One of the problems often dealt in Statistics is minimization of the objective function. And contrary to the linear models, there is no analytical solution for models that are nonlinear on the parameters such as logistic regression, neural networks, and nonlinear regression models (like Michaelis-Menten model). In this situation, we ... [Read more...]

In my previous article, we talked about implementations of linear regression models in R, Python and SAS. On the theoretical sides, however, I briefly mentioned the estimation procedure for the parameter $boldsymbol{beta}$. So to help us understand how software does the estimation procedure, we'll look at the mathematics behind ...

[Read more...]Consider the linear regression model, $$ y_i=f_i(boldsymbol{x}|boldsymbol{beta})+varepsilon_i, $$ where $y_i$ is the response or the dependent variable at the $i$th case, $i=1,cdots, N$ and the predictor or the independent variable is the $boldsymbol{x}$ term defined in the mean function $... [Read more...]

A family of pdfs or pmfs ${g(t|theta):thetainTheta}$ for a univariate random variable $T$ with real-valued parameter $theta$ has a monotone likelihood ratio (MLR) if, for every $theta_2__theta_1$, $g(t|theta_2)/g(t|theta_1)$ is a monotone (nonincreasing or nondecreasing) function of $t$ on ${t:g(t|...

[Read more...] More on Likelihood Ratio Test, the following problem is originally from Casella and Berger (2001), exercise 8.12.ProblemFor samples of size $n=1,4,16,64,100$ from a normal population with mean $mu$ and known variance $sigma^2$, plot the power function of the following LRTs (Likelihood Ratio Tests). Take $alpha = .05$. $H_0:muleq 0$ versus $H_1:mu__0$$H_0:...

[Read more...]In this post, I would like to share a simple problem about sampling analysis. And I will demonstrate how to solve this using Python and R. The first two problems are originally from Sampling: Design and Analysis book by Sharon Lohr.ProblemsLet $N=6$ and $n=3$. For purposes of studying sampling ... [Read more...]

As promised from my recent article, here's my tutorial on how to layout and design an infographic in R. This article will serve as a template for more infographic design that I plan to share on future posts. Hence, we will go through the following sect...

[Read more...] The Philippine government has launched Open Data Philippines (data.gov.ph) last year, January 16, 2014. Accordingly, the data.gov.ph aims to make national government data searchable, accessible, and useful, with the help of the different agencies of go...

[Read more...] In imaging, we deal with multivariate data, like in array form with several spectral bands. And trying to come up with interpretation across correlations of its dimensions is very challenging, if not impossible. For example let's recall the number of s...

[Read more...]Ever wonder what's the mathematics behind face recognition on most gadgets like digital camera and smartphones? Well for most part it has something to do with statistics. One statistical tool that is capable of doing such feature is the Principal Component Analysis (PCA). In this post, however, we will not ... [Read more...]

Authors:Arnold R. Salvacion [email protected] Analysis and Visualization using R (blog) Al-Ahmadgaid B. Asaad (maintainer)[email protected] Land Use Evaluation System (ALUES) is an R package that evaluates land suitability for different crop production. The package is based on the Food and Agriculture Organization (FAO) and the ... [Read more...]

Enough with the theory we recently published, let's take a break and have fun on the application of Statistics used in Data Mining and Machine Learning, the k-Means Clustering.k-means clustering is a method of vector quantization, originally from signa... [Read more...]

Currently, I am taking Statistics for Image Analysis on my masteral, and have been exploring this topic in R. One package that has the capability in this field is the EBImage from Bioconductor, which will be showcased in this post.InstallationFor those... [Read more...]

There will be upcoming meetups for R User Group Philippines and Python Philippines (PythonPH) Community. Below are the details:R Meetuptopic: R for SAS users, and planning of RUG activities venue: 9/F Sun Life Centre, 5th Avenue corner Rizal Drive... [Read more...]

It's been two weeks for search and rescue operations on Malaysia Airlines Flight MH370, after it vanished from the radar on March 8, 2014. And wherever they are, we hope and pray for them.Photo from VENUS - Wall of Hope & Prayers for MH370In this p... [Read more...]

To the R users based in the Philippines, there will be upcoming meetup, here are the details:topics: Markov Switching Models in R by Ohly Santos How to use the op... [Read more...]

There is one package that I've been longing. A package that will give me the power to manipulate and do any 3D stuffs in R. I tried persp and wireframe, but I find them difficult to use especially on complicated mathematical functions, like doing param...

[Read more...] One great package in R is the animation made by Yihui Xie. And just for fun, we are going to explore that. Our aim is to create simple animated 2D and 3D plots. Here is the first one, 2D of courseThe code,It's a piece of cake right? The function ...

[Read more...]A friend of mine asked me to code the following in R:Generate samples of size 10 from Normal distribution with $\mu$ = 3 and $\sigma^2$ = 5;Compute the $\bar{x}$ and $\bar{x}\mp z_{\alpha/2}\displaystyle\frac{\sigma}{\sqrt{n}}$ using the 95% confidence... [Read more...]

I've been thinking that it might be better to explore the Box-Jenkins ARIMA (Autoregressive Integrated Moving-Average) three-iterative modelling on Shiny. So here is what I got, this app is intended for ARIMA(2, 2, 2) subclass family only.The app has s... [Read more...]

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