# 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 $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$

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### 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 ...
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### How to estimate the log-likelihood of 2 independent coins [closed]

Coin A has a probability p of landing on heads, and coin B has a probability q of landing on heads. Calculate log-likelihood of p and q given X
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### True or false and why true and why false [closed]

i) In the presence of multicollinearity, the variance of OLS estimators are quite fine only that t and F test are highly misleading. ii) Forecast is the quantitative estimation of the likelihood of ...
1 vote
41 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 ...
63 views

### The Likelihood Approach a.k.a. the 'third way' versus Bayesian

In his book "In All Likelihood" Yudi Pawitan writes that "the likelihood approach offers a distinct 'third way', a Bayesian-frequentist compromise. We might call it Fisherian as it owes ...
1 vote
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### Maximum Likelihood Estimator for Bernoulli distribution

Given a random sample $X_1, X_2,..., X_n$ from Bernoulli distribution. The log-likelihood function is: $\mathcal{L}(\theta) = \sum_1^n x_i^*\log{\theta} + (n - \sum_1^n x_i^*)\log{(1-\theta)}$ Score ...
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1 vote
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### Does approximating the likelihood function violate the likelihood principle in Bayesian Inference?

Suppose we have a prior $p(\theta)$ and a likelihood function $L(\theta|x)$, and that the likelihood $L(\theta|x)$ is intractable somehow (difficult or impossible to compute) and we instead replace it ...
138 views

1 vote
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### How to sample and compute the likelihood from a Mollified Uniform distribution?

I want to draw samples from the mollified Uniform distribution presented in another Cross Validated thread, cf the answer from whuber. What is the best way to do so?...
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### Equivalent ways of writing the log-likelihood of a sample of normal RVs

I am going through my econometrics textbook right now and the textbook writes the log-likelihood equation for a sample of normal random variables in a way I have never seen before. Specifically, for a ...
410 views

### AIC, BIC and log likelihood which more important?

I am currently searching for the best ARMA(p,q) model for my conditional mean. When comparing the AIC, BIC and LL, I see that some model perform better in AIC, some in BIC and some in LL. The AC and ...
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### Is the likelihood of a discrete binomial variable same as it probability? Like in the case of tossing a coin lets say 12 times

I am working on a probability project where we first generate random variables for a given Binomial experiment and then we generate a PMF for 10 coin tosses using the list of random variables we ...
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### fitting left censored models using software for right censored data

When analyzing a lognormal data with left-censored values using a regression model, I have read that you can use methods that fit right-censored data but “flip” the data by subtracting from some large ...
1 vote
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### Impact of Laplace smoothing on likelihood in Naive Bayes

When 1 is added to word count in Laplace Smoothing in Naive Bayes, the new probabilities either increase or decrease as shown below. Though the problem of "zero" probability has been solved. ...