Questions tagged [hierarchical-bayesian]

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

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84 views

Interpreting the results of hierarchical bayes model including one covariant using ChoiceModelR

There are 5 different features of a product (in this case gyms): ambiente, trainingstools offered, atmosphäre, gastronomie and location. Within the participants there are people who train on a ...
4
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2answers
322 views

Is the posterior of a random variable's mean necessarily the mean of that random variable's posterior?

Let's say I have a model that's like, $$ Y \;|\; \theta_1 \sim P(Y \;|\; \theta_1) $$ $$\theta_1 \;|\; \theta_2 \sim P(\theta_1 \;|\; \theta_2) $$ $$ \theta_2 \;|\; \theta_3 \sim P(\theta_2 \;|\; \...
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18 views

Bayesian Inversion - choice of likelihood function and whether to invert for standard deviation

Good evening, There are my main questions before a brief explanation of my work: 1. Should I be inverting for multiple standard deviations (for different portions of the data, or even at each data ...
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1answer
152 views

Hierarchical Version of Bayesian Change Detection Model in JAGS

I am trying to create a hierarchical changepoint detection model in JAGS, estimating group difference in changepoint based on individual changepoints in scores for an outcome variable (fictional in ...
2
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0answers
54 views

Hierarchical Black Box Variational Inference : Choice of inverse flow

I am reading through Black Box Variational Inference, and having trouble understanding the section for hierarchical inference, where the normalizing flow is introduced. Should this be an arbitrary ...
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37 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\...
2
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1answer
163 views

What problem do these trace plots indicate?

The following plots are trace plots of 3 variables for MCMC results of a hierarchical Bayes probit model. The plots are fairly linear and seem to grow (or decline) without bound. This looks like a ...
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59 views

¿Any suggestions? GLM, HLM, MLM Problem (lme4)

I'm new to Multilevel modeling and currently I been working on a business project and its data is related to multilevel modeling. I know a lot of things about how to approach this problem, but I will ...
2
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1answer
190 views

Plate notation for a hierarchical regression model (bayesian)

I've been recently studying hierarchical bayesian regressio (with pymc3), and I was wondering, how does the following example: http://twiecki.github.io/blog/2014/03/17/bayesian-glms-3/ look like ...
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1answer
104 views

Bayesian multilevel model in practice - selection of package, specification and interpretation

I am trying to fit a Bayesian multilevel model in R and have several questions. I found two packages (brms and rstanarm) and am able to perform the analysis with both of them, so the technical part is ...
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1answer
62 views

Bayesian model - how to emphasize later observations?

I have a very general question, any links to relevant papers or which book I should consult should suffice. So, let's say I've got a Bayesian model (for example) to predict the outcome of a soccer ...
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1answer
33 views

Multiple classifier comparison with Bayesian statistics

I've been recently working on some classifier comparisons. I've come to realize, the critical distance diagrams introduced $\approx$ 10 years ago might not be the most relevant solution for this ...
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2answers
110 views

In Bayesian statistics, what does this notation formally mean?

I've seen Bayesian models specified as \begin{align*} Y_i|v_i &\overset{ind}{\sim} f_i(y_i|v_i),\\ v_i & \overset{ind}{\sim} g_i(v_i). \end{align*} My question is about the top line $Y_i|v_i\...
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0answers
65 views

How to interpret Gelman's multivariate Gaussian prior for multinomial distribution?

Andrew Gelman suggested the use of a multivariate Normal distribution as prior for hierarchical models that have a multinomial distribution at the lowest level (http://andrewgelman.com/2009/04/29/...
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2answers
84 views

Bivariate/multivariate models for multinomial response variables

I need to fit two categorical (potentially correlated) response variables (each has three classes) on a set of explanatory variables, while considering for the response variables' correlation. What ...
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135 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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0answers
70 views

Confusion about Bayesian Hierarchical Models

I'm having a little confusion over hierarchical models and I was hoping for some clarification. I will share my understanding of what it is, and highlight my confusion. Suppose we start with some ...
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0answers
176 views

Trace plots for MCMC simulations and interpretation of lack of convergence

I am simulating a hierarchical model with MCMC Bayesian methods. The model has three groups of individual effects modelled as random effects drawn from normal priors with mean zero and variances ...
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1answer
89 views

Marginal prior derivation in hierarchical Bayesian model

I am working on a model that is closely related to the normal gamma shrinkage prior setup discussed in Griffin & Brown (2010). Suppose we want to draw $P$ parameters $\beta_p$ with $p=1,...,P$. ...
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0answers
47 views

Decision rule for Bayesian variable selection

I'm fitting a spike-and-slab regression model to sparse data and obtaining posterior probabilities of association (PPA). I now would like to 'declare' associations based on the latter. I'm concerned ...
3
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0answers
28 views

Bayesian modeling: likelihood function for continuous random variables, why is it not always 0? [duplicate]

