Some thoughts on density surface updating 1.Major Updates every X years: refitting models (perhaps new kinds of models) to accumulated data over large.

Slides:

Advertisements

Similar presentations

Sampling Design, Spatial Allocation, and Proposed Analyses Don Stevens Department of Statistics Oregon State University.

Advertisements

Spatial modelling an introduction

Spatial point patterns and Geostatistics an introduction

Lecture 23 Spatial Modelling 2 : Multiple membership and CAR models for spatial data.

CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.

Change Detection C. Stauffer and W.E.L. Grimson, “Learning patterns of activity using real time tracking,” IEEE Trans. On PAMI, 22(8): , Aug 2000.

Literature Review Kathryn Westerman Oliver Smith Enrique Hernandez Megan Fowler.

Bare Surface Tension and Surface Fluctuations of Clusters with Long–Range Interaction D.I. Zhukhovitskii Joint Institute for High Temperatures, RAS.

David Prado Oct Antarctic Sea Ice: John N. Rayner and David A. Howarth 1979.

Basic geostatistics Austin Troy.

The loss function, the normal equation,

Lecture Notes for CMPUT 466/551 Nilanjan Ray

Time series analysis - lecture 5

Spatial Interpolation

Relevance Feedback based on Parameter Estimation of Target Distribution K. C. Sia and Irwin King Department of Computer Science & Engineering The Chinese.

Cycles and Exponential Smoothing Models Materials for this lecture Lecture 4 Cycles.XLS Lecture 4 Exponential Smoothing.XLS Read Chapter 15 pages

Effective Gaussian mixture learning for video background subtraction Dar-Shyang Lee, Member, IEEE.

Active Appearance Models Suppose we have a statistical appearance model –Trained from sets of examples How do we use it to interpret new images? Use an.

Bayesian Methods for Monitoring Public Health Surveillance Data Owen Devine Division of STD Prevention National Center for HIV, STD and TB Prevention Centers.

Distribution Function Estimation in Small Areas for Aquatic Resources Spatial Ensemble Estimates of Temporal Trends in Acid Neutralizing Capacity Mark.

Fishing in a stirred ocean: sustainable harvest can increase spatial variation in fish populations Heather Berkley Bruce Kendall, David Siegel, Christopher.

Ordinary Kriging Process in ArcGIS

Team 2: Final Report Uncertainty Quantification in Geophysical Inverse Problems.

1 An Introduction to Nonparametric Regression Ning Li March 15 th, 2004 Biostatistics 277.

Distribution Function Estimation in Small Areas for Aquatic Resources Spatial Ensemble Estimates of Temporal Trends in Acid Neutralizing Capacity Mark.

Lecture II-2: Probability Review

Thematic Maps Choropleth, Proportional/Graduated Symbol, Digital Image, Isoline/Isopleth and Dot Distribution Maps.

Transition Matrix Theory and Loss Development John B. Mahon CARe Meeting June 6, 2005 Instrat.

Objectives of Multiple Regression

Physics 114: Lecture 15 Probability Tests & Linear Fitting Dale E. Gary NJIT Physics Department.

Geo479/579: Geostatistics Ch13. Block Kriging. Block Estimate  Requirements An estimate of the average value of a variable within a prescribed local.

Gaussian process modelling

Chapter 15 Modeling of Data. Statistics of Data Mean (or average): Variance: Median: a value x j such that half of the data are bigger than it, and half.

Applications of Bayesian sensitivity and uncertainty analysis to the statistical analysis of computer simulators for carbon dynamics Marc Kennedy Clive.

Bayesian inference review Objective –estimate unknown parameter  based on observations y. Result is given by probability distribution. Bayesian inference.

R. Kass/W03P416/Lecture 7 1 Lecture 7 Some Advanced Topics using Propagation of Errors and Least Squares Fitting Error on the mean (review from Lecture.

CSC321: Neural Networks Lecture 12: Clustering Geoffrey Hinton.

The probability that a person visits a location. ~ means that two locations are equivalent.  Grids -> close to the border of two different.

Gridding Daily Climate Variables for use in ENSEMBLES Malcolm Haylock, Climatic Research Unit Nynke Hofstra, Mark New, Phil Jones.

TRADING SPACE FOR TIME IN BAYESIAN FRAMEWORK Nataliya Bulygina 1, Susana L. Almeida 1, Thorsten Wagener 2, Wouter Buytaert 1, Neil McIntyre 1 1 Department.

Mixture Models, Monte Carlo, Bayesian Updating and Dynamic Models Mike West Computing Science and Statistics, Vol. 24, pp , 1993.

CS 782 – Machine Learning Lecture 4 Linear Models for Classification  Probabilistic generative models  Probabilistic discriminative models.

Spatio-Temporal Surface Vector Wind Retrieval Error Models Ralph F. Milliff NWRA/CoRA Lucrezia Ricciardulli Remote Sensing Systems Deborah K. Smith Remote.

