have a hierarchical data set structured as follows:
Drug Groups
...
CommunityBot
- 1
1
vote
1
answer
666
views
Making sure that the design matrix is positive (semi-) definite
In Bayesian linear regression, how do I make sure that the design matrix produced by a neural network $ \Phi$ is positive definite?
Computing the covariance matrix on the weight requires inverting --- ...
CommunityBot
- 1
0
votes
1
answer
272
views
Bayes Formula with Joint Probability: Is this Correct?
I'm having trouble with the Bayes formula when I have a conditional probability, as part of the result of the equation.
If this is the initial equation:
$$\text{Pr}(A|B)=\frac{\text{Pr}(B|A)\text{Pr}...
CommunityBot
- 1
2
votes
0
answers
30
views
Incorporating knowledge of aggregate outcomes to constrain predictions on finer scales
I've got county-level longitudinal data on the timing of an event between the years 1998 and 2012, and I want to use it to form a predictive model for the time that that event will occur in future ...
- 74.7k
2
votes
0
answers
16
views
Derive ELBO for Mixture of Gaussian
I am working through "Variational Inference: A Review for Statisticians" by Blei et al. (see https://arxiv.org/abs/1601.00670) and they illustrate Variational Inference using a Bayesian ...
- 41
8
votes
2
answers
310
views
Is Bayesian structural equation modelling better than maximum likelihood with smaller sample sizes?
Does using the bayesian estimator to complete SEM in Mplus mitigate some concerns with a limited sample size (n=120). I.e is this approach preferred over using the traditional ML estimator with ...
- 1,332
2
votes
0
answers
41
views
Confusion about assumptions in classification problems
I was studying Linear Discriminant Analysis, and this general case came up which used Bayes theorem.
Suppose we observed response values of $Y \in \{0,1\}$ and predictors $X \in \mathbb{R}$. Suppose ...
- 6,962
0
votes
1
answer
44
views
How to statistically discover significant process change effectiveness?
I am currently working on a project where I need to assess the effectiveness of changes made in a production process. Our initial success rate was 50%, and after making some alterations, we've ...
- 301
0
votes
0
answers
15
views
Comparing Bayesian hierarchical models with different sample sizes
I have observation data covering a certain period of time. I follow a block-maxima approach where the data are segmented into equal time intervals .My goal is to first develop a Bayesian Hierarchical ...
1
vote
1
answer
183
views
Posterior Distribution in a Bayesian Multivariate Normal Model
I am currently working on a Bayesian inference problem and would appreciate some help on computing the posterior distribution of a hyperparameter within a specific multivariate normal model. Below, I ...
- 5,340
1
vote
1
answer
248
views
Expressing one-sided p values of directional hypothesis tests as Bayes factors
Assume we want to test the directional hypothesis that $µ<0$. From a frequentist angle we use a one-tailed $t$-test and imagine we obtain a 1-sided $p$ value of say 0.07, which then would imply ...
- 71.9k
2
votes
0
answers
25
views
Analogue of landscape conjecture in likelihood theory or Bayes?
The so-called landscape conjecture in machine learning says that in high dimensions, most critical points of the loss surface are saddle points rather than poor local minima.
Out of curiosity I was ...
- 955
3
votes
1
answer
250
views
Combining bootstrap and maximum a posteriori estimation
I've recently read interesting paper Uncertainty in Neural Networks: Approximately Bayesian Ensembling by Pearce et al (2020), who suggested algorithm for approximating the posterior distribution by ...
CommunityBot
- 1
2
votes
1
answer
176
views
How to maximize the ELBO in coordinate ascent variational inference
In the lecture by D.Blei: https://www.cs.princeton.edu/courses/archive/fall11/cos597C/lectures/variational-inference-i.pdf
Variational inference is explained and he shows how to derive the optimal ...
- 36
4
votes
2
answers
3k
views
Gaussian is conjugate of Gaussian?
