Questions tagged [parameterization]

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

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41
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 ...
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 ...
19
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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 ...
12
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2answers
3k views

Random Forest: what if I know a variable is important

My understanding is the the random forest picks randomly mtry variables to build each decision tree. So if mtry=ncol/3 then each variables will be used on average in 1/3 of the trees. And 2/3 of the ...
11
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2answers
14k views

Cross validation and parameter optimization

I have a question about the parameter optimization when I use the 10-fold cross validation. I want to ask that whether the parameters should fix or not during every fold's model training , i.e. (1) ...
10
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2answers
1k views

Fisher information matrix determinant for an overparameterized model

Consider a Bernoulli random variable $X\in\{0,1\}$ with parameter $\theta$ (probability of success). The likelihood function and Fisher information (a $1 \times 1$ matrix) are: $$ \begin{align} \...
10
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0answers
407 views

Asymptotic property of tuning parameter in penalized regression

I'm currently working on asymptotic properties of penalized regression. I've read a myriad of papers by now, but there is an essential issue that I cannot get my head around. To keep things simple, I'...
9
votes
1answer
190 views

Parametrizing the Behrens–Fisher distributions

"On the Behrens–Fisher Problem: A Review" by Seock-Ho Kim and Allen S. Cohen Journal of Educational and Behavioral Statistics, volume 23, number 4, Winter, 1998, pages 356–377 I'm looking at this ...
9
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1answer
376 views

Accounting for discrete or binary parameters in Bayesian information criterion

BIC penalizes based on the number of parameters. What if some of the parameters are some sort of binary indicator variables? Do these count as full parameters? But I can combine $m$ binary parameters ...
8
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1answer
4k 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 ...
8
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1answer
1k views

What is the point of graphical models?

I spent the day learning about the bnlearn package in R only to discover that Bayesian models do not work with undirected graphs. I'm trying to learn about the Markov Random Field Network, and so far ...
8
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2answers
3k views

Matrix Factorization Model for recommender systems how to determine number of latent features?

I am trying to design a matrix factorization technique for a simple user-item, rating recommender system. I have 2 questions about this. First in a simple implementation that I saw of matrix ...
8
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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 ...
7
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1answer
11k 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
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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 ...
7
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3answers
365 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)...
7
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1answer
2k views

Which distributions are parameterization invariant when based on the Jeffreys prior?

I understand that the Jeffreys prior provides a method for constructing a prior distribution over parameters for a given model (likelihood function) such that the prior distribution is "invariant ...
7
votes
1answer
269 views

Generalized Normal Distribution

Is there a known distribution, $f(x|\theta_1,\theta_2,\theta_3,\theta_4)$, with the following properties: $E(X^n)=\theta_n$ for $n \in \{1, 2, 3, 4\}$. If $\theta_3=0$ and $\theta_4=3\theta_2^2$, ...
7
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1answer
3k views

CV for model parameter tuning AND then model evaluation

I have a basic question on using cross-validation for model parameter tuning (model training) and model evaluation (testing) similar to this Model Tuning and Model Evaluation in Machine Learning I ...
7
votes
1answer
15k 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 ...
6
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2answers
2k views

gamma parameter in xgboost

I came across one comment in an xgboost tutorial. It says "Remember that gamma brings improvement when you want to use shallow (low max_depth) trees". My understanding is that higher gamma higher ...
5
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2answers
5k 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?) ...
5
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1answer
4k views

Algorithms for weighted maximum likelihood parameter estimation

What are the computational or algorithmic considerations for weighted maximum likelihood parameter estimation? That is, I want to get $$ \theta^* = \arg\max\limits_\theta \sum_i w_i \log(\mathcal{L}(\...
5
votes
2answers
4k views

How to interpret slope parameter estimates for linear models in R?

I wish to analyse a simple lab experiment. I have 8 fish. Four are fed on diet A, and four on diet B. I measure their Nitrogen (N) over 5 time periods (so 5 repeated measures per fish). I wish to know ...
5
votes
1answer
222 views

Parameters in a non-parametric model

I have not understood this Wikipedia statement: The difference between parametric model and non-parametric model is that the former has a fixed number of parameters, while the latter grows the ...
5
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2answers
393 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 ...
4
votes
1answer
6k views

Find the mode of a probability distribution function

I am trying the find mode of a probability distribution function given by \begin{equation} g(x/\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha \right)\beta^{\alpha}}exp\left\{{-\frac{x^2}{2\sigma^{...
4
votes
2answers
3k views

What are the implications of a perfect fit model?

I perform logistic regression with a relatively small dataset (N=65), using 12 parameters (11 variables, one constant, no interactions), which results in a perfectly fitting model (in SPSS). I have a ...
4
votes
2answers
3k 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 ...
4
votes
1answer
1k views

What is the parameterization of exponential distribution for survival in Stata?

