Questions tagged [parameterization]

For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.

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19
votes
5answers
2k views

What's in a name: hyperparameters

So in a normal distribution, we have two parameters: mean $\mu$ and variance $\sigma^2$. In the book Pattern Recognition and Machine Learning, there suddenly appears a hyperparameter $\lambda$ in the ...
39
votes
7answers
6k views

Would a Bayesian admit that there is one fixed parameter value?

In Bayesian data analysis, parameters are treated as random variables. This stems from the Bayesian subjective conceptualization of probability. But do Bayesians theoretically acknowledge that there ...
7
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1answer
3k views

Interpreta​tion of main effect when interactio​n term is significan​t (ex. lme)

As an example I use Pinheiro, J. C. & Bates, D. M. 2000. Mixed-effects models in S and S-PLUS. Springer, New York. page 225. Rats whose body mass has been measured are fed by 3 different diets ...
31
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1answer
6k views

For which distributions are the parameterizations in BUGS and R different?

I have found some distributions for which BUGS and R have different parameterizations: Normal, log-Normal, and Weibull. For each of these, I gather that the second parameter used by R needs to be ...
7
votes
1answer
8k views

What does the cost (C) parameter mean in SVM?

I am trying to fit a SVM to my data. My dataset contains 3 classes and I am performing 10 fold cross validation (in LibSVM): ...
7
votes
3answers
358 views

GLMs must be 'linear in the parameters'

I am experiencing some cognitive dissonance about what 'linear in the parameters' means. For example, here and here. For example, my understanding is $y_i = \beta_0 + \beta_1\beta_2x_1 + \exp(\beta_3)...
8
votes
1answer
3k views

Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
5
votes
2answers
4k views

Scale parameters — How do they work, why are they sometimes dropped?

I'm having difficulty wrapping my head around scale parameters. How exactly do they work? Why are they sometimes ignored? (in other words, when is it important to preserve them in a calculation?) ...
3
votes
0answers
2k views

Why glmnet can be calculated parameters for all category?

For my understanding, multinomial logit model requires to restrict the parameters for one category to zeros. However, package{glmnet} seems to allow different parameters to every class. Could someone ...
7
votes
2answers
7k views

How to use the SD of a normal sampling distribution to specify the gamma prior for the corresponding precision?

The gamma distribution is a commonly used prior distribution for the precision ($1/sd^2$) of a normal distribution in Bayesian hierarchical modeling. I want to use an informed prior for the variance ...
6
votes
1answer
14k views

How to compare dbscan clusters / choose epsilon parameter

I am currently trying to make a DBSCAN clustering using scikit learn in python. I would like to compare the different outputs when varying the epsilon parameter in order to choose the right epsilon ...
5
votes
2answers
384 views

The vcov function cannot be applied?

I originally asked a question about the delta-method in the context of the hyperbolic distribution. I got an answer there, which is useful, except that it says I should apply the ...
2
votes
2answers
621 views

Justification of simulated annealing versus random search

I have a set of 16 integer parameters to optimize. The parameter space is too big for an exhaustive search, so I am using simulated annealing instead. I think my simulated annealing works - it finds ...
3
votes
1answer
2k views

t-distribution parameter estimation

I know there are already several threads on this, but none seem to explicitly cover what I want. I have a set of financial data (pulled straight from Bloomberg) and am trying to fit a t-distribution (...
4
votes
2answers
2k views

Confusing Holt-Winters parameters

I have got a model for forecasting using holt-winters. However the parameters confuse me... The parameters show that there is no trend or seasonality even though there is definite trend and ...
2
votes
1answer
135 views

Are the Feller-Pareto and the generalized beta distributions really the same?

The Feller-Pareto distribution was originally is defined in terms of a transformed beta distribution. If $Y\sim \beta(\gamma_1, \gamma_2)$ then $W=\mu + \sigma\left(\left(1/Y\right) - 1\right)^\gamma=...
2
votes
2answers
576 views

Estimation of probability mass function using finite samples [closed]

Suppose $X_1, X_2, \dots, X_N$ are $N$ random samples of a discrete probability distribution such that $X_i \in \{1, 2, \dots, K\}$. The probability distribution $p$ used for sampling is ...
1
vote
2answers
615 views

Spherical Parameterization of Variance-Covariance Matrix in Mixed-Effects Regression

I wonder if someone can please help me with a passage on the article by José Pinheiro and Douglas Bates on unconstrained matrix parametrization. hat ties directly into the question. Although the ...
1
vote
3answers
248 views

What is the difference between parameter and variable?

This is a question that I have in order to reconcile a difference in terminology. In the linear regression setting, we have $y=\beta x + \theta$. Here, we call $x$ a variable. When we are trying to ...
1
vote
1answer
713 views

parameter tuning using nested cross validation

Parameter tuning in SVM has been performed using a nested cross-validation(CV) approach with 45 folds(outer loop) and 13 folds(inner loop). In this process, the outer loop will have 45 prediction ...