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.

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15 views

Can you recycle posterior probability distributions into the same model and experiment?

Suppose I have some classifier which is reasonably good at discriminating classes. I have a new dataset which I know has a very unbalanced class distribution, but I don’t know anything about this ...
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what is the difference between Naive Bayes and NON-Naive Bayes?

In Naive Bayes Why is it necessary for Naive to assumes that the input features are independent and not co-related . can anyone explain with a very simple example on what is the problem of events ...
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Modelling a race

If we imagine an outdoor race with two obstacles: If the participant fails an obstacle attempt they exit the race Historical data shows that about 50% of participants will fail each obstacle That ...
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34 views

What is the actual distribution that we are modelling in case of a Bayesian Regression Model?

I have come across blog posts that speak about modelling a regression problem using Bayesian approaches. I completely understand that, to set up example data, they generate a sine wave using a one ...
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Forecast survey response rate

I am new to Bayesian forecasting and hope you can help me get started with this problem: I need to forecast the likely survey response rate to a paid-for survey Background information: Each person ...
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Using Bayesian model selection with extreme heterogenous data

Assume I have a dataset collected from $N$ individuals. However, the generating process differs between individuals. For example, if I have two different types of individuals that would use different ...
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25 views

Bayesian estimation of case fatality rate?

Let's say we're tracking a global epidemic, such as COVID-19, and we want to estimate the case fatality rate (CFR). The formula for CFR is just ...
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Unclear explanation of Bayes theorem

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Inverse probability: the Bayesians of chapter 1 says the ...
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Using probabilistic scores in Bayesian Optimisation

I was reading up on Bayesian Optimization and in one of the articles, I came across the following passage. We could just use the surrogate score directly. Alternately, given that we have chosen a ...
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Why are frequentists uncomfortable with bayesian statistics when “optimization” algorithms used in frequentist statistics is bayesian?

In Step 1, we have a prior. Using bayes rule we construct the posterior. In step 2 of some iterated bayesian procedure, the prior becomes the posterior from step one and use bayes rule to calculate ...
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1answer
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Marginal posterior distribution, likelihood mean sum of two standardnormal priors

How would I compute the marginal posterior distribution of $\mu_1$ and $\mu_2$ if the likelihood $(y | \mu_1,\mu_2) \sim N(\mu_1+\mu_2,1)$ and $\mu_i \sim N(0,1)$
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Setting specific proportions for priors in BRMS()

I need to set the proportion of the dependent variable and one of the independent coefficients to specific proportions: Response/Dependent variable is between 0 - .30 X1 needs to be between 0 and .17
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Why is it easier to estimate $P(X|Y)$ rather than $P(Y|X)$ in terms of number of parameters?

In chapter 3 of the book by Mitchell ("Generative and discriminative classifiers: Naive Bayes and logistic regression") he states that "accurately estimating P(X|Y) typically requires many more ...
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Bayesian Linear Regression: pyMC3 vs. analytical solution

I was re-poducing the plots by Bishop 2006 p.155 and thought it might be interesting to compare both, the analytical solution provided by Bishop and an approximated MCMC soultion with ...
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Conditional density estimation review

Can anybody suggest textbooks/papers presenting a relatively up to date literature review on the subject of conditional density estimation? Specifically, I'd be interested in a comprehensive summary ...
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18 views

Bayesian Multiple Regression

I am trying to fit a model that has multiple parameters to experimental data. I can do this pretty easily only considering one parameter, but when I have multiple, I am having trouble. Here is my code:...
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How can I understand if my Beta Distribution is converging?

I am evaluating a Bayes AB Test on 2 variants, A and B. I then plotted a graph which shows the Probability of B is better than A on a daily basis. My worry comes in on the topic of 'peeking'. Let's ...
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How do I choose a prior for this hierarchical model? (Kruschke book)

I am working through Kruschke's "Doing Bayesian Data Analysis", currently working on the Hierarchical models chapter. The book uses JAGS for MCMC. One of the exercises asks the reader to compare two ...
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1answer
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Do I need to evaluate acceptance rates in Metropolis within Gibbs algorithm?

Consider the Gibbs sampler Sample $\theta' \sim p(\theta|\tau, D)$ Sample $\tau' \sim p(\tau|\theta', D)$ where $\theta,\tau$ parameters of the data $D$. Now assume that we can only sample from $p(\...
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$P(X>Y)$ for $X$, $Y$ not necessarily independent

I am interested in deriving an expression for the probability of a value $X$ being larger than a value $Y$. More specifically: I want to calculate an expression for $P(X>Y|I)$ and I know the ...
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How to implement Bayesian Model Combination on machine learning?

I'm working on combining the result of different forecast from machine learning models and i know we can use bayesian model averaging to calculate the weights but i still don't understand how since i ...
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In Jags, how does the stochastic node work? [closed]

...and what does the ~ sign mean compared to R in y[I] ~ dnorm(m[i],tau) vs ...
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71 views

Formal proof of Occam's razor for nested models

I consider 2 models $M_0$ and $M_1$, $M_1$ being more complicated than $M_0$ in the sense that it has more parameters (I usually assume than $M_0$ is nested within $M_1$). They are respectively ...
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Does there exist a Bayesian analysis of bias-variance decomposition of an estimator?

I was wondering if anyone could spare a moment to help with the answers to the following questions. Suppose we have an estimator $\hat{\theta}:\mathbb{R}^{d}\rightarrow\mathbb{R}$ such that the ...
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35 views

Posterior probability of hypothesis distributions

Suppose I have $K$ classes with distribution $\theta$ over $\{1,...,K\}$ and an underlying domain $D$ on which each class defines a categorical distribution $\phi_i$. Given a draw $i\sim\theta$ and $...
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whats the difference between sample and evaluate?

