# Questions tagged [likelihood]

Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as the probability of observed data as a function of $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$

1,417 questions
Filter by
Sorted by
Tagged with
1 vote
27 views

### Normalising likelihood for BIC/AIC calculation

I am running some model inference using AIC and BIC. My problem is that when I go and calculate the (maximum) loglikelihoods of my models, they are usually really high (range between 4700 and 1400 ...
• 13
38 views

### How to determine if the log likelihood of logistic regression is too large or not?

I am running a logistic regression on STATA with binary response variable, and 2 predictor variable that are discrete, as such one is in % (but takes only 2 values strictly i.e., 5% or 10%) and ...
• 51
1 vote
40 views

### Is it practical to derive the prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"?

Is it practical to derive the optimal prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"? Suppose you assume a probability distribution. You ...
22 views

### Marginal Likelihood Computation for Bayesian Linear Model

Given a simple Bayesian linear model with $N$ observations $y = X\beta + \varepsilon \quad \quad \varepsilon \sim \mathcal{N}(0, \Sigma)$ with known error variance-covariance matrix $\Sigma$ and ...
• 651
32 views

### Likelihood of a random vector with each component following a different distribution

How do you write down the likelihood for random vectors when each component follows a different distribution with a dependence structure? For example, Suppose there are n-random vectors, mutually ...
13 views

### Which is the likelihood function of the logit model? [duplicate]

I'm wondering which is the likelihood function for a logit model and how I can derive it. Thanks!
1 vote
30 views

### Derivation of Box-Cox and Yeo-Johnson Log-Likelihood Functions

The scipy documention lists expressions for the Log-likelihood functions for the Box-Cox and Yeo-Johnson transformations here and here. I'm looking for a source ...
• 314
43 views

### How to find the regression model log likelihood of data $(x, z, b)$ where $b$ indicates whether $y > z?$

I have a dataset where I don't have the exact output labels $y$ but what I have is if $y$ is larger or smaller than another value $z.$ There is another binary parameter $b$ that decides if y is ...
47 views

### Coding the likelihood function for logistic regression

I would appreciate help in understanding if I made a correct interpretation and coding of the likelihood function for logistic regression. Background: For a task I am going to write a function in <...
• 23
17 views

### Does adding more covariates always increase the condition number of the Hessian, and can you have a high-condition number but higher log-likelihood?

Does adding more covariates always increase the condition number of the Hessian, and can you have a high-condition number but higher log-likelihood/more optimal model? Should we ever not use the model ...
39 views

• 343
10 views

### Variational Autoencoder Not Explicit Likelihood

I was reading the Wikipedia page for flow-based generative models. On the page, it says "In contrast, many alternative generative modeling methods such as variational autoencoder (VAE) and ...
19 views

1 vote
30 views

### Binomial vs Bernoulli Likelihoods: Difference assumptions of independence across observations

In Bayesian statistics, logistic regression can be facilitated by priors, a link function, and a likelihood choice of either the Bernoulli or Binomial distributions. My question is whether this design ...
• 1,728
10 views

### Is the log-likelihood a good metric to determine the appropriate number of gauss-hermite quadratures for GLMM?

Is the log-likelihood a good metric to determine the appropriate number of gauss-hermite quadrature for GLMM? I saw a case where the estimation does not converge for some values of quadratures, and ...
1 vote
28 views

### Likelihood function-expectation

Given likelihood is a function of parameters, I cannot understand why the expectation of likelihood functions is not calculated with respect to the the parameter space but the sample space, as put ...
• 11
1 vote
17 views

• 133
15 views

### Test for seasonality with LR-test?

I have an economic time series in monthly frequency. I want to test for seasonality using LR-Test. So the idea is to: Regress the time series y on a model with a time trend and 12 seasonal dummy ...
1 vote
223 views

### Understanding the Evidence Lower Bound (ELBO)

I am reading this tutorial about Variational Inference, which includes the following depiction of ELBO as the lower bound on log-likelihood on the third page. In the tutorial, $x_i$ is the observed ...
• 1,487