Questions tagged [parameterization]
For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.
214
questions
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14 views
How to implement the estimation of parameters in negative binomial distribution in python?
Assuming the negative binomial distribution, How can I implement the estimation to parameters(r & p) especially by MLE? Which function or package should I use? scipy.stats, sympy?
1
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1answer
41 views
Why is it easier to estimate $P(X|Y)$ rather than $P(Y|X)$ in terms of number of parameters?
In chapter 3 of the book by Mitchell ("Generative and discriminative classifiers: Naive Bayes and logistic regression") he states that "accurately estimating P(X|Y)
typically requires many more ...
0
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0answers
28 views
Starting values for an nls model in R [duplicate]
I'm trying to fit an exponential model using nls, but I don't know how to select the starting values for the parameters. I know this question has been answered multiple times, but I spent some days ...
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:
<...
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29 views
parameterize distribution of subsets
Suppose there is a set $S=\{1, 2, 3, ..., n\}$, then I need a distribution of its subsets with fixed size k, which can be denoted as $A=\{x_1, x_2, ..., x_k\}$ where $x_1$ to $x_k$ are from 1 to n.
...
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0answers
26 views
What is the definition of a scalar parameter?
I'm having trouble understanding what explicity is a scalar parameter. I understand what a location parameter and scale parameter represent but what exactly is the definition of a scalar parameter? ...
0
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0answers
14 views
Reparameterize b(K,pi) in terms of theta
Question: $X_1, ... , X_n$ follows a binomial distribution with parameters K and 0 < $\pi\ <1.$
Use properties of Regular Exponential Class of distributions to show that the sample total $T = \...
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0answers
13 views
Delimit the area in that parameter space that contains 95.4% confidence
Given the equation
$y = fc + fe\times \sin(2\pi(x-t_0)/12)$
Considering the two parameters of amplitude fc and fe simultaneously, delimit (using the χ2 variation method) the area in that parameter ...
2
votes
1answer
28 views
How to parameterize a bivariate Normal distribution output for a neural network?
For a neural net where the output is a Gaussian distribution, the output is usually parameterized as $(\mu=O_1, \sigma^2=e^{O_2})$. That is to say, the neural net will output the mean, and also output ...
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0answers
35 views
Robustness of a model to learnt parameters
There is a recent push to study how sensitive a model is to small changes in its input. This has also been studied from an adversarial point of view: e.g what is the smallest input perturbation that ...
0
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2answers
85 views
Why can't algorithms avoid overfitting themselves?
So, I understand overfitting (bonus question: precise statistical definition of overfitting?). You don't want to match the noise in your sample.
What I don't understand is why this requires a ...
3
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0answers
30 views
Why are these 2 ARIMA formulations equivalent?
In the "Understanding constants in R" section of his book, Hyndman & Athanasopoulos textbook "Forecasting: Principles and Practice" claims that the following AR processes equations are equivalent:
...
2
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0answers
11 views
Alternative to plug-in estimation for log-tranformed linear model
I want to estimate a relationship of the form:
$$y=ax^b\times\epsilon$$
If I log this model i get:
$$\log(y)=\log(a)+b\log(x)+ \log(\epsilon)$$
If I then proceed and estimate this model using a ...
0
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0answers
29 views
Estimate distribution of aleatoric variable using Bayesian inference
Given a model as follows:
$$y = cx + e$$
where y is the model output, x is the model input, c is an unknown variable and e is a Gaussian model error with zero mean: $$e \sim N(0,\sigma)$$
Data is ...
0
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0answers
41 views
Is this parametrization identifiable?
So I have this problem which I'm unsure of my answer. Any tip on how to treat it differently is more than welcome.
X and Y are independent $\mathcal{N}(\mathcal{\mu_1},\sigma^2)$ and
$\mathcal{N}(...
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0answers
27 views
Why are decision trees (especially ID3) non-parametric?
I was going through the definition of parametric and non-parametric models. So the parametric are the ones which have a fixed number of parameters that you are trying to learn and this number is ...
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0answers
25 views
State whether the model in question is parametric or non-parametric
The number of eggs laid by an insect follows a Poisson distribution with an unknown mean $\lambda$. Once laid,
each egg has an unknown chance, $p$, of hatching and the hatching of one egg is ...
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(...
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0answers
23 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 ...
1
vote
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 ...
1
vote
0answers
17 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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1answer
31 views
Flexible models and parameters
I just started reading Introduction to Statistical Learning with R and I am currently trying to work through the exercises.
One of the questions is "What are the advantages and disadvantages of a ...
6
votes
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 ...
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votes
0answers
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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vote
0answers
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 ...
