On kalman filtering, posterior mode estimation and fisher scoring in dynamic exponential family regression

Metrika ◽  
1991 ◽  
Vol 38 (1) ◽  
pp. 37-60 ◽  
Author(s):  
L. Fahrmeir ◽  
H. Kaufmann
Keyword(s):  
Kalman Filtering ◽  
Exponential Family ◽  
Fisher Scoring ◽  
Mode Estimation ◽  
Posterior Mode ◽  
Posterior Mode Estimation

How to extend Elo: a Bayesian perspective

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Martin Ingram
Keyword(s):  
Kalman Filtering ◽  
Time Varying ◽  
Mode Estimation ◽  
Log Likelihood ◽  
Professional Tennis ◽  
Elo Rating System ◽  
Posterior Mode Estimation ◽  
Approximate Bayesian ◽  
Chess Players ◽  
Probabilistic Justification

Abstract The Elo rating system, originally designed for rating chess players, has since become a popular way to estimate competitors’ time-varying skills in many sports. Though the self-correcting Elo algorithm is simple and intuitive, it lacks a probabilistic justification which can make it hard to extend. In this paper, we present a simple connection between approximate Bayesian posterior mode estimation and Elo. We provide a novel justification of the approximations made by linking Elo to steady-state Kalman filtering. Our second key contribution is to observe that the derivation suggests a straightforward procedure for extending Elo. We use the procedure to derive versions of Elo incorporating margins of victory, correlated skills across different playing surfaces, and differing skills by tournament level in tennis. Combining all these extensions results in the most complete version of Elo presented for the sport yet. We evaluate the derived models on two seasons of men’s professional tennis matches (2018 and 2019). The best-performing model was able to predict matches with higher accuracy than both Elo and Glicko (65.8% compared to 63.7 and 63.5%, respectively) and a higher mean log-likelihood (−0.615 compared to −0.632 and −0.633, respectively), demonstrating the proposed model’s ability to improve predictions.

Delivering Sustainable Water Systems Using Kalman Filter and Statistical Approach

2017 ◽  
Vol 4 (1) ◽  
pp. 41-52
Author(s):  
Dedy Loebis
Keyword(s):  
Kalman Filtering ◽  
Statistical Approach ◽  
Water Systems ◽  
Data Sets ◽  
Pressure Data ◽  
Burst Event ◽  
Sample Data ◽  
Other Information ◽  
Supply Systems ◽  
Frequency Features

This paper presents the results of work undertaken to develop and test contrasting data analysis approaches for the detection of bursts/leaks and other anomalies within wate r supply systems at district meter area (DMA)level. This was conducted for Yorkshire Water (YW) sample data sets from the Harrogate and Dales (H&D), Yorkshire, United Kingdom water supply network as part of Project NEPTUNE EP/E003192/1 ). A data analysissystem based on Kalman filtering and statistical approach has been developed. The system has been applied to the analysis of flow and pressure data. The system was proved for one dataset case and have shown the ability to detect anomalies in flow and pres sure patterns, by correlating with other information. It will be shown that the Kalman/statistical approach is a promising approach at detecting subtle changes and higher frequency features, it has the potential to identify precursor features and smaller l eaks and hence could be useful for monitoring the development of leaks, prior to a large volume burst event.

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