Questions tagged [parameterization]

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

Filter by
Sorted by
Tagged with
2
votes
1answer
2k 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
700 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) ...
1
vote
1answer
343 views

How do models, parameters, specifications, restrictions and assumptions relate?

So this has been something I've been struggling with for a long time: The specification of a particular model is subjective. However, there seems to be objective ('true') values of the parameters we ...
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 ...
1
vote
0answers
71 views

Do assumptions for estimators affect population parameters?

TL;DR: Specifying a model (a collection of restrictions over a sample space) specifies the model parameters. Specifying an estimation procedure adds additional number of restrictions (assumptions?). ...
0
votes
1answer
203 views

Calibrating Generalized Hyperbolic distribution in R - which parameters are valid and allow for a numerical calculation of absolute moments

I am using the R-package ghyp in order to calibrate and model. In fact my coding is based on this paper. I know that I could do quite a robust fit using ...
1
vote
1answer
123 views

Stable Distribution Log-likelihood and AIC values

I have used the stableFit function from the fBasics package to come up with parameters (alpha, beta, gamma, and delta) for a stable distribution as you can see below: ...
-1
votes
1answer
2k views

Definition of Parameters [duplicate]

I imagine this either extremely simple or extremely complex. I am trying to understand the interpretation of the term 'parameter'. A couple of quick online searches deliver an intuitive understanding ...
1
vote
1answer
663 views

Parameters for a Levy distribution in R

Can someone help me figure out how I can get parameter estimates for a levy distribution using R? Unlike the normal distribution and Student T distribution which has functions ...
3
votes
1answer
635 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 ...
1
vote
1answer
79 views

Choosing between two parameters in a model

I have a few parameters that are related (let's call them X1 and X2), and I want to use whichever one will provide the strongest model. The model has many other parameters. Would I simply be able to ...
2
votes
1answer
302 views

Best statistical notation for expected probability density

Assume that we have two multivariate normal distributions $\mathcal{N}_1 = \mathcal{N}(\mu_1, \Sigma_1)$ and $\mathcal{N}_2 = \mathcal{N}(\mu_2, \Sigma_2)$. We do these two steps: Pick a point, say $...
1
vote
1answer
83 views

Tuning paramaters SVM, DT, k-NN, NN

I'm trying to compare the predictive strenght of four different algorithms: support vector machines k-NN decision trees neural networks I've got a few questions concerning the parameter tuning: ...
1
vote
0answers
118 views

Assumptions implied by “pairwise marginal” parameterization of MRF

I'm trying to understand the assumptions of different parameterizations in a Markov network. In this case, I'm trying to understand the assumptions (and effects) that result from parameterizing ...
1
vote
2answers
10k views

How many parameters in this specific linear model with interaction?

I have a question where I am not sure about the answer: A linear model has the following characteristics: *A dependent variable ($y$) *One continuous variable ($x_l$), including a ...
0
votes
1answer
46 views

Reparametrisation of a model when an interaction is significant to facilitate the interpretation

It is admitted that it is complex to interpret main effects when they are involved in an interaction. Lets take a regular linear model, with two categorical 2 level variables A and B who are ...
1
vote
2answers
529 views

Is it reasonable to measure standard deviation from true value rather than mean?

I am evaluating the accuracy of GPS watches, taking many readings over a known distance. I've been calculating standard deviation using the mean reading, but because I know what the reading should be, ...
1
vote
0answers
38 views

Floor effects in Bayesian estimate, can I reparameterize?

I'm replicating an old study and I have two sets of existing estimates which measure a similar effect, namely the presence of a studied item in memory over time: ...
0
votes
1answer
77 views

What do you call a parameter that is estimated from historical values?