I'm new to data analysis so this is kind of a simple question. I would like to understand why I cannot reproduce a survival curve generated by a fitted exponential model from Stata. I use the ...
4
votes
1answer
407 views

Correct understanding of De Finetti`s representation theorem

I am currently interestend in understanding De Finetti`s representation theorem. As I am only familiar with Frequentist thinking I have some problems to understand its meaning. I have already read the ...
4
votes
1answer
812 views

Questions Regarding Item Response Models – the 3PL model vs. the mixture of 2PL and 3PL model

I currently work on an item analysis for an assessment. The assessment consists of 25 multiple-choice questions. Each question has 4 choices with one correct answer. I used different IRT models to ...
4
votes
1answer
189 views

Normalize a periodic parameter

I am using inverse modelling software (PEST) to estimate a periodic parameter for the direction of anisotropy, $\hat{\theta}$, which is somewhere in $[0^{\circ}, 180^{\circ})$ (i.e., has a wavelength ...
3
votes
4answers
1k views

Fitting SIR model with 2019-nCoV data doesn't conververge

I am trying to calculate the basic reproduction number $R_0$ of the new 2019-nCoV virus by fitting a SIR model to the current data. My code is based on https://arxiv.org/pdf/1605.01931.pdf, p. 11ff: <...
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 (...
3
votes
3answers
131 views

Can you ever have known parameters?

Maybe a bit of a philosophical question - but can you ever truly have known parameters in data? I have a set of data for which the dataset is complete, but the parameters will still be estimates i ...
3
votes
1answer
257 views

Gaussian process scale targets

I am currently playing around with Gaussian process regression. I discovered some confusing facts that I would like to be answered: When I optimize the parameters like the length and error terms for ...
3
votes
1answer
2k views

What is exponential family criterion to test the sufficiency and completeness of an estimator?

I am struggling to understand the following result from Casella and Berger about sufficiency and completeness for exponential families: Let $X_{1},X_{2},...,X_{n}$ be iid observations from an ...
3
votes
1answer
777 views

Fitting t-distribution to data and deriving moments

I'm fitting the t-distribution to financial data and I know of two methods to do this using R: (A) fitdistr(mydata, "t") Output: ...
3
votes
1answer
5k views

What is the formula for lognormal hazard?

I'm plotting a bunch of survivor and hazard curves. The lognormal survivor function is: $S(t)=1-\Phi(\frac{log(t)-\mu}{\sigma}) $ Where $\mu$ is the scalar parameter. From a website (http://www....
3
votes
1answer
114 views

Formula for cross-classified (a.k.a., crossed random factors) mixed effects model with interaction between two “second level” variables

I have a crossed-classified (Hox, 2010) mixed effects model—also known as crossed random factors (West, Welch, & Galecki, 2015), but I am struggling with how to write the formula for an ...
3
votes
1answer
647 views

Smoothing parameter for spline curve with duplicate points

I have body mass and age data for a population of individuals. I want to fit a cubic smoothing spline curve to the data. I'm using smooth.spline in R, which warns against using cross-validation to ...
3
votes
1answer
298 views

Understanding the definition of a location parameter

In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ...
3
votes
1answer
77 views

Sampling parameters from exponential family

So suppose PDF $f_{X|\theta}(x_1,...,x_n;\theta_1,...,\theta_m)$ is from the exponential family. Is there any theory or general guidelines for sampling parameters from this PDF? This question is not ...
3
votes
1answer
313 views

Parameter estimation for Kumaraswamy distribution

I'm interested in estimating the shape parameters of a Kumaraswamy distribution from sample data. The closest research I can find is Jones' paper from 2009 which analyses a maximum likelihood method, ...
3
votes
1answer
119 views

Estimating parameters using a different method?

I have a probability distribution which has two parameters $a$ and $b$ I have re-parametrized the distribution such that the new distribution has two parameters $c$ and $d$ where: $c=a$ but $d = \...
3
votes
1answer
67 views

The meaning of a parameterization of the logarithmic distribution

In calculus one learns that $$ p + \frac{p^2} 2 + \frac{p^3} 3 + \frac{p^4} 4 + \cdots = -\log(1-p). \tag 1 $$ Thus a discrete probability distribution on the set $\{1,2,3,\ldots\}$ is given by $$ \Pr(...
3
votes
1answer
95 views

good terminology for the parameters of a lognormal distribution?

Is there any good short terminology for the two parameters of a lognormal distribution? I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
3
votes
1answer
35 views

Is there a standard name for a certain parameter for the beta distribution?

The beta distribution is $$ (\text{constant})\times x^{\alpha-1}(1-x)^{\beta-1} \, dx \quad\text{for } 0\le x\le 1. $$ Supposing $X$ to be so distributed, one has \begin{align} & \mu = \...
3
votes
1answer
219 views

Weibull Parameter Estimation

I am doing a project in which I need to estimate Weibull parameters for car part failures (I know the data follow Weibull). I have data for 1000 cars (part failure data). Now the problem is suppose ...

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