Bayesian prediction interval from pystan output

On this article, I’ll leave the simple memo to get bayesian prediction interval from the sampled points of PyStan output and visualize it.
Basically, I’ll use the code from the article, Simple Bayesian modeling by Stan.

How to make the local level model with seasonal effect

Overview

On time-series analytics, we frequently need to think about a recurring pattern. In the context of time-series analytics, a recurring pattern is referred to as a seasonal effect.

For example, please see the image below. This image is the plotting of a time series data. As you can see, it has recurrent pattern.


On this article, I'll make the local level model with seasonal effects on Stan.

Simple trial of various types of time series analytics

By air passengers data, which is typical time-series data, I'll try some time-series analytics methods. Actually, about some points, I'm not sure if it is really appropriate or not. So, if you find some wrong or incorrect points, please let me know.

Summary of local level model and local linear trend model to time series data

Overview

On this article, I’ll leave the summary about local level model and local linear trend model.
The both models are for time series analysis. Those are too simple to adapt for real data as they are. But those are very fundamental in many cases and by adding some other factors, those can become practical. So, here, I’ll leave rough memos about those.
As a text book, I’m using the following book. This article responds to chapters two and three.

Local Linear Trend Model for time series analysis on Stan

Overview

On this article, I’ll make the local linear trend model to artificial time series data by Stan. Before, I made a local level model on Stan on the article, Local level model to time series data on Stan.
By adding the slope variable to that model, I’ll make the local linear trend model.
I used this book as reference.

Local level model with explanatory variable to time series data on Stan

Overview

On this article, I'll make the local level model with explanatory variable to time series data on Stan.
Before, I made the simple local level model on Stan. In the practical situation, we frequently need to make model with some explanatory variables. So, I'll make simple local level model with explanatory variables here.
As a reference, I’m using the following book. This article is dealing with the chapter 5 of the book.

Time series analysis to predict future points on Stan

Overview

Before, I made the simple local level model to time series data. At that article, I just showed the sampled points traced the data. This time, I also do sampling to predict the following points of the data.



Roughly, on the image above, the blue points are data you already have and the red points are the predict target. The purpose of this article is to make model by blue points, data and predict red points, the values of future.

Local level model to time series data on Stan

Overview

On the articles below, I tried local level modeling to time series data on Edward and am still struggling.

Time series analysis on TensorFlow and Edward: local level model

Deep learning and Machine learning methods blog

Time series analysis on TensorFlow and Edward: local level model:P.S. 1

On the article below, I tried to analyze time series data with local level model. On Stan, I could do it before without problem. But on Edward and TensorFlow, I have been struggling. Deep learning and Machine learning methods blog From the situation above, although it doesn't work well yet, I got some progress.

On this article, I’ll express by Stan what I wanted on Edward. In a nutshell, I’ll write local level model to time series data on Stan.

Hierarchical Bayesian model's parameter Interpretation on Stan

Usually, Hierarchical Bayesian model has many parameters. So apparently, the interception to the sampled point’s statistical information looks complex.

On the article below, I made a Hierarchical Bayesian model to the artificial data. Here, by using almost same but simpler data, I’ll make a model and try to interpret.

Hierarchical Bayesian model by Stan: Struggling

I'll try to make Hierarchical Bayesian model to the artificial data by Stan. Hierarchical Bayesian model lets us write the model with a high degree of freedom.

Hierarchical Bayesian model by Stan: Struggling

I’ll try to make Hierarchical Bayesian model to the artificial data by Stan. Hierarchical Bayesian model lets us write the model with a high degree of freedom.

From Wikipedia,

Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.[1] The sub-models combine to form the hierarchical model, and the Bayes’ theorem is used to integrate them with the observed data, and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.

Bayesian modeling to data with heteroscedasticity by Stan

Before, I wrote about the data with heteroscedasticity.

What is heteroscedasticity and How to check it on R

Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have. Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

How to deal with heteroscedasticity

On the article below, I wrote about heteroscedasticity. Linear regression with OLS is simple and strong method to analyze data. By the coefficients, we can know the influence each variables have. Although it looks easy to use linear regression with OLS because of the simple system from the viewpoint of necessary code and mathematics, it has some important conditions which should be kept to get proper coefficients and characteristics.

This time, I’ll make the model again but with Python and Stan.

Simple Bayesian modeling by Stan

Overview

About Bayesian modeling, we can use some languages and tools. BUGS, PyMC, Stan. On this article, I made simple regression model by using Stan from Python.