Questions tagged [hierarchical-bayesian]

Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions

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6
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2answers
3k views

Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...
13
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3answers
5k views

Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters

I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta. Then, I assume the parameter ...
8
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4answers
6k views

Covariance matrix proposal distribution

In a MCMC implementation of hierarchical models, with normal random effects and a Wishart prior for their covariance matrix, Gibbs sampling is typically used. However, if we change the distribution ...
8
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1answer
427 views

Is rstan or my grid approximation incorrect: deciding between conflicting quantile estimates in Bayesian inference

I have a model to achieve Bayesian estimates the population size $N$ and probability of detection $\theta$ in a binomial distribution solely based on the observed number of observed objects $y$: $$ p(...
8
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1answer
799 views

Hierarchical Bayesian modeling of incidence rates

Kevin Murphy's book discusses a classical Hierarchical Bayesian problem (originally discussed in Johnson and Albert, 1999, p24): Suppose that we are trying to ...
4
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2answers
582 views

What are some statistical tests for exchangeability of a data set?

The representation theorem of de Finetti is seen by some as motivation for the use of Bayesian and/or hierarchical modeling. In some settings, it may be plausible to assume measurements are ...
5
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1answer
617 views

Relation between Bayesian analysis and Bayesian hierarchical analysis?

I have been studying a Bayesian hierarchical model. In that model all I am dealing is with the estimation of parameters. In Bayesian analysis, loosely speaking, we update our prior knowledge (in light ...
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0answers
170 views

Classification of Bayesian posterior probabilities

I have run a series of Bayesian models with flat priors in which I obtain a posterior probability distribution for my coefficient of interest. The reviewer of my paper wishes us to classify these ...
17
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2answers
3k views

Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
4
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2answers
2k views

Bayes-factor for testing a null-hypothesis?

I heard somewhere, that I can directly test (or gather support for) a null-hypothesis using the Bayes-Factor. In my specific experiment, I hypothesize that an experimental manipulation does not have ...
11
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2answers
1k views

What is a good analogy to illustrate the strengths of Hierarchical Bayesian Models?

I'm relatively new to bayesian statistics and have been using JAGS recently to build hierarchical bayesian models on different datasets. While I'm very satisfied of the results (compared to standard ...
6
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1answer
309 views

Bayesian Aproach: Infering the N and $\theta$ values from a binomial distribution

I am doing a homework about infering the N value of a binomial distribution for my Bayesian Statistics Course and I have seen a paper in Biometrika magazine published in 1988 for doing so. The ...
5
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1answer
967 views

Crossvalidation in hierarchical bayesian models (HBMs)

I am trying to find a way to cross-validate Hierarchical Bayesian Models used for predicting and modelling abundance in Species Distribution Models. For this purpose, I have tried posterior predictive ...
11
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2answers
6k views

Differences between prior distribution and prior predictive distribution?

While studying Bayesian statistics, somehow I am facing a problem to understand the differences between prior distribution and prior predictive distribution. Prior distribution is sort of fine to ...
10
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1answer
2k views

Hyperprior distributions for the parameters (scale matrix and degrees of freedom) of a wishart prior to an inverse covariance matrix

I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R. Instead of specifying a scale matrix and degrees ...
8
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1answer
758 views

What level to use when comparing subjects in a hierarchical Bayesian analysis?

Say that I have an experiment where I test the reaction time of a number of subjects where each subject makes many reaction time trials. In a Bayesian framework the reaction times ($y$) could be ...
7
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0answers
3k views

Hyper-prior for negative binomial in hierarchical model using JAGS/BUGS

Below I'm using a negative binomial because it is more flexible than a simple poisson model. The data are counts $y$ of events for 16 individuals $x$. There are 14 counts (i.e. counting periods) for ...
5
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2answers
3k views

Use of Bayesian hierarchical model

What is the purpose of Bayesian hierarchical model? When should I use such models? I've found many questions here and references on the web but they are all too technical. My doubts are about the ...
4
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1answer
254 views

Bayes Rule with Model Comparison

In Doing Bayesian Data Analysis 2ed, by Kruschke, in chapter 10, we get two equations (10.1, 10.2) for which no hint as to how they are obtained is given... How does one get the second equality in ...
3
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1answer
1k views

Gibbs sampling with mixed prior using a Metropolis-Hastings step

My questions are about a sampling procedure for fitting a Bayesian hierarchical model where one of the priors is a mixture distribution of discrete and continuous parts. The model is not my own but I ...
3
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0answers
445 views

Appropriate Distribution for Diagonal Covariance Matrices

Let's say I have a model like: \begin{align} X\mid\mu,\Sigma_X &\sim \mathcal{N}(\mu,\Sigma_X)\\ \mu\mid m, \Sigma_\mu &\sim \mathcal{N}(m,\Sigma_\mu) \\ \Sigma_X\mid \Psi, c &\sim \...
4
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1answer
192 views

Bayesian regression with independent variable drawn from distribution

I'm trying to set up a bayesian regression of the form $y_i \sim f(\beta_0 + \beta_1 x_i)$ but rather than $x_i$ fixed, they themselves are drawn from a distribution of (known) mean $x_i \sim g(\...
3
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1answer
222 views

How to predict using Spatial temporal hierarchical bayesian models

I am using the R package CARBayesST to fit a Spatial-temporal Bayesian models. I want to use piece-wise ST model proposed by Lee and Lawson, 2017. The package does not have a built-in predict ...
2
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1answer
168 views

Is there any reason to prefer a bayesian model with few variables?

