# 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 $θ: \text{L}(θ)=\text{P}(θ;X=x)$

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### Does the newton-raphson either find the maximum of the loglikelihood function or estimate the MLE and likelihood function? [closed]

Does using newton-raphson method or some other optimization method used in nlme package or mixed effects models actually find the maximum of the log-likelihood function's height or does it simply find ...
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### Difference Between $L(θ | X=x)$ and $P(θ | X=x)$? [closed]

Although statistically different, I feel like they both say the same thing? $L(θ | X=x)$ = the probability that a sample provides support for particular values of a parameter in a parametric model. ...
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### Choosing between two normal distributions

I have two normal distributions with different means and variances: N(u1, s1) N(u2, s2) And I have some data points (X) that were sampled from each of them. For each data point, I want to calculate ...
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### How to transform/convert likelihoods to scores?

I have the probability of loan default for a labeled dataset where the distribution of probabilities is heavily skewed. Labels are defined as "good/0" for no default and "bad/1" for defaults. My goal ...
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### On likelihood functions and characteristic functions

Let me preface this by saying that if someone manages to provide a solution to my problem, I will forever be indebted to them, as this problem has driven me crazy. Let us first assume that the ...
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### Extend likelihood equation to P(Y>=y) in R

This question involves both math and coding in R. Apologies if this should be on Stack Overflow, but I decided statisticians would ultimately provide better support....
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### Is it not necessarily to put observed data at the right of the bar symbol $\mid$ when computing likelihood?

This Machine Learning course with timestamp is talking about PERFORMANCE MEASURE. Assume there are 3 loan officers A, B and C (correspond to you, blank, your "Friend" on the blackboard) , assigned ...
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### Likelihood for aggregated survival data?

Most literature on survival models assumes that the data is either a collection of individual survival times or right-censored individual survival times (so you know when some subjects failed but for ...
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### Using Likelihod Ratio vs Hypothesis Testing to test claims?

I don't know if I am missing something obvious but it seems likelihood ratio and hypothesis test serve the same function, to test claims about population parameters using sample data ( correct?). I ...
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### Delimit the area in that parameter space that contains 95.4% confidence

Given the equation $y = fc + fe\times \sin(2\pi(x-t_0)/12)$ Considering the two parameters of amplitude fc and fe simultaneously, delimit (using the χ2 variation method) the area in that parameter ...
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### Post-hoc t-tests for ANOVA

My sociology professor said that when performing multiple t-tests between two groups after the ANOVA f-test, the likelihood to make at least one type-1 error adds up by 5% with each t-test. So for one ...
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### Likelihood ratio test for language modeling

I am trying to use a likelihood ratio test to evaluate whether one language model is significantly better than another. (Note: In the example below, the language models should not be very different, ...
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### Invariance of maximum likelihood estimates to rearrangements of parameters/constants in the model?

I know that maximum likelihood estimates are invariant to re-parametrization (https://stats.stackexchange.com/a/335368/267430). Is the MLE also invariant to rearrangements of the constants and ...
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### How to calculate 'times likely' for a percentage and whole number data set?

I'm analyzing speech data for single people vs those in group. I have two types of datasets for which I want to calculate "times likely". ...
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### How to compute statistical significance using a likelihood ratio?

The title really says it all. Suppose I have a change in log-likelihood (i.e., $\Delta LL = LL_{fitted} - LL_{null}$), and I would like to compute the $1\sigma$, $2\sigma$, etc. confidence region from ...
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### Maximum likelihood estimator when $\sum_{j} \theta_j = 1$. How to impose this condition? [duplicate]

I have a sample $x_1,\dots,x_n \stackrel{iid}{\sim}f(;\boldsymbol{\theta})$, where $\boldsymbol{\theta} = (\theta_1,\dots,\theta_d)$, and , $0<\theta_j<1$, $\sum_{j=1}^d\theta_j = 1$. I can ...
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### Explanation of Equation 5.3 from Gaussian Processes for Machine Learning

I am currently reading through C. E. Rasmussen & C. K. I. Williams' Gaussian Processes for Machine Learning and was going through chapter 5. I could not exactly understand the derivation of ...
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### likelihood function of a line regression equation

I am a bit confused at how can i find the likelihood function and the solutions of likelihood function for a line equation, for example y=3x+15
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### likelihood functions

Assuming that a linear regression model is fitted to 5 distinct datasets and that in all cases the regression line is y = ax+b+e . Will The likelihood functions are the same for the two different ...
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### Calculating Likelihood from misfit?

I am performing a geophysical inversion where the result is an ensemble of models (~400000) with their misfits. I want to calculate the likelihood of each model from the misfit values which is given ...