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 $θ: \text{L}(θ)=\text{P}(θ;X=x)$

learn more… | top users | synonyms

1
vote
1answer
14 views

Picking a probability distribution for observed intensities

I have an experiment that measures "intensity" (in this case, electron density of a molecule) on a grid. The values it gives are non-negative,. I'd like to write a likelihood for this observation ...
1
vote
0answers
25 views

Determining a greater than chance cutoff for an assessment's results

I recently collected a set of data, and before I completed an analysis of it, I wanted to remove any "bogus" entries from participants that didn't actually read the stories. The study I conducted had ...
0
votes
1answer
49 views

Gradient of Log-Likelihood

Considering the following functions I'm having a tough time finding the appropriate gradient function for the log-likelihood as defined below: $a_k(x)=\sum_{i=1}^D w_{ki}\cdot x_i$ $P(y_k|x) = ...
3
votes
1answer
32 views

dirac delta function in likelihood function

I have tried to understand this myself but what I have found on the internet so far has not helped. I have a likelihood function that for part of it has the following statement: d0 is the Dirac ...
3
votes
2answers
44 views

Finding sampling distribution of normal MLE and likelihood

I'm reviewing old exams in preparation for a statistics final, and I'm stuck on a particular question: Suppose that you have n independent random variables $Y_i$, with each distributed normal with ...
7
votes
2answers
182 views

What would be an example of a really simple model with an intractable likelihood?

Approximate Bayesian computation is a really cool technique for fitting basically any stochastic model, intended for models where the likelihood is intractable (say, you can sample from the model if ...
-1
votes
0answers
7 views

Estimates of log-likelihood function for mixed of Bernoulli and beta distributions for overlapped summations of ranges of data [closed]

If the log likelihood function summed overlapped ranges of observations and it has the following form: llh=-∑(y(iϵ[0,1]))▒〖log⁡(1+e^(x∝) ́ )+∑(y(iϵ(0,1]))▒〖((x∝) ́)-〗〗 ...
0
votes
0answers
25 views

Bayesian Logistic Regression Likelihood Computation for Binary Data

For computing the likelihood function for a Bayesian Logistic Regression model, I understand the original form to be $$p(y_i|\beta,X) = \prod_{i=1}^{k}\left( \frac{ \text{exp} \{ \beta^{\prime} x_i ...
1
vote
1answer
19 views

Marginal Likelihoods for Bayes Factors with Multiple Discrete Hypothesis

If I have some data that I believe is Normally distributed and I just want to test the hypotheses that the mean is equal to 1 of 3 values, my understanding is that the Bayes Factor is the ratio of ...
3
votes
0answers
48 views

Explain log likelihood behaviour

(This question is related to a previous one I made, here) I have a set of 2D observations (measured data) of sample size $N$: $$O = \{(x_1, y_1), (x_2, y_2), ..., (x_N, y_N)\}$$ I also have a model ...
1
vote
1answer
70 views

Likelihood ratio test for comparing two exponential distributions

I am trying to use a likelihood ratio test to compare the parameters of two exponential distributions. by this thread Likelihood Ratio for two-sample Exponential distribution I found that I can use ...
0
votes
1answer
36 views

Point estimation MLE and MME

Consider the family of probability mass functions given by f(x;k) = 3(4^(k-x)) x = k + 1, k + 2,.... and indexed by parameter k E Z. For a random sample of size n, derive with justification: a) ...
0
votes
0answers
37 views

Question on Nested Likelihood Ratio Model

Suppose I want to calculate a likelihood test statistic distribution for background only MC using following Likelihood Function with Signal Fraction = $ns$ and $\theta = (a,b,c)$: ...
0
votes
0answers
5 views

Multiplying distributions with different conditioning

I saw this expression in a UBC machine learning class lecture, and I'd like to understand how the math works. Suppose we're trying to predict a class label $y$ given some data $x$. There are prior ...
3
votes
1answer
78 views

“weight” input in glm and lm functions in R

I am confused with the definition of the weights in glm and lm. Using the McCullagh and Nelder (1989)'s notation, If random variable $y_i$ is from the Generalized Linear Model (GLM), then its density ...
0
votes
0answers
32 views

