The likelihood tag has no wiki summary.
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48 views
How to implement this maximum likelihood algorithm?
I have a log-likelihood function
$$l(b) = \sum_{i=1}^n \left( \log(b_0 + b_1 x_i + b_2 x_i^2) \right) - \sum_{i=1}^{n+k} \left( \int_a^{x_i}\exp(b_0 + b_1u + b_2u^2 + b_3 u^3) du \right)$$
For ...
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2answers
80 views
Why is the Likelihood function NOT a case of the inverse fallacy?
This may be a trivial question, but as a research psychologist I do not have a robust statistics background to answer it.
It appears to me that the likelihood function--$L(\theta | \text{data}) = ...
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1answer
43 views
Multi-parameter log likelihood of Normal distribution for two separate samples
I have been given two sets of independent random variables distributed by two different normal distributions $X_1,...,X_n \sim N(\theta_1,1)$ and $Y_1,...,Y_m \sim N(\theta_2,1)$. And have been asked ...
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2answers
90 views
Computation of likelihood when $n$ is very large, so likelihood gets very small?
I am trying to compute this posterior distribution:
$$
(\theta|-)=\frac{\prod_{i=1}^{n}p_i^{y_i}(1-p_i)^{1-y_i}}{\sum_{\text{all}\,\theta,p_i|\theta}\prod_{i=1}^{n}p_i^{y_i}(1-p_i)^{1-y_i}}
$$
The ...
3
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1answer
55 views
Questions on likelihood analysis
Whilst studying likelihood methodologies, I've come across some results that I haven't been able to work out.
If $X$ and $Y$ are Poisson with means $\mu_{X}$ and $\mu_{Y}$, then the conditional ...
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0answers
83 views
What is the relationship between R² and Log Likelihood?
I estimated a non-linear model using the MATLAB function @fmincon which returns me a Log-likelihood value.
I also estimate a linear model (OLS) from which I can compute the R².
Here I need to ...
2
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0answers
42 views
MLE estimation together with volatility estimation
When I am estimating a linear time series model (i.e. ARMA) with Maximum Likelihood Estimation, if I also estimate volatility with a model like GARCH (or some other model) and use that variance value ...
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76 views
Model comparison when models differ in complexity and the data used fit them
Let's say I have two models and two data sets. Lets call them $M_1$, $M_2$ and $D_1$, $D_2$. We fit $M_1$ to $D_1$ and $M_2$ to $D_2$.
Now I would like to compare how well they did. When doing that I ...
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0answers
29 views
Possible outcomes of approximate profile-likelihood estimator (APLE) for spatial autocorrelation
I've been working with spatial autocorrelation for a while and now I'm trying to move from more traditional estimators such as Moran's I or Geary's C to the new APLE estimator. I read Li's papers on ...
3
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1answer
100 views
Calculating the likelihood of time series data when there are missing data
I am trying to calculate the log-likelihood of some time series data given parameter sets estimated in BUGS. I can not figure out how to handle some missing values at random points in time.
For the ...
2
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1answer
232 views
Calculating log-likelihood for given MLE (Markov Chains)
I am currently working with Markov chains and calculated the Maximum Likelihood Estimate using transition probabilities as suggested by several sources (i.e., number of transitions from a to b divided ...
2
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0answers
51 views
Confusion related to calculation of likelihood
I was reading this paper related to Learning from multiple annotator using Gaussian processes. The idea is if we don't have the actual ground truth of a certain data, but only the labels from some ...
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0answers
25 views
Help in calculating of gradient [closed]
I have a function $f(D) = \sum_{n=1}^N \frac{1}{2}(o_n-Dy_n)^T*\phi^{-1}*(o_n-Dy_n)$
I want to know what its gradient with respect to $D$ will be . I tried a couple of things but I am not sure what ...
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0answers
156 views
Comparing non-nested models with out of sample likelihood
I recently read a paper in which the authors claim that in order to compare the forecasting performance of two non-nested models, models A and B, a valid procedure is to fit models A and B on the same ...
1
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1answer
121 views
Likelihood ratio test for sex ratio
I am trying to solve this problem:
Assume that each child is male with probability $p$ independently of all other children.
We observed 19711 male births out of a total of 38562 births in American ...
