Questions tagged [hierarchical-bayesian]

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

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Bayesian hypothesis testing with multiple beta-binomials

I want to test questions relating to whether individual ants of a certain species have personal food preferences, using a Bayesian model built up of multiple beta-binomial distributions. My problems ...
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66 views

Excellent fit, zero convergence hierarchical dirichlet model in JAGS

I am fitting a hierarchical dirichlet model to some data in JAGS. My samples (referred to as cores in the code) are observations of the relative abundance of 3 ...
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56 views

using rstanarm for quantile regression

I understand that rstanarm can be used for GLMs, GAMs and hierarchical models. Does anyone know, if I can use it to estimate quantile regression models? If not, are there other Baysian R package, ...
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157 views

Problem fitting multinomial model with MCMCglmm

I am trying to fit the following model with MCMCglmm $$Y_i \sim \text{Multinomial}(\pi_i)$$ $$\pi_i = \phi^{-1}(\eta_i)$$ $$\eta_i = \Lambda X_i + E_i\quad E_i \sim N(0, \Sigma)$$ $$\Lambda \sim MN(\...
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42 views

Question about Bayesian inference of the distribution of a categorical variable

I am trying to build a Bayesian models in JAGS that infers probabilities about count data for past events and having trouble setting up the model. The observable data: pairs of count data and times. ...
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40 views

Informative priors

I have a general query regarding informativeness of priors, since my laptops gone down and not able to run this on Stan to check (but from previous runs I think this was the case). If the priors used ...
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46 views

linear mixed model gives wrong results

I am currently learning Stan (MCMC C++ engine with wrappers in python and R) and implemented a linear mixed model $y_{i,j} = \beta_0 + \mathbf{x}_{i,j}^T\beta + \alpha_i + \epsilon_{i,j},\ 1\leq i\...
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166 views

Why am I getting low effective samples and high rhats with multilevel Bayes models using brms?

I've been using the brms package in R to run some multilevel Bayes models. I've been getting some strange results however (such as extreme predictions and not ...
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91 views

Predict race position (data provided)

I have data from race competitions consisting of race time for a competitor, their position in the race, an independent variable x and raceid. I'm looking for a way ...
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1answer
46 views

Why intercept not equal to dependent var. mean after Centering: rstanarm package

Package rstanarm in R, by default, centers the predictor variables. But I'm wondering in the case of a simple linear regression ...
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1answer
97 views

Bayesian hierarchical model with multidimensional input

I'm faced with the following statistics problem that I thought a Baysian hierarchical model would give useful results, but I'm not sure how to apply it. A summarised description: I have daily sales ...
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1answer
73 views

Computing the posterior mean using a Gaussian prior?

I was reading through "Machine Learning: A Probabilistic Perspective" by Kevin Murphy and came across this example using priors but I don't understand how the posterior mean was calculated (page 168): ...
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79 views

Strength Parameter in ICAR Spatial Model

As I understand it, the parameter $\alpha \in [0, 1]$ that controls strength of spatial association in a CAR model gets set to 1 in an Intrinsic CAR model. Does this mean that an ICAR model cannot/...
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91 views

Sampling from Bayesian Hierarchical Logistic Regression Posterior

Suppose we fit a Bayesian logistic regression model of the form $$Y_i \sim Bernoulli(p_i)$$ $$logit(p_i) = \beta_0 + \beta_1*x + \alpha_{j[i]}$$ $$\alpha_j \sim N(0,\sigma_\alpha^2)$$ $$\beta_i \...
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1answer
48 views

How to use Selective Bayesian Forest Classifier (SBFC) in R?

I came across with this r package 'sbfc'. It appears very interesting as they talk about Bayesian Forest and it competes with random forest performance. If someone can walk me through this package ...
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48 views

Hierarchal Bayes: logistic regression

We have the following model that was proposed to me. It takes yes, no and maybe responses to try and predict attendance $y_{i}$. $$ \begin{align} y_i &\sim \mathsf{Bin}(n, p_i) \\ p_i &= \...
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36 views

Hierarchial Bayesian approaches versus simple prior based approaches

The point of Hierarchical Bayesian models is that you can get parameters for different "hierarchies" within your data. For example, if you have 10 data points for one person, 10 for the next and so on,...
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163 views

Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used ...
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1answer
28 views

What distributions might describe the percentage of a population with a trait across groups?

Suppose I have a large number of urns, each with a different ratio $r$ of white and black balls. Some urns may be full of white balls or full of black balls. What kinds of distributions or processes ...
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1answer
34 views

learning a gaussian distribution through dependent vairiable observations

Is it possible to infer the parameters of a gaussian random variable by sampling from a distribution that is linearly dependent on the variable of interest? For example: y = Ax + n With x ~ N(u,S) ...
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879 views

In Bayesian statistics, what do mu, eta, and tau tend to represent?

In the eight schools example from Gelman, he sets his parameters as mu, eta, and tau. ...
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1answer
278 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 ...
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116 views

Help! Newton-Raphson explodes!

I am trying to find the posterior mode of a log likelihood in order to implement maximum a posteriori. The parameter I am trying to estimate is actually a vector. I can find the first and second ...
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97 views

Left or right skewed prior in WinBUGS

I am trying to find a proper way of defining a right or left skewed continuous (0...100) distribution for my priors in a simple linear regression. Furthermore, I expect to find some outliers in my ...
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31 views

Multilevel modelling of effects for positive values: Which distributions to use

I am currently trying to figure out what would be the best way to model a bayesian hierarchical regression for data, where the criterion value can only be positive and I am assume that the effects are ...
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367 views

Tuning my proposal distribution - where does the tuning parameter go?