Two Gaussian Likelihoods with Two Decision Boundaries , 0/1 loss function

we assume that Y := {1, 2}. Then our decision can be re-written as y ∗ = {1 if p(x|y = 1) > p(x|y = 2) , 2 otherwise} with a decision boundary at p(x|y = 1) = p(x|y = 2). How can we construct an ...
0
votes
1answer
44 views

Maximizing Log-Likelihood Estimation for Changepoint Detection

I'm trying to code the changepoint detection algo described here: ...
0
votes
0answers
24 views

Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood

I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...
1
vote
1answer
49 views

Probability to Likelihood

I have a problem on calculating the likelihood of observing a data point x given the predicted lable. My application is on text classification where I have to detect Spam and No Spam documents. I ...
2
votes
1answer
68 views

What would be the likelihood function of a pdf, $p(n)=1-|n|$ for $|n|<1$?

This might seem like a basic question to some but I am utterly confused by the fact that the given pdfs are not Gaussian or any other distribution commonly seen in examples. I have two hypotheses ...
0
votes
1answer
83 views

Gaussian Process Regression/ Classification

How do we estimate parameters of the model while performing Gaussian Process Regression or Classification? While performing regression, we estimate parameters such that the model is the best fit to ...
1
vote
0answers
35 views

Cross validation with unequal sample size for the left out sets

I am trying to do cross validation on several (20) subsets of samples, which all have unequal sample size. I cannot subsample so that sizes are equal. Example: batch 1: 500 samples batch 2: 400 ...
1
vote
1answer
74 views

R - MLE of modified Champernowne density

I've come across an article (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=704903), in which author wrote about maximum likelihood estimates of parameters in the so called modified Champernowne ...
8
votes
1answer
107 views

Observed Fisher information under a transformation

From "In All Likelihood: Statistical Modeling and Inference Using Likelihood" by Y. Pawitan, the likelihood of a re-parameterization $\theta\mapsto g(\theta)=\psi$ is defined as $$ ...
2
votes
1answer
30 views

Copula estimation

I want to fit a copula distribution. My question is: Is it equivalent to estimate the marginal distributions using marginal samples and later estimate the parameters of a copula to estimating all the ...
1
vote
0answers
20 views

Marginal pseudo-likelihood and consistency?

For a given set of random variables, $X_1,...,X_n$ we know that in many cases finding the maximum of the pseudo likelihood: $$PL(x_1,\ldots,x_n) = \prod_{i=1}^n p(x_i | ...
3
votes
1answer
46 views

How is it meaningful to give fitted values for random effects if they don't appear in the likelihood function?

Software for fitting random effects models tends to output values for the random effects. For example, suppose the model is $$y_i = \alpha_i + \varepsilon_i, \qquad 1 \le i \le n$$ where $$\alpha_i ...
0
votes
0answers
7 views

Segregation Analysis for predicting age-specific cancer risk

I am relatively new to the worlds of bioinformatics and genetics research. I have been tasked with presenting to my lab the potential value of a paper that uses Complex Segregation Analysis for a risk ...
0
votes
0answers
18 views

How adapt MCMC when (constant) weights for oberservations are introduced?

I have the following problem: I have already set up a model and MCMC sampler for a mixed model without weights, i.e., every observation contributes the same amount of information. Now I would like to ...
1
vote
1answer
28 views

Distribution of log-likelihood gradient

My question is simple: Is there any results regarding the distribution of log-likelihood function gradient? It may be asymptotic results as well.
0
votes
0answers
30 views

likelihood problem with exponential distribution using R

How can I solve this problem using likelihood in R? The data below are the survival time (in years) for 10 patients over 65 years after the diagnosis of a particular type of cancer: 10.5 0.2 7.4 0.8 ...
0
votes
0answers
13 views

In-sample likelihood ratio test for losses

Probably a very simple question for practitioners but I am doing this the very first time: I have written a programm for the estimation of a conditional variance model (HEAVY) of return data and an ...
2
votes
0answers
55 views

Problem with Finding Likelihood: Bayesian

I am really unfamiliar with Bayesian methods particularly parameter estimation. Suppose I have a test to find a parameter, theta which is the number of packaged bag for retail sale that could contain ...
0
votes
0answers
10 views