For continuous random variables, evaluating p(x) for a specific value of x is always 0 as show here, here and here. So when we're calculating the likelihood for a random variable X that is represented ...
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84 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
40 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 ...
3
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1answer
221 views

Stick-breaking construction of Dirichlet process

In the stick-breaking construction of Dirichlet (let me base things on Sethuraman's construction - slide 6 of this) do we sample one $\phi$ vector from the base distribution $H$ and use it for ...
4
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0answers
195 views

Likelihood function of a hierarchical model

I have the following model: $$ y\sim\textrm{MvNormal}\left(\mu,\Sigma\right)\\ p=\textrm{logistic}\left(y\right)\\ k\sim\textrm{Binomial}\left(p,n\right) $$ Where $\mu$ and $\Sigma$ are free ...
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2answers
361 views

comparing distributions - bayesian decision analysis

I am attempting to use Bayesian analysis to compare distributions to help with decision analysis - when to treat a patient based on a blood measurement X. Here you can see 1000 samples from two ...
2
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0answers
127 views

Hierarchical Linear Regression should always outperform Ordinary Linear Regression

I am building a hierarchical linear model with varying intercepts. It takes the form for each unit $i$ in group $j$: $$y_{ij} = \alpha_j + \beta_1 x_{ij,1} + \beta_2 x_{ij,2} \quad (1) $$ I am ...
4
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0answers
119 views

Run MAP estimates before MCMC in most cases?

I am learning Bayesian statistics. I found that this pymc3 introduction sometimes uses MAP to estimate the parameters for the MCMC input (the regression example), but the intro doesn't run MAP for ...
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1answer
89 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
57 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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0answers
67 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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0answers
84 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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0answers
179 views

How to fit newer cohorts using Pareto/NBD or Beta/Geo for CLTV

I am trying to fit the popular Pareto/NBD or Beta/Geometric models for non-contractual, continuous customer data. On top of that I then fit the Gamma/Gamma model for monetary value (using the very ...
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1answer
62 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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1answer
162 views

sampling behind bayesian hierarchical models

I'm unsure how sampling is done in Bayesian Hierarchical modelling, i'm reading a book on how to use it in PyMC3 but it doesn't explain the math and i'd like to understand it. Suppose i want to ...
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1answer
41 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 ...
1
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1answer
230 views

Fitting regression spline [closed]

I am reading the paper by Willemsen et al (2015), "A multivariate Bayesian model for embryonic growth", Statistics in Medicine, 34:8, 1351–1365 I have a model like $$y_{ij} = \gamma_{i2} + f((t_{ij} ...
6
votes
1answer
203 views

Can Kalman Filtering be done hierarchically - estimated from multiple time series with the same parameters?

I have a large number of of noisy time series recordings (trials), for which I wish to estimate the state transition model underlying them using the Kalman filter. The process generating the time ...
8
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2answers
248 views

Feature selection on a Bayesian hierarchical generalized linear model

I am looking to estimate a hierarchical GLM but with feature selection to determine which covariates are relevant at the population level to include. Suppose I have $G$ groups with $N$ observations ...
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0answers
43 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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1answer
241 views

Using PyMC3, how could I force a maximum to posterior distribution?

I am pretty new to bayesian statistics and PyMC3. I am doing a hierarchical model where the output variable I am trying to predict is a percentage with a maximum of 100%. My problem is that my ...
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2answers
220 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 ...
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0answers
35 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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0answers
42 views

Understanding covariance in Bayesian regression model

I am confused about when to model covariance in a Bayesian regression. Here's what I am trying to model. I have a dataset which has scores for a set of students who did a set of practice exam problems....
2
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0answers
71 views

Applications of Hierarchical Dirichlet Process to Continuous Data

I read Yee Whye Teh et al.'s paper on Hierarchical Dirichlet Process. In section 5, they show sampling algorithm using base distribution H and data distribution F. One of their applications is HDP-...
1
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1answer
314 views

Problem with “log(0)” error while using brms in R to do Bayesian analysis [closed]

I'm using brms to conduct a multilevel regression in R. I've been getting warnings and errors of the following type: ...
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1answer
100 views

Selecting Bayesian priors for the dependent data

I have goal of measuring CTRs of several titles of an article on a website using Bayesian approach. In a simple setup, what one will do is to select Beta Prior (for example Uniform distribution) and ...
2
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1answer
163 views

Hierarchical linear modelling in R

I am trying to build a hierarchical linear model based on data structured like this dataset below. The model form I am looking to build is Purchased ~ f(price + color + more item attributes + age + ...
1
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1answer
51 views

Robbins estimate Empirical Bayes

From the compound sampling model where: $Y_i | \theta_i \sim Poi(\theta_i)$ The marginal distribution of $\theta_i$ is $G$, non-parametric. We get that the Bayes estimate of $\theta_i$ under ...
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1answer
53 views

Best modeling approach for “two-factor varying slope” model?

I'm new to this forum so I hope this question is appropriate. Please let me know if there is anything I can do to improve the question. I simply have a situation in which I am considering the best ...