Questions tagged [bayesian]

Bayesian statistics is a statistical paradigm that contrasts with that of frequentist statistics. Bayesian methods rely on prior information do determine the degree of belief in the probability of a value.

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How does posterior distribution relate to model parameters

I want to know how the estimation of a posterior through a sampling method for example HMC could help with predicting a model, and why predicting model weights/parameter is important and how it is so?
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What is the Bayesian distribution of two p.d.f's?

I whant to make this: Theese are the inputs I'm traying to replicate this for my app, but don't know how its done. As you can see, there must be a preset value for the sigma with the inputs of type ...
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Hamiltonian Monte Carlo Potential Expression

Going through the literature i noticed two different expressions for the potential U expression used for the Hamiltonian Monte Carlo method: The first one depending on ...
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Probability for Nth Place in Race from Bradley-Terry Model Inputs and Outputs

I have created a motorcycle race prediction model that is given pairs of racers and outputs the probability of each rider beating the other in each pairwise comparison. That info is then processed ...
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Bayesian state description in Reinforcement Learning

What's the best approach to feed a bayesian description of an observed state to a Reinforcement Learning agent? Brief context: I have an agent situated in an environment, which it perceives through a ...
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Why aren't Bayesian models straightforwardly superior to all/most other models if they model the real-world better?

Why aren't Bayesian models straightforwardly superior to all/most other models if they model the real-world better? As possibly displayed by the following chart: source
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How "much" should belief be weighted against numerical measures of accuracy/correctness?

How "much" should belief be weighted against numerical measures of accuracy/correctness? It's possible to devise numerically low-quality models, but that have very good empirical validity, ...
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How to guide exploration in reinforcement leanring/model predictive control/dual control problem

Consider the following optimization/control problem: We aim to maximize the cumulative reward R during the horizon H by every day allocating a portion of total budget B to our two different investment ...
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How calculate probability when we have continuous features?

Suppose that we have a dataset with four features and each feature follows different distribution (normal,beta,gamma...). All features are continuous. So, how we can calculate the probability of any ...
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Problem understanding the forward algorithm for HMMs

I found a recursive version of the forward algorithm on wikipedia, however I don't understand the notation given in the pseudocode: What means $$x_{t-1}$$ under the summation sign? What do I need to ...
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What methods I could use to analyze the contingency table?

I am data science beginner, and I have a question about methods that I could use to analyze the following data. It is a simple case, I am trying to check the influence of cohabitation before marriage ...
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Understanding error in bayesian inference

Let us say we have: Data $X$ Parameter that we are trying to estimate is $\Theta$ The Bayesian estimation method is to Assume a prior on $\Theta$ Sample $x$ from $X$ Use Bayes theorem. Compute the ...
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How to combine data measurements with underlying model?

The problem I am trying to solve is this: Imagine you are in the situation where you want to predict car performance according to some characteristics (horse power, car dimensions, etc...). The data ...
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Computing probabilities in Plackett-Luce model

I am trying to implement a Plackett-Luce model for learning to rank from click data. Specifically, I am following the paper: Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for ...
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What are the requirements for a word list to be used for Bayesian inference?

Intro I need an input file of 5 letter English words to train my Bayesian model to infer the stochastic dependency between each position. For instance, is the probability of a letter at the position 5 ...
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Incorrect example of applying Bayes theorem

I have been reading the book "The Data Science Design Manual" (by Steven S. Skiena) and I came across an example that explained how the Bayes theorem can be applied that confused me and made ...
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Why and how Variational Inference underestimates variance?

I referred to the Quora link here as well, but could not understand clearly. Can anyone please help me understand why and how variational inference underestimates the variance of the true posterior ...
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Confusion regarding which distribution Monte Carlo considers for sampling

Considering Bayesian posterior inference, which distribution does Monte Carlo sampling take samples from: posterior or prior? Posterior is intractable because the denominator (evidence) is an ...
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Model transfer with limit to none label information

I have this problem I hope to get some help here. Say I have a type of product A whose measurements are X_A and an outcome property is ...
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How to test if a curve is well described by an ellipse?

I have a set of data points in 2D, and I am trying to come up with some sort of statistical to determine if the points fall along an ellipse. My idea so far is to fit an ellipse to the points, take ...
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Confused on Naive Bayes classifier

In the last part of Andrew Ng's lectures about Gaussian Discriminant Analysis and Naive Bayes Classifier, I am confused as to how Andrew Ng derived $(2^n) - 1$ features for Naive Bayes Classifier. ...
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Hierarchical Bayesian model

Are Multinomial Naive Bayes, Multi-variate Bernoulli Naive Bayes, and semi-naive Bayes, considered to be Hierarchical Bayesian models?
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What thought processes do people use for generating priors on a variable's probability distribution?

Example Consider a block of text with a variety of sentence types within it, of which there are 7. Within a text these sentences will be more or less likely to appear, dependent on where in the text ...
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Probability distributions for Directed Cyclic Graphs

Given a directed cyclic graph where vertex A is 'infected', and there are different infection probabilities between each node, what is the best approach towards computing the conditional probability $...
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Hidden Markov Model with control input?