Suppose you are interested in sampling some parameter $x$. We sample proposals of $x$ (called $x^{*}$) from some normal distribution $q \sim N(\mu_{x},\sigma^{2}_{x})$. Denote $x'$ as all other ...
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149 views

In calculating the Schwarz Criterion (BIC) what does the “number of samples” (n) mean?

The Bayesian Information Criterion is calculated with: $BIC = k\ln(n) - 2\ln(\hat{L})$ where $n$ is defined as the number of data points in $x$, the number of observations, or equivalently, ...
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2answers
73 views

How to set the index valued M in Hierarchical model to compute Bayesian model probability?

I'm incorporating a Bayesian Model Averageing(BMA) approach in my research and strapped in trapped in the estimated of Pr(theta|D). Professor John K. Kruschke(2014)'s book in chapter 10 offers an ...
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1answer
70 views

Shrinkage in hierarhical models based not on observations

When we have a hierarchical model, such as: $$log(y_{i,t})=\beta_0 + \beta_i*log(x_{i,t})+\epsilon_{i,t}$$ Where $\beta_i$ ~ $N(B,\Sigma)$, and the sampling model is normal (normal disturbances.) ...
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226 views

Translating user-defined joint-distribution from PyMC to PyMC3

I'm attempting to set up a simple beta binomial hierarchical model with an uninformative prior in PyMC3. I've read that the uninformative prior for this model should have alpha and beta hyper-...
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1answer
177 views

pyMC produces values outside range of uniform distribution while sampling from Bayesian hierarchical model [closed]

I have a hierarchical Bayesian model consisting of a Uniform prior distribution, between a minimum and maximum value (hyperparameters) at the top level of the hierarchy. I sample a "mean" from the ...
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76 views

How to construct prior for two variables based on known distribution of their product?

Building a hierarchical Bayes model, and I am interested in Bayesian inference of two parameters $a > 0$ and $b > 0$. Right now I am using uninformative priors on both $a$ and $b$. But I ...
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140 views

How the De Finetti's Representation Theorem works in this case?

For the special case of infinite sequence of $\{0,1\}$ valued random variables the theorem is stated as $$ Pr(x_1, \ldots, x_n) = \int_0^1 p^{(\sum_{i=1}^n x_i)}[1-p]^{(n - \sum_{i=1}^n x_i)} dQ(p)\,. ...
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169 views

Multiple linear regression as a Hierarchical model in Bayesian framework, cant solve

In lecture notes on introductory graduate course on Bayesian statistics, there is a short discussion of how Multiple linear regression may be treated in the paradigm of "borrowing strength" aka "...
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1answer
156 views

Relationship between 0-1 Loss and error Type I and II in Neyman Pearson

In the context of hypothesis test $$H_0:\theta\in \Theta_0$$ $$H_1:\theta\notin \Theta_0$$. Find the relationship between the 0-1 loss defined by $$L(\theta,\delta)= \begin{cases} 1-\delta & \...
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160 views

Replacing ridge regression with Bayesian MCMC

I have a ridge regression model $ y = \beta_1 x_1 + \beta_2 x_2 + ...$ The $x$s are highly collinear but are all physically relevant, hence use of ridge regression. And am considering replacing ...
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24 views

Problems in notations in a paper on Bayesian space-time models

Suppose I have been given some process $Y$. Let $Y(s,t)$ denote the value of process at location $s$ and time $t$. For my experiment, I consider a model described as - $$Y(s,t) = \mu(s) + M(t;\beta(s)...
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47 views

Is it possible to find the distribution parameters of a normal hierarchical model given specific values for the hyperparameters?

I would like to find out if it is possible to calculate the distribution parameters, i.e., determine $\mu$, $\sigma$, for a random variable $y$, given that: \begin{align} y &\backsim Normal(\mu,...
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465 views

How would you explain Hierarchical Bayesian modeling?

To the widest audience ? The people I have to present some of my models are not statisticians and I don't have a simple way to put it or simple self-explanatory graphs.
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1answer
35 views

Hierarchical process of exponentials

I'd like to work with a what I believe is a called a "hierarchical process" -- given by the multiplication of a pair of exponential distributions such that the random variable from one process is the ...
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210 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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1answer
34 views

Representing confidence ratings on choices as a variable or as part of the choice alternative in Mixed Logit Simulation

I am estimating a mixed logit model with hierarchical Bayes procedures to deal with my categorical data. I am wondering if I'm representing the data correctly. The data comes from experiments where ...
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0answers
65 views

Numerical sampling in hierarchical Bayesian models (HBM) [duplicate]

I am reading chapter 5 of $\textit{Bayesian Data Analysis}$ by Gelman $\textit{et al.}$. There it explains the few steps of data analysis for hierarchical models and if I quote from the book it will ...
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721 views

Regression estimate of a non-negative variable

I have to estimate linear weight $\beta$ for regression $Y \sim \mathbf{X}$, where $Y$ are non-negative samples. If I perform vanilla regression (lets assume ridge regression) it will find $\beta$ ...
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399 views

Non-converging coefficients in hierarchial Bayes analysis of discrete choice

I am trying to analyse repeated responses from a discrete choice experiment. The DCE had one continuous parameter and five 3-level categorical parameters. I started with a multinomial logit and the ...
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1answer
66 views

I have this 3 clustering algorithms and I want to figure out which algorithm has the best algorithm for clustering

I'm new with clustering. I have this 3 algorithms and I want to figure out which algorithm has the best algorithm for clustering. I posted an image below, to show my clusters. I am confused on how to ...
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2answers
272 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 + \...
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1answer
39 views

Bayesian updating of a probability density for evidence on its cumulative distribution

Suppose that I have a continuous variable E as a result of a simulation, which has a probability distribution as in the figure below: As seen from the cumulative plot, ...