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Questions tagged [parameterization]

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

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I have two marginal distributions $(Y_1,Y_2)$ that follow distributions $N(\mu_1,50)$ and $N(\mu_2,100),$ respectively. I can allow for a total of 100 observations to estimate the parameter $\theta = \... 1answer 138 views Normalizing Flows, Real NVPs and Inverse Autoregressive Flows - Used for Probabilty Density Approximation or for Sampling? Suppose we have a parametric family$g(x;\theta)$, where$\theta$are the parameters. As far as I can tell, there are two ways we can use this family to model a probability distribution: Probability ... 0answers 137 views How to fit parameters of a stochastic model applied to agent modeling? I have a network of agents, these are modeled roughly according to the paradigm of "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science". The main feature is that the equations ... 1answer 218 views Finding a closed-form solution of nonlinear function for parameter estimation I've come across this problem of estimating parameters of nonlinear model using closed-form solution. I've read that logarithms can be used for certain forms, but they can't be applied to everything. ... 0answers 219 views Degrees of freedom of a hierarchical model I have a nonlinear regression model that has two independent parameters,$a$and$b$, and one dependent parameter,$c$, which is dependent on the independent parameters$\alpha$and$\beta$estimated ... 0answers 28 views How to map 2 vectors on the hyper plane to a similarity metric? I am working on a face recognition application and one of the features I want to include is to compare if two pictures of$2$people is the same. I have written code (Convoluted neural network) to ... 0answers 44 views How could one prove that b in the GB2 distribution is a scale parameter? In the Generalized Beta distribution of the second kind (GB2), where a, p, and q are shape parameters and b is a scale parameter, the pdf is defined on$\mathbb{R}_+$by: $$GB2(y;a,b,p,q) = \frac{|a|... 0answers 73 views Basics of Akaike's Information Criterion in GIS/Hydrology I have been asked to use the AIC to assess the relative fitness of various terrain wetness index (TWI) methods for predicting soil moisture in a specific study site. The TWI is calculated from a ... 0answers 49 views What set of parameters should I choose for Naive bayes and GBM models so that it creates minimal fitting error? I understand that different set of parameters has to be chosen for each model so as to avoid under or over fitting. But is there is a 'safe set' of parameters which can be used for the widest range of ... 2answers 150 views Parameter estimation of exponential distribution depending on multiple factors/attributes for a simulation I’ll need to simulate project delays. I’ve data on 20k projects with delays in quarters. Some of them were finished ahead of plan (i.e. neg. delays) others with a delay of 1-16 ... 1answer 1k views GARCH vs ARCH models - which is more parsimonious? As I understand the inclusion of the GARCH term, \sigma^2, in a GARCH model allows for an infinite number of time series terms, \epsilon^2, to influence the conditional variance. Is this the case? ... 1answer 192 views Merits of reparameterizing the Gamma and inverse Gamma Wikipedia states that the PDFs for the Gamma distribution is:$$ f(x|\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}\exp(-\beta x) $$However, in Rasmussen 2000, the pdf for the ... 1answer 75 views Optimize a regression forest (Better parameters and how to obtain them) I'm currently working on sales forecasting. I'm using a Regression Forest to make my forecast. (with MLLib from Spark on Databricks) I'm trying to find what features are useful in my forecasting. ... 1answer 52 views Is this sensible: P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu)) I want to write:$$P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$$to say: The probability of Y being between y_1 and y_2 given that Y is a random variable distributed according to ... 3answers 237 views Normal distribution parametrization I have the following hierarchical model: y_{i} = \alpha + \beta_{i}x_{i} + \varepsilon_{i} where \varepsilon \sim N(0,\sigma^{2}). \beta_{i} \sim N(\gamma x_{i},\sigma^{2}x_{i}^{-2}) ... 1answer 2k views What does phi mean in arima simulation I'm learning time series and following this tutorial When it comes to simulation, there are 2 types AR: AR1: x1 = arima.sim(list(order=c(1,0,0), ar=.9), n=100) ... 1answer 308 views Identifiability of Poisson parameters Assume that you have two Poisson random variables, y_{jk} ∼ Poi(\lambda_{jk} \psi_j) and y_{kj}∼Poi(\lambda_{jk}\psi_k). I've read that this parameterization is not unique, but for me it is not ... 0answers 164 views Parameters estimation in custom chi-squared distribution For modeling purposes, I need to add a parameter (denoted by \alpha) allowing us to control the location of a Chi-squared distribution (instead of always beginning at 0). The probability density ... 1answer 26 views Articles that work with covariates for mean, variance, and correlation simultaneously Does anyone know of articles in which, in addition to modeling the mean parameter, are also modeled the variance and correlation parameters? I know the double generalized linear model, but they only ... 1answer 338 views What does mean the “B” in a GLM result? 0answers 27 views No loss of generality Let$$ \underset{n \times n}{\Sigma_t} = \underset{n \times m}{A} \underset{m \times m}{\Sigma_t^f} \underset{m \times n}{A'}, \qquad m <n. $$In this model A is the parameter matrix. The authors ... 0answers 656 views glmnet returning lambda that gives all-zero coefficients as optimal lambda Before I start, I have already looked at the answers for related questions: How to interpret all zero coefficients in the results of cv.glmnet? Why is cv.glmnet giving a lambda.min that is ... 0answers 47 views What are some interesting parameterizations of 4 \times 4 correlation matrices, and also perhaps their associated jacobians? I am studying (mainly using Mathematica) some constrained integration problems in which the six-dimensional convex set of 4 \times 4 correlation matrices plays a central role. In light of this, I ... 1answer 631 views Fitting t-distribution to data and deriving moments I'm fitting the t-distribution to financial data and I know of two methods to do this using R: (A) fitdistr(mydata, "t") Output: ... 