Bayesian inference is a method of statistical inference that relies on turning the model parameters into random variables and applying Bayes' theorem to deduce probability statements about the parameters or hypotheses, conditional on the observed dataset.

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R: multicollinearity issues using glib(), Bayesian Model Averaging (BMA-package)

I am experiencing difficulties estimating a BMA-model via glib(), due to multicollinearity issues, even though I have clearly specified which columns to use. Please find the details below. The data ...
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1answer
11 views

JAGS choosing a random subset of a vector

I would like to allow the subset of a vector I am summing over to be a random quantity. My model is of the form (albeit more complex): ...
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4 views

Deriving conditional distributions for a normally distributed change point problem

So, considering the change point problem of $y_i \left\{ \begin{array}{ll} y_i \tilde{~} N(u_1, \sigma) & i=1,..,t \\ y_i \tilde{~} N(u_2,\sigma) & i= t+1,...,n \\ \end{array} ...
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19 views

Is the MAP estimate always identical to the ML estimate when a diffuse prior is used?

Let's say I have two normally distributed variables: say height and body mass. I want to estimate the Pearson's correlation coefficient between them. I have a model that estimates the mean and SD of ...
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16 views

Model checking versus posterior predictive checks

I am interested in knowing if there are any difference in modeling checking versus posterior predictive checks in the Bayesian framework. Are posterior predictive checks a type of model checking?
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24 views

Binning by standard deviations

Quick question: I came across a fairly respected source on running Markov Chain Monte Carlo for bayesian statistics in ...
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20 views

Incorporating background knowledge into a model?

I have built a model that predicts the class of an observation, based on explanatory variables A; i.e. predicting P(y|A). From domain knowledge and academic literature, we know that other variables, ...
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35 views

Relationship between low identifiability and prior weight in Bayesian model

I'm trying to get intuition into the relationship between low identifiability and prior weight in Bayesian model. Is it true to say that in lowly identifiable model + data the prior will have a higher ...
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12 views

Marginal likelihood and coordinate ascent

When updating posterior distributions in Bayesian inference using coordinate ascent, is the marginal likelihood of the data guaranteed to increase after each update?
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1answer
57 views

Simulating non-normal correlated data for Bayesian regression

I'm interested in generating data for three separate datasets where each contains three IVs and a single DV that are correlated with one another based on meta-analytic data. For example, I would like ...
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3answers
78 views

Are there alternatives to the Bayesian update rule?

Are there any other methods to update my belief in a hypothesis aside from the Bayesian update rule?
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25 views

Bayesian Model For Churn

I need to evaluate how long a customer stays with the company given a retention offer she accepted $r\in\{r_1,\dots,r_k\}$ I'd like to use Bayesian inference for modelling churn. What prior ...
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1answer
39 views

Variational Inference: good inference but ELBO decreases instead of increasing

I am playing with Variational Inference for clustering within a mixture of Gaussians. My first implementation seems to work fine (this is for the geyser dataset): ...
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16 views

German tank variant: estimate resolution of camera given cropped photo sizes

Make whatever assumptions you like, but I like the flavor of nonparametric techniques. I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same ...
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32 views

Approximating the marginal likelihood in Bayesian Model Comparison

Given some data $y$, my interest centers around a collection of models $\{\mathcal{M}_1,\mathcal{M}_2,\cdots,\mathcal{M}_L\}$ representing competing hypotheses about $y$. Each model $\mathcal{M}_l$ ...
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12 views

How do I model chapter-verse references?

Context: I am part of an 8-person group in which each person posts a Bible verse every day. For those who don't know, that is of the format "Psalm 30:1" where first we reference the chapter, then the ...
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1answer
27 views

Prior predictive density given by $f(y) = {f(y\mid \lambda) g(\lambda)}\big/{g(\lambda | y)}$?