I'm reading a paper from F. 0. Bunnin, Y. Guo and Y. Ren. They state: Therefore we choose the SIR algorithm, a simulation procedure that requires only the ability to evaluate the likelihood ...
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1answer
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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 ...
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Likelihood in Bayes theorem vs in MLE

I know that similar questions have already been answered on this platform but none of them were really answering my specific question which is the following: Bayes' theorem arises solely by ...
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25 views

A beta distribution multiplied by a constant and a binomial distribution based on it are equal?

To get the number of "positive cases" I'm in doubt between two strategies. The first one is to draw samples from a Beta distribution: $p \sim Beta(\alpha + cases, \beta + non\ cases)$, using these ...
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28 views

Calculating marginal likelihoods for coin flip with/without prior beta distribution

I was given a problem where I need to "compare a simple and complex model by computing the marginal likelihoods" for a coin flip. There were $4$ coin flips, $\{d_1, d_2, d_3, d_4\}$. The "simple" ...
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37 views

Why can I use a PDF when computing bayes rule?

My understanding is that PDFs are 0-valued at all individual points, and only when we integrate over a specific region do we get a non-zero value. However, my professor keeps using PDFs when ...
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12 views

Time-dependent variable with varying delay between measures?

I would like to assess the association between a time-dependent variable, measured at different intervals in several subjects, the intervals being different between each subject and each measures, ...
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39 views

Linear regression $Y=X\beta+e$ with random coefficients $\beta$

Consider a linear regression model $Y=X\beta_0+\epsilon$. Here $Y$ is the response random vector of length $n$, $X$ is an $n\times p$ matrix, $\beta_0$ is a constant vector of length $p$, and $\...
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Is it possible to make predictions with Gaussian process regression using noise-free observations with the GPML toolbox?

I have just started to use the GPML toolbox for Gaussian process regression, and I need to apply it to a case where my observations are noise-free. From reading the GPML manual it is my understanding ...
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1answer
26 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 ...
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Proof of a causual (line) Bayesian graph model

Given a simple Bayesian graph model, and $A$ is observed. A <---- B <---- C The joint model is $$ p(A,B,C) = p(A\mid B,C)p(B\mid C)p(C), $$ which is true....
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28 views

Bayesian hypothesis test to compare theta >= 1 vs. theta < 1

Brand new to Bayesian statistics. I'm working a problem in R where I've used a Jeffrey's prior with a Poisson distribution to get a Gamma posterior. It's a simple problem where I've been able to ...
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44 views

Regression model with (almost) non-negative residuals

I would like to fit a regression model with continuous response and predictors. A fraction of the response is a non-negative linear combination of several predictors. What is not covered by this ...
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12 views

Mistake bound in halving with prior?

Some of the answers I found where - Question: What if we had a "prior" p on the different functions in C? Can we make at most lg(1/p_f) mistakes, where f is the target function? Ans: Sure, ...
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1answer
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Are p-value and Bayesian probabilities equivalent when applied to conversion rates?

For evaluating AB-tests, one can use the frequentist approach or a Bayesian one. Using these websites I compared both with some example data: https://abtestguide.com/bayesian/ https://abtestguide....
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How to sample in Bayesian inference model?

I have the following problem to model in R. If we have $X_1, ..., X_n \sim N(\theta,1)$ and want to estimate $\theta$, we assume $\theta$ has a prior distribution, and the Bayes estimate of $\theta$ ...
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42 views

Conditional Probability: Exponential and Multinomial

Problem There are 10 different drinks, labelled as $d_1,\cdots,d_{10}$, a runner can take during a marathon, each time he stops he takes (randomly) one drink, before running again. The distance (or ...
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9 views

How to Input to Neural Network Based on Discretely Observed Processes

I'm attempting to estimate the posterior mean for a set of parameters governing a Markov process, using a neural network to minimize squared error (and uninformative priors, along the lines of http://...
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Does Bayes theorem apply to joint distributions of discrete and continuous random variables?

Bayes theorem is defined for both discrete variables in terms of probabilities and continuous variables in terms of densities. If random variables $X,Z$ are jointly distributed, with $f_X(x)$ ...
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Extending Pareto / NBD Model with Regression

I'm interested in finding out how customer level features correlate to customer lifetime value. My idea is to use a Bayesian Hierarchical model that takes the Pareto NBD model and extends it with ...
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How to interpret variance of hyper parameters in Bayesian Linear/Logistic Regression

I'm building some models in PYMC for linear and logistic regression and placing priors over the parameters of the coefficients' distributions, e.g. model below. I've noticed that often the ...
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3answers
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Confusion about Bayesian statistics. Does the probability for heads change from .5 to 1, after observing heads?

P(A): The coin has a 50 percent chance of being Heads. P(A|X): You look at the coin, observe a Heads has landed, denote this information X, and trivially assign probability 1.0 to Heads and 0.0 to ...
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Would a posterior distribution with a flat prior look identical to the likelihood?

Graphically, let us assume that we have a flat prior for a normal distribution (a horizontal line at y=1 over all real numbers). Then, we have a likelihood function that resembles a normal ...
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How do I use the MCMC method to find the joint posterior of 4 parameters ($\lambda$,$\lambda_s$,$\mu$,$\beta$) of exponential distributions

Essentially, the problem statement is as follows. I have 2 functions in reliability theory called MTTF(Mean time to failure) and Availablity, both with inputs as $\lambda$,$\lambda_s$,$\mu$ & $\...
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Sensitivity of a diagnostic test

Diagnostic tests A1 and A2 are used to detect the presence or absence of a disease. The results of A1 and A2 are a priori independent of the presence or absence of the disease. A1 and A2 have ...

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