I have two alternative hierachical bayesian models that were designed to the describe the same process (from a high-level point-of-view). Both model provides comparable (but not identical) inferences ...
2
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1answer
421 views

Risk and posterior expectation Bayesian Statistics

Consider $x\sim B(n,\theta)$ with $n$ known a)If $\pi(\theta)\sim Beta(\sqrt{n}/2,\sqrt{n}/2)$ give the associated posterior distribution and posterior expectation $\delta^\pi(x)$ b)Show ...
2
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1answer
85 views

Are pseudopriors required in Bayesian model selection with hierarchical models?

Say I have a set of $K$ models and I want to perform Bayesian model selection to see which one of those best describes my data. So I add a categorical variable with $K$ different values that indicates ...
4
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0answers
1k views

Is this correct hierarchical Bernoulli model?

I have a question about correctness of a model that I used for a fairly simple experiment. I'm not sure if it should go to stackoverflow or crossvalidated, because I feel like my question is both ...
2
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2answers
606 views

Confusion about Cross-Validation for Hierarchical Bayesian Regression Models

I had two questions regarding model selection for a Hierarchical Bayesian (HB) Regression Model and the purpose of Cross-Validation. 1). I understand cross-validation as one way to perform model ...
2
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0answers
126 views

If all components of a hierarchical model have not converged, can we say that any parameters have truly converged?

I'm working with a hierarchical regression model of the following form similar to that presented in Peter D. Hoff's book, A First Course in Bayesian Statistical Methods: $\boldsymbol{Y}_j \sim \text{...
1
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1answer
448 views

What is the correct form of Metropolis Hasting step in scaled Inverse Wishart prior for covariance matrix?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed ...
1
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2answers
485 views

Bayesian Modeling: Yes, No and Maybe Responses

Respondents replied in the following way: Yes: they will be attending No: they won't be attending Maybe: they attach a percentage certainty as an estimate that they'll be attending. E.g. 40% sure ...
3
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1answer
745 views

How to find the Likelihood Function in a Bayesian Model given some Data

How should I find the likelihood function of a Bayesian Model? For example, if I'm given a coin, I can use the Bernoulli Distribution as the likelihood function (because I know in advance that the ...
2
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0answers
23 views

Hypothesis testing : Constant mean over time for two conditions within an experiment

What is an approach to testing/showing that within a particular period of time, there is no change in values. So, I have my response variable measured over 30 seconds, in two conditions. I want to ...
2
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1answer
2k views

Jeffrey's prior for variance

I'm dealing with hierarchical model where $Y_i$ are from normal distribution. About variance the formulation is the following: Similarly, the data contain substantial information about the measurement ...
2
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0answers
91 views

How to model a multiplicative effect of a parameter

I am having difficulty in fitting a model on data. Basically, I have data about the evaluation of phenotypic property (i.e. hard) of 65 palm trees by 5 judges. As an evaluation scheme, each judge ...
1
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1answer
388 views

Why semi/nonparametric models?

Increasing the flexibility of models makes it prone to overfitting. On the other hand, it looks to me that, if the space function classes $\mathcal{F}$ is too big, it is hard to prove bounds on ...
1
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0answers
66 views

Mixed model with panel data when some cases have constant responses (zero) over time

I have a panel data with about 300 units observed over a period of 4 weeks. In each week, I recorded a response that is a binary variable, y, for each unit of that week. For about 50% of the units, ...
1
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1answer
58 views

Bayesian model: binomial(s) conditional on Poisson

I am struggling a little with how to conceptualize and specify a particular Bayesian model. I suspect the solution is rather simple but for some reason I am having a hard time thinking about this. ...
1
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0answers
35 views

How to model whether discrete count data are statistically-enriched in certain regions for spatial data?

I feel like there is a straightforward way to model this dataset, but I'm a bit stuck. Let me give you a metaphor for the data first: Let's say that we are looking at a strip of land of fixed ...
0
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1answer
73 views

Can I use beta priors in zero inflated poisson model?

Please I have a two fold questions and I am not sure how to phrase the title of my post to capture both. I am trying to fit a regression model in jags, and I am new Bayesian modeling. In my model I ...
0
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1answer
35 views

Lognormal model: reporting median or geometric mean

I have a bayesian lognormal model as follows (brms package): m = brm(y ~ 1, data = df, family = lognormal) Model was run with default priors. This is model's ...
0
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1answer
527 views

Metropolis-Hastings in a Bayesian Hierarchical model

I am trying to estimate a Bayesian Hierarchical model using the random-walk Metropolis-Hastings algorithm. While in a non-Hierarchical model, the algorithm is staight-forward, I am not sure I am ...
0
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1answer
183 views

Bayesian analysis of multilevel model with lagged dependent variable

Currently, I am constructed a bayesian multilevel model to analyze a panel data set which now basically looks like the following: $y_{ijt} = \beta_{0ij} + X\beta + \epsilon_{ijt}$. So, now only a ...