(I guess stats.SE is the right place for this) I'm reading Albert's book "Bayesian computation with R". To get theprior predictive density, he extensively uses this formula $$f(y) = \frac{f(y\mid ...
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2answers
279 views

Question about the true nature of errors

In frequentist statistics, in regression analysis, errors, like random variables, have a distribution. Errors, like parameters, can be estimated and the residuals of the model are their estimates. So ...
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11 views

Confidence and credible interval: cases

I am having difficulties in understanding these two approaches. Let's say given the data I compute both confidence and credible interval, then what is the intuition/interpretation of having: Big CI ...
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8 views

analytically finding the dispersion of beta distribution in multilevel bayesian model

I want to create a multilevel bayesian model of the format depicted in the in figure below. I am examining # of conversions (out of total number of exposures) in multiple subgroups. The conversion ...
4
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1answer
46 views

Derivation of Normal-Wishart posterior

I am working on the derivation of a Normal-Wishart posterior but I'm stuck at one of the parameters (the posterior of the scale matrix, see at the bottom). Just for context and completeness, here is ...
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24 views

Bayesian inference on default probabilities

I have a doubt, I don't have great experience in Bayesian inference and I wondered if it is possible to construct the following model: I'm interesting in copula-dependent probabilities of default ...
4
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1answer
71 views

Semicolon in probability expression

I run in to this formula when reading a tutorial: $$ \begin{align} P(\pi|\mathbf L;\gamma_{\pi1}, \gamma_{\pi0}) & =P(\mathbf L|\pi)P(\pi|\gamma_{\pi1},\gamma_{\pi0})\tag{28} \\ &\propto ...
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125 views

Bayesian modelling, measurement error & carrying-over posterior distributions

I have a (fairly convoluted, but well-inentioned) model in my head, and am trying to figure out if it's possible to code (I am currently getting to grips with R2WinBUGS). The final model is basically ...
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2answers
70 views

When Bayesian and frequentist statistics give different answers, is there a way to empirically test which one corresponds more closely to reality?

For example for this problem: You have a coin that when flipped ends up head with probability p and ends up tail with probability 1−p. (The value of p is unknown.) Trying to estimate p, you ...
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2answers
75 views

Bayesian analysis: Estimate whether a parameter is 0 or not

I have the following problem: I need to assess whether a given parameter $B$ is equal to 0. Let's consider the following model (my problem is more complicated but I think that this example is ...
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16 views

What is meant by “weakly dependent” on p. 64 of Bayesian Reasoning and Machine Learning?

I'm reading Bayesian Reasoning and Machine Learning (here is a free online copy). On page 64, beginning with equation (4.2.20), Barber says Our aim is to show that a distribution of the form ...
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1answer
29 views

Multinomial distribution - where is the normalising constant?

I've been reading up on Multinomial/Dirichlet priors and came across this note. I'm wondering why the normalising constant for the multinomial distribution drops out in the derivation of the joint ...
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13 views

BayesFactor Error Output in R

I am an R novice and I am trying to perform a Bayesian ANOVA (one-way) using R with the BayesFactor package. I want to test the null hypothesis that scores on a test do not differ between three groups ...
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10 views

Adjust Bayesian GARCH sampler to incorporate mean

I am using the BayesGARCH package in R. The code of the sampler is publicly available here https://github.com/cran/bayesGARCH/blob/master/R/sampler.R The specification of the model in the package is: ...
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1answer
35 views

Forecast bayesian GARCH model

I am using this package in R to do Bayesian estimation of GARCH models. I want to forecast $y_t$ (i.e. the mean equation), but it seems that the package has no built-in function for this. The model ...
3
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1answer
63 views

What is the value of $\mu_0$ and $\kappa_0 $in $N(\mu_0,\sigma / \kappa_0)$?

In a Bayesian analysis I want to sample $\sigma \sim \text{inverse-Wishart}(\nu_0,M)$ where $\nu_0$ is the degrees of freedom, equal to dimension+1 and $M$ is a scalar matrix Then I will sample the ...
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27 views

Joint or marginal?