Trying to reproduce predictive likelihood

I'm trying to reproduce the average predictive likelihood from page 13 (Eq 4.1) from the following paper and I'm struggling to find the function f_M,k(...). It details more about it on page 14 but I ...
0
votes
0answers
42 views

Distribution of a MA(1) process

Suppose I have this MA(1) model: $y_t = \mu + \epsilon_t + \theta \epsilon_{t-1}$ with $\epsilon_t \sim \mathcal{N}(0,\sigma^2)$ The marginal distribution of $y_t$ for all $t$ is ...
0
votes
0answers
19 views

Log likelihood of a Markov network

This is the plot of the log likelihood function from Daphne Koller's course. Two axes are $\theta_{a_1, b_1}$ and $\theta_{b_0, c_1}$. Can someone please explain for me the shape of this plot? From ...
1
vote
0answers
57 views

log-likelihood for a beta-binomial in R

Although I may ask a question that is already solved (but I found none that would explicitly refer to this), I would like to know, if (and I am no statistician) I am right with programming the ...
1
vote
0answers
18 views

Marginal Likelihood Latent Variable Model

I am trying to apply the method proposed by Chib in Marginal Likelihood from the Metropolis Hastings output to calculate the marginal likelihood of a logit model the includes latent variables. ...
0
votes
0answers
20 views

Can we use log-likelihood to cluster classes?

I have an SVM classifier for m classes and n data points (somewhat evenly distributed across each class). Could I use the resulting MxN log likelihood matrix to merge classes that are similar?
1
vote
1answer
62 views

Loglikelihood and unusual transformations with binary response models

I was just doing some thought on the transformation for likelihoods to log likelihoods for binary response models and I realized what I am sure many people have realized before that the transformation ...
2
votes
2answers
77 views

Log-likelihood (and AIC) of robust nlrob model differs from standard nls model

Comparing models generated by nlrob to ones generated by nls, I've noticed that even though the models might be nearly identical, the log-likelihood of the models is sometimes significantly different, ...
2
votes
0answers
42 views

Estimation of log-likelihood via importance sampling

I am looking at a model trained with stochastic gradient variational Bayes. In this paper an importance sampler is proposed to estimate the likelihood: $$p(x) \approx {1 \over S} \sum_{s=1}^S ...
1
vote
0answers
16 views

Simulated MLE does not exist, when trying to Bootstrap likelihood combinant

Consider this simple logistic model: We have ten $0/1$ observations $y_1,...,y_{10}.$ We model with an intercept and a predictor variable.The ten first observations have predictor value $X_i=0$, ...
3
votes
2answers
53 views

ABC: Why not use the distance measure as a pseudo-likelihood instead?

I've read about the ABC rejection algorithm when not being able to calculate the likelihood directly, and my question is: if we have to introduce a distance measure $\rho(D,D')$ anyways, why not use ...
0
votes
0answers
59 views

Pseudo-likelihood and RBMs

I need to train a restricted Boltzmann machine to model the joint probability of categorical variables. For this I adapted a Bernoulli RBM to have groups of softmax units in the visible layer. The ...
1
vote
1answer
121 views

Why likelihood is not always a density function? [duplicate]

I try to self-learn Bayesian machine learning (mostly by studying Bishop and Kevin Murphy's books). While working with formulas I was puzzled by the quote that "Note that the likelihood function is ...
2
votes
1answer
149 views

fitdistr loglik in R

I am fitting a few time series using fitdistr in R. To see how different distributions fit the data, I compare the log likelihood from the ...
2
votes
1answer
72 views

How to construct a reasonable prior and likelihood for Bayes modelling?

To apply Bayes inference for data analysis or machine learning, we have to construct prior and likelihood, right? But if I fail to come up with a reasonable prior and likelihood, then the Bayes model ...
3
votes
0answers
43 views

Likelihood Function for Complicated Transformations

Suppose that data X have a Normal distribution with some mean $\mu$ and some variance $\sigma^2$. However, you don't get to see X. Instead, you see $Y = g(X)$ where $g$ is a known function. Assume ...
0
votes
0answers
18 views

Marginal Likelihood & Truncated Posterior Mixing

It has now become common to use Bayesian inference to find the best solution for exoplanet orbits fitting. In order to find the best solution one has to explore a very large parameter space and some ...