Questions tagged [parameterization]

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

67 questions with no upvoted or accepted answers
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388 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'...
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84 views

Probability distribution over shapes (or: How to parameterize arbitrary polygons)

Has there been work on modeling variations of a 2D shape? E.g., say you want a distribution over 5-sided polygons, or over ellipses, or curved shapes? For simple shapes, like circles, rectangles, ...
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45 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 ...
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56 views

How to parameterize coefficient matrix to restrict eigenvalues?

Consider the $r-$dimensional autoregression $$ y_t = Ay_{t-1} + v_t, v_t \overset{iid}{\sim}N(0,\Sigma). $$ It is well known that if all eigenvalues of $A$ have modulus less than unity then this ...
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53 views

Verification of an optimal parameter from an empirical CDF

Suppose we have the following model for the variable $V_5$: $$V_5 = \prod_{k=1}^5(e^{\mu + 0.2X_k}+0.05e^{0.05Y_i - 0.00125}), X_i,Y_i\sim N(0,1)$$ What I wish to do is to solve the problem $\min_{\...
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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 ...
2
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10 views

Is there a formal relation between weight regularization and compression?

In my understanding, compression, strictly speaking, means that we diminish the amount of data required to describe something, such as a model. E.g. compressing an image file means to create a file ...
2
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31 views

Choosing Gaussian PDF basis bandwidth depending on number of bases and range of data

Summary (details below!) I have a basis expansion of $m$ (univariate) Gaussian PDFs to model the density of a sample $X$. The means of these PDFs are spaced equidistantly through the domain of $X$ ...
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42 views

Linear combination of two non-independent random variables

I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ...
2
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41 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|...
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631 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 ...
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235 views

MCMC efficiency and nonlinear reparametrizations

The efficiency (e.g., effective sample size per density evaluation) of most MCMC methods depends on the parametrization. However, so far I have come across little work in the MCMC literature that ...
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111 views

how to find the aleatory uncertainty in parameter using Bayes?

Generally, the uncertainty can be categorized into aleatory and epistemic according to whether it can be reduced or not. In Bayesian statistics, one "true fixed parameter" is presumed as discussions ...
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923 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 ...
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1answer
184 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 ...
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22 views

Strategies for analyzing the functional relationship between two time series?

Suppose we have time-dependent survey data about name recognition for a political campaign. We're interested in learning how campaign spending effects that name recognition. My interest is in ...
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1answer
25 views

Expected value without complete sample space

The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
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8 views

How do I create error bounds after parameter calibration?

I have a power transform $f$ I am applying to an Ornstein-Uhlenbeck stochastic process $\{X(t), t\geq 0\}$: $$dX(t) = \kappa (\mu - X(t)) dt + \sigma dW_{t}.$$ From here, I was able to plug in my ...
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24 views

Parameter estimation of 3d model

Suppose we have cost data on some product line, let's say clothing. A simple model of the true cost of the clothing could look something like this: C$_{i,j,k}$ = c$_i \cdot \alpha_j \cdot \beta_k $, ...
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1answer
43 views

How to select optimal observation number n from two marginal distributions?

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 = \...
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128 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 ...
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211 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 ...
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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 ...
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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 ...
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158 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 ...
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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 ...
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46 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 ...
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0answers
154 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 ...
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80 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} & = {\...
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92 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 ...
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17 views

How the process parameters changes with the length of data aggregation?

Is there any general relationship for a process(e.g. ARMA, O-U process) applied to financial data over different time intervals. e.g.In this question there is an answer telling the O.P. to aggregate ...
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66 views

What is a parameter in Bayesian analysis?

In any case study, when we use Bayesian analysis to solve our problem we consider a model parameter which is sometimes known and sometimes unknown. And using this parameter(and of course prior data) ...
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0answers
56 views

Support of distribution (distribution fitting)

This might be a weird question. I want to know why Matlab still run to produce estimated parameter whenever I input data which doesn't belong to the support of the distribution? E.g. I want to know ...
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0answers
142 views

Choosing the good initial value of the Newton-Raphson iteration method for Maximum Likelihood Estimation

I want to estimate the four parameters of Exponentiated Modified Weibull Extension (EMWE) distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation. Because the first ...
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0answers
396 views

Help: Random Forest optimization (image classification)

I'm having trouble classifying images using a random forest. The images all have a very similar scale, but they may be rotated arbitrarily around a fixed point in the image. The core problem is ...
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0answers
57 views

Completely understanding the Confidence Interval - how is it not a probability of containing a population parameter?

I've been doing data analysis for a while, but recently I questioned my understanding of the oft-misunderstood confidence interval. So, I read multiple sources. Many of them say explicitly that the ...
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0answers
22 views

Get level set from 3D dataset obtained exploring a 2D space parameter

I am exploring a 2 parameter space performing simulations. As a result I get a surface as a function of these 2 parameters. I know this is probably simple but I don't know how to look for it. Now I ...
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23 views

p-test for parameter

Statisticians, number magicians, I was wondering what the best way is to check for the equality of two parameters including possibly a confidence interval and p-value. $$H_0:\beta_1=\beta_2\vert\ \...
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150 views

Under what assumptions can parameter estimate uncertainty be estimated from the Hessian?

Given a model with some parameters, some data it's attempting to reproduce, and a distance function to quantify how well the predictions correspond to the data, I can fit parameters via a general ...
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1answer
41 views

Is there a family of processes centred on the Poisson process?

I am looking for a model, characterized continuously by a single parameter, to describe the arrival times of buses with unit expected interarrival time. At one extreme of the parameter (say $\theta=1$)...
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120 views

What have I done wrong implementing this Bayesian method for fitting a circle to noisy data?

I have noisy measurements of movement along a circle. I want to fit a circle to these measurements. I tried two methods, a straight forward moment fit, and then an ODR fit (described here. However ...
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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?). ...
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116 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 ...
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0answers
36 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: ...
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0answers
626 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). ...
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0answers
14 views

Hypothesis test practice question

" Prof. J conducts a hypothesis test on whether the proportion of all students who bike to school (denoted as p) equals 30%. Specifically, Prof. J has H0: p=0.3 versus HA: p≠0.3. He obtains a P-value ...
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11 views

Speed of transition parameter constraints

Given a logistic smooth transition regression \begin{equation} y_{t}=x_{t}^{\prime }\beta _{1}(1-{g}(z_{t};\gamma ,\delta ))+x_{t}^{\prime }\beta _{2}{g}(z_{t};\gamma ,\delta )+\varepsilon _{t}% \text{...
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0answers
18 views

Parameter Tuning for auto-regressive Neural networks (NNETAR)

I am analyzing time series data on electricity prices using a variety of methods (ARIMAX, TBATS, STLM) including the auto-regressive feed-forward neural network NNETAR, which is implemented in the ...
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0answers
46 views

What to do when the meaning of a variable has changed over time?

I have dataset of a company with 2014 data with 15 variables then 2018 data with same 15 variables.I want to combine both the datasets however the meaning of 1 variable has changed meaning that ...
0
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0answers
32 views

Changing a conditional probability to a deterministic function

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...