My parameters of interest are say $\theta_{1:3}$ which I declare as multivariate normal as their prior distribution. I then get the posterior distributions $\theta_1$, $\theta_2$, $\theta_3$. Can I ...
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9 views

Estimation of a Probit model via data augmentation using JAGS [migrated]

I'm trying to estimate a Probit model with data augmentation. This works without data augmentation, but the end goal is to estimate a multinomial Probit model, where data augmentation is helpful. ...
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17 views

A way to make Bayes' rule common sense to me? [closed]

Although I understand Bayes' rule/theorem I always forget its intuition. I solved a lot of exercises to practice it. I remember the equation, but I find it hard to remember the intuition itself. I ...
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22 views

In a EI RxC model, how can I incorporate additional external information?

I'm fitting an ecological inference RxC model, such as described by the Rosen et al. (2001) paper and implemented by the EI R package. I'm estimating voice transfer from the first round to the second ...
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2answers
30 views

Mixture Model with dependant observations

I am trying to model a process in which each datapoint is generated sequentially, so the current observation depends on the last one. Some example data could look like, ...
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10 views

What is an example of a highest posterior density region which is not scale invariant?

The title says it all, I think. Feel free to give an example without going through the computations.
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57 views

Identifiability in factor analysis

Say we model $\mathbf{x}_t \in \mathbb{R}^d$ as a linear combination of factor loadings: $$\mathbf{x}_t = \mathbf{E}\mathbf{F}_t + \boldsymbol{\epsilon}_t, \qquad \boldsymbol{\epsilon}_t \sim ...
2
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1answer
33 views

Gibbs sampler for a particular distribution

I'm trying to implement Gibbs Sampler for the distribution: $$\pi(x,y)=e^{-10(x^2-y)^2-(y-1/4)^4}$$ So, like the first step, I need to find: $$\phi(t) = \int_{-\infty}^{t} e^{-10(x^2-y)^2-(y-0.25)^4} ...
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1answer
23 views

What is this bivariate distribution called and how to make it posterior?

I am trying to make this bivariate density function as posterior f(x,y) = k x^2 exp( - x y^2 - y^2 + 2y - 4x) and try jags instead of implementing in R as in ...
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33 views

Estimation with ML or Bayesian

A marketing department is supposed to find the market share of their product. To answer this question, a survey among 720 representative people is conducted, 696 of which complete the poll with ...
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16 views

How can I calculate the posterior mean of a two-point distribution?

I am trying to reproduce some of the results in this paper. Specifically, there is a two-point distribution with one probability mass concentrated at $pfd_A \times pfd_B$ and the other mass ...
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42 views

can you analytically solve this bayesian hierarchical model - bernoulli trials

Is it possible to analytically solve (i.e., use a conjugate prior) the hierarchical model shown in the image below to obtain the posterior distribution. The data are composed of bernouli trials ...
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20 views

Attraction/ likelihood of going somewhere given similar people have already gone

Given a venue which has previously been attended by a demographic of people (e.g. old, young, middle age) I want to compute the affinity those demographics have for a venue and therefore compute the ...
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2answers
78 views

Large? Number of parameters in MCMC model [closed]

I am implementing a Hierarchical Bayesian Modeling in order to model the relation between the independent and dependent parameters $(x, y)$. I assume the relation is: $$ y_i = \alpha + \beta x_i + ...
2
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0answers
39 views

Hierarchical Bayesian model with heterogenous errors

I have an experiment where I repeatedly show subjects two lights, and I ask which light is brighter. I am interested in whether error rates decrease over time, holding all else constant. I also ...
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1answer
25 views

What is the predictive distribution of Bayesian supervised Learning? (rigorous argument)

I was trying to understand the posterior predictive distribution for any supervised predictor (by that I mean any classifier or regression predictor $f$). The exact equation I am unsure of is: $$ ...
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30 views

In Bayesian analysis, how to sample from full conditional given uniform prior and normal data likelihood?

In Bayesian analysis, assume a simple linear regression model with two straight lines that meet at a certain changepoint $c$. The basic setup is as following. \begin{align*} Y_i \ & \sim \ ...
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36 views

Setting up posterior and likelihood of Bayesian for more than one model

If I have a data-set and I would like to fit a model and determine its two or three free parameters, while I know that I can fit twice or three times the model to my data and obtains the free ...