Given that HMMs and Kalman Filters are both state space models with recursive aspects and KFs allow for control inputs to influence the prediction at each step, I'm wondering if any similar methods ...
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Linked Bayes Boxes

(You might think that this is more a more appropriate question for MathEd, but they tell me that it's more appropriate here, so go figure...) I'm trying to use linked Bayes Boxes in a spreadsheet to ...
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Combine prior knowledge probability with ML model probability results

I want to combine prior knowledge to improve my machine learning model. According to Bayes rule, max posterior is obtained when multiply prior with MLE. I multiply prior probability with the machine ...
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Markov Process and transition matrix

I would like to find some good courses but also a quick response on how to model transition matrix given the states. Imagine having 4 states and the following array [1,2,4,1,3,4,2 etc etc]. What ...
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Are there any implementations of non Naive Bayes Classifier in Python?

Naive Bayes assumes that predictors are independent. Though this assumption is quite powerful, in some scenarios it fails miserably . So are there any implementations of non Naive Bayes in Python ? ...
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Lasso (or Ridge) vs Bayesian MAP

This is the first time I have posted here. I am looking for some feedback or perspective on this question. To make it simple, let's just talk about linear models. We know the MLE solution for the $l_1$...
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Bayesian Linear Regression using the Kernel Trick vs Constructing features using Kernels as Prototypes

How different is it to do Bayesian linear regression using the GP approach (kernel trick) versus constructing features using kernels to prototypes? As far as I know, this very basic question is ...
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Expectation of ELBO in Variational Autoencoder

I am working with VAEs. My input is x, which is a product of two variables $x_1$ and $x_2$. The objective (ELBO) of VAE in terms of x is: $E_{z\sim Q}[\log P(x|z)] - \mathcal{D}[Q(z|x)||P(z)]$. I want ...
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How to predict categories without class labels using Bayesian methods?

Suppose I have the following financial data. I have to output a column with its result that shows what type of categories each row belongs. It can be an income, an expense, or a Capex (Capital ...
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Bayes theorem on the probability of an object drawn at random using percentages (not Naive Bayes)

It's the normal Bayes equation but I'm not sure if I've calculated this correctly or how to check my work, here is a somewhat similar question but I wasn't sure if our math was the same, the question ...
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Multivariate testing

I'm going to run a test with 4 different variants (3 variants and a control group), and we want to find the variant with the highest conversion. Are there any resources/methods in R/python to: ...
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Really confused with characteristics of Naive Bayes classifiers?

Naive Bayes classifiers have the following characteristics-: They are robust to isolated noise points because such points are averaged out when estimating contiditional probabilities from data. Naive ...
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How does bayesian optimization with gaussian processes work?

Could someone explain in simple words what are gaussian processes how does bayesian optimization work and their combination?
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How useful is Bayesian Inference

Last few months, I had been exposed to Bayesian Inference in ML course With further investigation, I come to place where there is MCMC technique to simulate the ...
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Update of mean and variance of weights

I'm trying to understand the Bayes by Backprop algorithm from the paper Weight Uncertainty in Neural Networks, the idea is to make a NN in which each weight has it's own probability distribution. I ...
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High Recall but too low Precision result in imbalanced data

I was training a model using XGBoost Classifier on a heavy imbalanced database with 232:1 of binary class. Because my training data contains 750k rows and 320 features (after doing many feature ...
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Is it a good idea to use the mean and standard deviation of coefficients from other models as my prior in Bayesian Regression?

I have a dataset that I’ve been playing around with for school I have gotten very good results with a bunch of methods (Ridge, Lasso, ElasticNet, SVM, Bagging, Stacking and NN even) Now I’m having a ...
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Calibration curve motivation

I struggle to understand the mathematical motivation for the binary classification model calibration curve. Why do we assume that the predicted probabilities should be consistent with the proportion ...
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Does the Bayesian MAP give a probability distribution over unseen data?

I'm working my way through the Bayesian world. So far I've understood that the MLE or the MPA are point estimates, therefore ...
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Algorithm to determine a single output value based on multiple input values [closed]

The main challenge is the lack of data. Input values come from tests results of patients. A patient takes a breath test at an interval during a timespan. The result values can range from 0 to ~200, ...
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Combining multiple probabilities from a classifier. Propagating probabilities

Let's say I have trained a classifier that classifies images of animals into 10 different classes. And let's say that I have 20 different images of a particular animal and because I know the ...
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What is the num_initial_points argument for Bayesian Optimization with Keras Tuner?

I've implemented the following code to run Keras-Tuner with Bayesian Optimization: ...
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Hyperparameter tuning with Bayesian-Optimization

I'm using LightGBM for the regression problem and here is my code. ...
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Changing the batch size during training

The choice of batch size is in some sense the measure of stochasticity : On one hand, smaller batch sizes make the gradient descent more stochastic, the SGD can deviate significantly from the exact ...
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How is bayesian risk computed to prune decision trees?

I've been trying to follow this paper on Bayesian Risk Pruning. I'm not very familiar with this type of pruning, but I'm wondering a few things: (1) The paper describes risk-rates to be defined per ...
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Visualize n-dimensional bayesian optimization results

I am working on a 6-dimensional bayesian optimization problem using (skopt's gp_minimize). After the optimizer ran for j iterations I would like to somehow visualize the "progress/result" of ...
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