1answer 4k views Algorithms for weighted maximum likelihood parameter estimation What are the computational or algorithmic considerations for weighted maximum likelihood parameter estimation? That is, I want to get$$ \theta^* = \arg\max\limits_\theta \sum_i w_i \log(\mathcal{L}(\... 3answers 281 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 ... 1answer 323 views SVM gamma parameter influence : 2moons data set I'm working on the two-moons data set, in which we can achieve a perfect discrimination, the classes are separable. I'm using the RBF kernel, and as a consequence, i have to tune the gamma parameter. ... 0answers 159 views Data simulations for SVM : study of parameters I'm studying SVM for classification. The first step of my work consists in making a data simulation in order to study the influence of the cost parameter C, the choice of the kernel, for examples. Do ... 1answer 558 views What is the difference between the parameters and the moments of a distribution? What is the difference between the parameters and the moments of a distribution? Are the moments of the distribution (mean, sd etc.) simply also parameters of a distribution? 1answer 1k views Holt-Winters parameters in R I'm trying to replicate some values from a holt winters calculation made in excel by someone else. I have the time series time_x, and I'm using the forecast package. The problem is when I run the ... 1answer 488 views Bayesian parameter estimation: Transforming parameters to use uninformed priors First of all: Please excuse my ignorance. There are some parts of the concept of bayesian inference I may have not yet understand! What I have so far: I have count data with a negativ binomial ... 1answer 128 views Consider systematic error in a fit My question arise directly from a lab situation. Let's say I have measured two sets of data$x_i$,$y_i$and i know both the statistic and systematic error for$y_i$(I assume no error on$x_i). ... 1answer 340 views Iterative parameter updates on student-t distribution (and approach for other distributions) In a paper I found an iterative algorithm based on Bayes working with the following distribution and update criteria: In another source, I found the same update criteria in a whole different context. ... 0answers 83 views Identifying the parameters of a linear state-space-model using Kalman Filter I have a linear state space model (SSM) that looks like this \begin{align} {\dot {x}} & = {\rm \textbf{A}}{x} + {\rm \textbf{B}}{u} \\ {y} & = {\... 1answer 89 views Neural Networks - Acceptable to choose best model after several trys? I have fitted several neural networks to some training data using different parameter settings for weight decay, nodes, max iterations etc. As I dealt with time series data I chose a form of rolling-... 1answer 290 views Parameterization of Gamma Distribution I have come upon different parameterizations of the Gamma Distribution, but not with regard to shape-scale or shape-rate. It is rather about the sign in the exponent. Wolfram lists the pdf as being ... 0answers 93 views Is it justified to estimate residual error by sample variance of residual in bayesian parameterization? I'm using Bayesian inference to estimate the parameters of a dynamical system which is comprised of several ordinary differential equations (ODEs). I use a gaussian error model. I would like to know ... 1answer 127 views Bayesian inference with conjugate priors - triplot I'm trying to make a "triplot" to illustrate Bayesian inference (so I'd like to have prior, likelihood and posterior in the same picture). For likelihood I'm using \begin{equation}\label{eq:lik} f(y|\... 0answers 122 views What do the parameters A, B, and C do in an equation of the formY = A + Be^{CX}$? [duplicate] I have read this article and those linked to it, but I am still having difficulties fitting a function of this form to data I have using the nls function in R. Invariably, I fail to get convergence ... 1answer 232 views Do I stick with the tuned model parameters even if they produce worse test scores? The shorter and more general version of this question: If tuning a model via cross-validation (within training set) produces worse results on the test set than my previous default/baseline model, do I ... 1answer 100 views Tune parameters from a specific equation in R This is the first time I am truing to tune model parameters in R. I have a fairly complicated equation with multiple parameters: ... 0answers 47 views Family of flexible parametric mappings$f_\theta:(0,1) \rightarrow \mathbb{R}$? For the purpose of reparameterizing a model (mostly with the goal of improving MCMC efficiency), I am looking for a family of flexible parametric mappings$f_\theta:(0,1) \rightarrow \mathbb{R}$such ... 1answer 9k 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): ... 1answer 178 views Estimate parameters for skew normal distribution I know there is already at least one question answer with this, but I think the solution does not apply in my case. I have a population for which I know the mean, variance and skewness. I saw how to ... 1answer 54 views Different logistic regression models I've been revising the concepts of logistic regression and suddenly realized that the probability function of the logistic model in the book ISL looks absolutely different from other sources. For ISL ... 1answer 528 views Using lasso regression in Matlab with constraints on lambda values I have successfully ran a lasso regression on Matlab, however, some of the lambda values result in a non-steady state solutions for my linear problem. I would like to basically force the regression to ... 2answers 7k views What are the model parameters and hyperparameters of Random Forest classifier? The parameters required for a Random Forest classifier are as follows: Depth,$d$No. of random features,$K$No. of trees,$I$Randomizer seed,$R$Which of the above are hyperparameters and which ... 1answer 445 views Posterior of Dirichlet distribution parameters I want to obtain posterior distribution for parameters of a Dirichlet distribution$x = (p_1,p_2,p_3) \sim Dir(p_1,p_2,p_3; a_1,a_2,a_3)$with uniform$P(a_1,a_2,a_3)$and observed data$X=\{x_1,x_2,.....
Consider a simple OLS model: $$y = \beta_0 + \beta_1x_1 + \beta_2x_2 +\epsilon$$ Suppose $x_2$ is dummy variable which has value either 1 or 0 and the model is successfully fitted with collected ...