0
votes
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
votes
1answer
49 views
What’s the difference between k-theta and alpha-beta parameterization for gamma distribution?
In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second :...
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0answers
72 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 ...
0
votes
1answer
136 views
Different notions of over-parameterization
While reading a paper, I came across the statement
This prediction function will be
parameterized by a parameter vector $\theta$ in a parameter space
$\Theta$. Often, this prediction function ...
0
votes
0answers
18 views
Confused by “mean” and “median” of $\alpha$ parameter in Lognormal Distribution
I read a book and find the following content (Fig.1). It is about lognormal distribution. What confused me is in the red box.
In Fig.1, $\alpha$ is said "the mean of $z$ on the log scale". Then I ...
2
votes
1answer
27 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 ...
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0answers
23 views
Estimation of covariance over a range of independent variable
I have a set of data that comprise 2 dependent variables (let's call them $x_1$ and $x_2$) evaluated at different temperatures, T.
There is an assumption that for a range of T ($T_0<T<T_1$) ...
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0answers
28 views
Mixed parameterization of sample from normal distribution
I am studying exponential families and mixed parameterizations. Now, I am told that
$$
\mathbf{\theta} = \begin{bmatrix}\mu\\ -\frac{1}{2\sigma^2}\end{bmatrix}
$$
is the parameter in a variation-...
1
vote
1answer
25 views
How can I write an asymmetric-BEKK(1,1,1) model
To write a BEKK(1,1) model, I would write something like this,
$$H_t=C^*C^{*'}+A_{11}\varepsilon_{t-1}\varepsilon_{t-1}'A_{11}'+ B_{11}H_{t-1}B_{11}' $$
How could I extend this to write the BEKK(1,...
3
votes
1answer
95 views
good terminology for the parameters of a lognormal distribution?
Is there any good short terminology for the two parameters of a lognormal distribution?
I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
3
votes
1answer
298 views
Understanding the definition of a location parameter
In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ...
3
votes
1answer
114 views
Formula for cross-classified (a.k.a., crossed random factors) mixed effects model with interaction between two “second level” variables
I have a crossed-classified (Hox, 2010) mixed effects model—also known as crossed random factors (West, Welch, & Galecki, 2015), but I am struggling with how to write the formula for an ...
2
votes
1answer
172 views
Some questions about exponential families
Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding.
The first is
Consider$$f(x|\theta)=h(x)\...
2
votes
0answers
36 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 $X$ ...
2
votes
2answers
121 views
Testing whether the conditional correlations/covariances differ between two groups
I have two samples of variables $\{y_{1i},y_{2i},x_i,s_i\}$. Where $y_1$ and $y_2$ are binary variables, $x$ is a continuous variable and $s$ is a sample indicator, taking the value 0 in one sample ...
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0answers
128 views
How to find parameter $k$ from a negative binomial distribution in R?
I want to find the value of parameter $k$ from my data set. The data set is composed of several populations. Should I calculate the parameter $k$ for each subpopulation, or for the population at large?...
2
votes
1answer
51 views
Can every parameter $\Theta$ in Bayesian modelling be explained via De Finetti`s representation theorem
My question is the following: I recently got to know (and love) De Finetti`s representation theorem and I now started to read a Book an Bayesian statistics. However this book simply takes as 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 ...
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vote
1answer
113 views
How to identify a Bayesian SEM parameter in R package blavaan
I have fit a Bayesian SEM using the R package blavaan.
...
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vote
1answer
30 views
Why are mixed effect methods more effective when data are limited
In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a ...
1
vote
1answer
91 views
From OLS to semi-parametric GAM: parametric vs no-parametric
I am quite new to this kind of topic, but for my master thesis i built an multiple linear regression with OLS. Now I want to control for non-linear relationships using a semi-parametric GAM. My ...
0
votes
1answer
49 views
GLMMs, stable isotope distribution analysis
I am currently working with a set of samples of stable isotopic concentrations obtained from a group of individuals.
I am trying to process this data through a glmm() from the package lme4 to ...
0
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0answers
62 views
How to Interpret Parameter Estimate Output from SPSS [duplicate]
Dear Community Members,
Given the outputs of the SPSS analysis, how can the exp (B ) and Beta values be interpreted in terms of odd ratio ? and in relation to how the independent variable affects the ...
0
votes
1answer
59 views
Calibration of an individual-based model of an epidemic
I am currently developing an individual-based (or agent-based) mathematical model (IBM) of an epidemic. I want to calibrate the transmission parameters in my IBM to match empirical data (epidemic ...
3
votes
0answers
99 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, ...