There are several methods to estimate parameters in a model (MLE, MAP, GMM). Does the process of estimating a parameter from historical data have a name?
0
votes
0answers
124 views

expressing this probability distribution over different variables

I have a likelihood function as follows: $$ P(y|x,w, \phi) = \frac{\phi}{2\pi} \exp ^{-0.5 (y-t(x, w)'\phi (y-t(x,w)) } $$ Here $y$ and $x$ are two observed values. $\phi$ is also some given ...
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 ...
2
votes
0answers
957 views

Rejection sampling from a Gamma distribution using a Cauchy proposal

i'm trying to find the parameters $ \gamma,x_0$ of a standard Cauchy distribution : $$T(x)= \frac{1}{(\pi \gamma (1+(\frac{x-x_0}{\gamma})^2))} $$ To perform rejection sampling from a gamma ...
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 (...
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 ...
3
votes
1answer
4k 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....
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 ...
3
votes
1answer
214 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 ...
6
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 ...
0
votes
1answer
54 views

Cross fitting with same params but differents models

What is the best fitting way with 2 variables to explain ($Z_1$ and $Z_2$) depending on the same variables ($X$ and $Y$) and parameters $\theta$ but with differents models ($f$ and $g$)? For instance:...
1
vote
1answer
723 views

Parameters and parameter estimation in graphical models

I try to understand parameter estimation and learning problems at Graphical Models, especially in directed ones (Bayesian Networks). But first of all, I try to understand what exactly a parameter ...
8
votes
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 ...
1
vote
0answers
601 views

When do we calculate the population parameter instead of sample statistics? [duplicate]

When do we calculate the population parameter instead of sample statistics? If there is a this kind of case which statistical tool should we use population parameter or sample statistics? A car ...
7
votes
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 ...
5
votes
2answers
391 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 ...
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 ...
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 ...
0
votes
1answer
84 views

Finding optimum point of parameters

I have an algorithm with 3 parameters and sum of these parameters is equal to one; $a_1+a_2+a_3=1$ and each of them must be between $0$ and $1$. I want to find the optimum point for this parameters. ...
1
vote
0answers
632 views

Parameters estimation of ODE system

I have all the data and an ODE system of three equations which has 9 unknown coefficients (a1, a2,..., a9). ...
0
votes
2answers
268 views

Finding a correspondence between time-series elements

My problem deals in particular with time-series data about server performance, but the solution is sure to be applicable to many types of data sets. Pardon me if the answer is well-known; I don't know ...
10
votes
0answers
398 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'...
7
votes
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 ...
-1
votes
1answer
38 views

Output of hyperbfit?

I want to fit a hyperbolid distribution to my data, in my notation, I have the density \begin{align*} H(l;\alpha,\beta,\mu,\delta)&=\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha \delta K_1 (\delta\sqrt{\...
0
votes
1answer
856 views

How do we usually select the best combination of parameters of a machine learning model (for a given dataset)?

Am I wrong, or the standard way of optimizing a machine learning model is by evaluating the algorithm over the (initial) dataset for all possible combinations of parameters, and then pick up the one ...
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?) ...
1
vote
1answer
109 views

Learning the parameter of linear model

I was reading the slides from the following http://www.slideshare.net/kunegis/searching-microblogs-coping-with-sparsity-and-document-quality In slide 7, the author proposed just a linear model and ...
2
votes
1answer
696 views

Mallow's Cp Question

When comparing each individually generated model's $C_p$ to the number of parameters, which number of parameters is the comparison to? Each individual model or the overall number of parameters?
1
vote
1answer
183 views

Proportionality in Bayesian Models: What Is Absorbed?

Considering two Bayesian models: Poisson Likelihood & Beta Prior: $p(y|\lambda) \sim \text{Pois}(\lambda)$, $p(\lambda) \sim \text{Be}(a, b)$: $$ p(\lambda|y) \propto \lambda^{a-1}e^{-b\lambda} ...
11
votes
2answers
13k 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) ...
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 ...
0
votes
1answer
745 views

Compound Poisson, preliminary work in R

I need help with following programming code: Beforehand: I tried to estimate Poisson-parameters, but M.L.E. and M.C. do not give satisfactory results regarding actual to expected, from actuarial ...