2
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1answer
130 views
What is the difference between 'Laplace approximation' and 'Modified harmonic mean'?
this question is about Bayesian and computational statistics. I am learning them right now, I have two very common output from my software, one is Laplace approximation and the other is Modified ...
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60 views
Can we conclude structural break from the following results?
The following figure shows the log-likelihood of individual observations for different subsets of a data set - the horizontal line shows the average log-likelihood:
So, the first subset includes ...
3
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1answer
173 views
Who invented profile maximum likelihood estimation?
Could anyone give me some information on who invented profile maximum likelihood estimation or who first use profile maximum likelihood estimation and the short history of profile maximum likelihood ...
1
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1answer
173 views
Normalization of likelihood
If I'm not wrong, likelihood functions are sensitive to the size of the sample, i.e. the larger the sample, the lower the likelihood value. Given a sample $x$ of a random variable $X \sim f(\theta)$, ...
1
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1answer
134 views
Can a neural network output represent a posterior probability?
I seem to remember from years ago when I first read Bishop's ANN book that it is possible to construct a neural network such that the outputs should represent the posterior probability that I would ...
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1answer
207 views
If the likelihood principle clashes with frequentist probability then do we discard one of them?
In a comment recently posted here one commenter pointed to a blog by Larry Wasserman who points out (without any sources) that frequentist inference clashes with the likelihood principle.
The ...
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96 views
Learning hidden Markov model where transition/emission/initial probabilities aren't independent
I'm working on a problem that I've cast as an HMM, except that unlike the "traditional" case where the transition probabilities $a(i,j) = p(s_i = j \,|\, s_{i-1}=i)$, emission probabilities $b(j,o) = ...
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0answers
95 views
Retrospective power analysis of samples from Poisson distributions
I understand how the simulation at Power calculation for likelihood ratio test can compute the alpha, using prop.test, and the power from a direct count of simulation values, for two Poisson ...
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122 views
Computation of log-likelihood in semi-supervised naive bayes
I have the following 2 questions about log-likelihood computation in semi-supervised Naive Bayes.
I have read on several documents online that, in every EM iteration of the semi-supervised Naive ...
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1answer
174 views
Specifying the Form of Prior, Likelihood and Posterior Distributions for Bayesian Analysis
I have recently begun to look into Bayesian Analysis, and, although I'm beginning to get to grips with the general framework (i.e. $\text{posterior} \propto \text{likelihood} \times \text{prior}$), ...
3
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2answers
237 views
Likelihood vs conditional distribution for Bayesian analysis
We can write Bayes' theorem as
$$p(\theta|x) = \frac{f(X|\theta)p(\theta)}{\int_{\theta} f(X|\theta)p(\theta)d\theta}$$
where $p(\theta|x)$ is the posterior, $f(X|\theta)$ is the conditional ...
1
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1answer
148 views
Hypothesis testing using the likelihood ratio test
How can I apply the likelihood ratio test when I have the following hypothesis for collocation discovery:
$$H_{1}: P(w^{2}|w^{1}) = p = P(w^{2}| \neg w^{1})$$
$$H_{2}: P(w^{2}|w^{1}) = p_1 \neq p_{2} ...
1
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1answer
209 views
How do I complete the square with normal likelihood and normal prior?
How do I complete the square from the point I have left off at, and is this correct so far?
I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get:
...
2
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1answer
95 views
Dealing with project uncertainties: is the sum of the most-likely estimates equal to the sum of the expected times?
I found this document on the internet: Dealing with Project
Uncertainties
In this article I read:
In order for uncertainties to be included in the project estimates it
is necessary to take ...
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2answers
175 views
How to estimate storage needs using the PERT distribution for filesizes? How to aggregate them without falling into the flaw of extremes?
Lets say I know that I am going to store the information of 10,000 people each year for 4 years, that is 40,000 files. Now If I estimate that on the best case scenario the information from each ...
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2answers
120 views
What's the difference between likelihood and confidence in claim being true
I'm reading the IPCC report on climate change from 2007.
In their uncertainity guide they make a distinction between likelihood and levels of confidence.
What's the difference between the terms?
...
2
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1answer
248 views
What is the difference between “priors” and “likelihood”?
I have been reading some papers regarding statistics and I seem to be confusing the terms priors and likelihood.
Would it be possible to explain the difference between the two terms? I am interested ...