Someone told me that the Gaussian distribution is conjugate to the Gaussian distribution because a Gaussian times a Gaussian would still be Gaussian distribution.
Why is that ? Say the following ...
- 316k
0
votes
2
answers
247
views
Bayesian A/B test - using an updated prior based on collected data
I have a question about whether I would be adding bias to an A/B test by updating my prior based on combined A & B data, and then running the A/B test on that prior.
My A/B test is click through ...
CommunityBot
- 1
1
vote
0
answers
56
views
Optimal method for estimating geometric mean ratio using Bayesian log transformed data
I'm working on a Bayesian analysis with a categorical variable involving two groups (A vs B). I'm seeking advice on the best method to compute the geometric mean ratio (GMR) together with the highest ...
- 531
4
votes
1
answer
283
views
Using Bayesian Lasso with an informed prior
I'm looking for advice on how best to go about setting an informative prior for the Bayesian Lasso and BART (I'm applying these in R using the rjags and bartMachine packages)
I have 3 proteomics ...
- 6,962
0
votes
1
answer
422
views
From Bayesian Network To Correlation Matrix
I have a Bayesian network where the edges are likelihood estimations from features {x1,...,xn}. How can I estimate the covariance matrix for x from this Bayesian net? I understand that we normally use ...
CommunityBot
- 1
16
votes
3
answers
10k
views
What are the definitions of semi-conjugate and conditional conjugate priors?
What are the definitions of semi-conjugate priors and of conditional conjugate priors? I found them in Gelman's Bayesian Data Analysis, but I couldn't find their definitions.
- 74.7k
1
vote
0
answers
51
views
Bayesian change detection (sampling the posterior of a Poisson distribution)
I'm trying to work out how the posterior of a Poisson distribution is derived to enable me to detect changepoints. I'm trying to follow the example here.
$Y_i$ (events per year) is modelled using two ...
- 54.1k
0
votes
0
answers
45
views
Naive Bayes classification for multivalued marginal
x
y
z
C
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
The dataset in the table above consisting of boolean variables x,
y and z and a single boolean output variable C. I ...
- 56.9k
0
votes
0
answers
138
views
References for the conjugate prior to the beta distribution? [duplicate]
The Wikipedia article about "Conjugate Prior" has a table containing information about Likelihood Distributions with their Conjugate Priors.
In the "Continuous Likelihood" table, ...
- 74.7k
7
votes
2
answers
7k
views
Why use mean of posterior distribution instead of probability?
I'm reading the Think Bayes (pdf link) by Allen B. Downey, and on this example I don't understand well the purpose of Mean in the chapter 3.2 The locomotive problem....
- 4,903
0
votes
1
answer
538
views
Problems with using Gibbs Sampling for Bayesian DAGs
Assume we want to sample from the variables of Bayesian belief network, which is a Directed Acyclic Graph (DAG), where we observe some of the variables, and do not observe the others. We can usually ...
CommunityBot
- 1
1
vote
0
answers
20
views
Given conjugate prior and posterior distributions, what is the PRIOR predictive distribution? [closed]
I am doing an assignment on my statistics class. We had 1 lecture about bayesian parameter estimation, where we were taught about the following formula (and it's discrete form, if $h(\theta)$ was ...
- 111
1
vote
0
answers
74
views
Estimating expected value with respect to posterior
I have a neural network and I need to calculate the following:
$$\mathbb{E}_{P(\theta|D)}[f(\theta)]=\frac{\sum_\theta P(D|\theta)P(\theta)f(\theta)}{\sum_\theta P(D|\theta)P(\theta)}$$
Where $f$, ...
- 253
4
votes
2
answers
228
views
When to use fixed effects or multi level models in regression?
Suppose you run an experiment where the treatment is Gatorade and the outcome is one-mile runtime. You’ve stratified on variables such as sex, height and weight so they’re well randomized and have no ...
- 7,168