Spatial Interpolation III

STAR Sti, main features V. Perevoztchikov Brookhaven National Laboratory,USA.

The Stock Synthesis Approach Based on many of the ideas proposed in Fournier and Archibald (1982), Methot developed a stock assessment approach and computer.

Digital Image Processing

1 GEOG4650/5650 – Fall 2007 Spatial Interpolation Triangulation Inverse-distance Kriging (optimal interpolation)

STAR Kalman Track Fit V. Perevoztchikov Brookhaven National Laboratory,USA.

A Review of Benchmarking Methods G Brown, N Parkin, and N Stuttard, ONS.

Analyzing wireless sensor network data under suppression and failure in transmission Alan E. Gelfand Institute of Statistics and Decision Sciences Duke.

Esri UC 2014 | Technical Workshop | Concepts and Applications of Kriging Eric Krause Konstantin Krivoruchko.

L15 – Spatial Interpolation – Part 1 Chapter 12. INTERPOLATION Procedure to predict values of attributes at unsampled points Why? Can’t measure all locations:

Chapter 13 (Prototype Methods and Nearest-Neighbors )

Esri UC2013. Technical Workshop. Technical Workshop 2013 Esri International User Conference July 8–12, 2013 | San Diego, California Concepts and Applications.

Data Analytics CMIS Short Course part II Extra Material: Forecasting Sam Buttrey December 2015.

2000 SEMINAR ON REINSURANCE PITFALLS IN FITTING LOSS DISTRIBUTIONS CLIVE L. KEATINGE.

INTEGRATING SATELLITE AND MONITORING DATA TO RETROSPECTIVELY ESTIMATE MONTHLY PM 2.5 CONCENTRATIONS IN THE EASTERN U.S. Christopher J. Paciorek 1 and Yang.

Special Topics in Geo-Business Data Analysis Week 3 Covering Topic 6 Spatial Interpolation.

Bayesian Approach Jake Blanchard Fall Introduction This is a methodology for combining observed data with expert judgment Treats all parameters.

Cycles and Exponential Smoothing Models Materials for this lecture Lecture 10 Cycles.XLS Lecture 10 Exponential Smoothing.XLSX Read Chapter 15 pages

Computational Intelligence: Methods and Applications Lecture 22 Linear discrimination - variants Włodzisław Duch Dept. of Informatics, UMK Google: W Duch.

INTERPOLATION Procedure to predict values of attributes at unsampled points within the region sampled Why?Examples: -Can not measure all locations: - temperature.

Introduction to emulators Tony O’Hagan University of Sheffield.

Summary of Prev. Lecture

Where did we stop? The Bayes decision rule guarantees an optimal classification… … But it requires the knowledge of P(ci|x) (or p(x|ci) and P(ci)) We.

The loss function, the normal equation,

Mathematical Foundations of BME Reza Shadmehr

Concepts and Applications of Kriging

Presentation transcript:

Some thoughts on density surface updating 1.Major Updates every X years: refitting models (perhaps new kinds of models) to accumulated data over large areas. 2.Minor Updates as and when new (reliable) survey estimates become available: Use new estimates to modify existing surfaces locally (spatially and temporally). a.Should be quick and easy. b.Must accommodate any kind of density surface model (including stratified density estimates).

Bayesian Update? Problem 1: How accommodate any kind of density surface model? (Models could have few/no common parameters.) Solution 1: Update densities cell-by-cell rather than parameters. – Assume (say) lognormal distribution of density. – Need variance-covariance matrix of cell densities. – (End product is a weighted average.)

3 Updating a cell

4 Multi-cell Example

5

Bayesian Update? Problem 2: How get smooth edges? Solution 2: Smooth via weights decaying with distance from edge – Easy to smooth; not so easy to find the best amount of smoothing.

Another Example Survey Estimates update current surface at single point in time. Two-stage updating: – Bayesian Update within survey region. – Smoothing across survey region boundary. Current surface and Updated surface apply for whole season (quarter), then jump/drop suddenly to that for next season. Survey Estimate Current Density Updated, Unsmoothed Updated, Smoothed

1. Smoothing Current Density (Example at single location)

Current Density Smoothed Smoothing: Periodic smooth (interpolate current estimates) Take account of uncertainty in fitting and reflect in fit. (not shown above)

2. Updating with New Survey Estimate (Example: single location, Month 2) Current Smoothed Estimate at Month=2

Updated estimate 2. Updating with New Survey Estimate (Example: single location, Month 2) New Survey Estimate

2. Updating with New Survey Estimate (Example: single location, Month 2) Updated Smooth

Another update and Smooth

And One More...

All Together

Cumulative Effect Smooth Temporal Updating: – Degree of Smoothness: more flexible with more data. – Effect of update decays with temporal distance. – Uncertainty in new smooth (not shown above) updated smoothly in time too.

Multiple Locations etc....

3. Spatio-Temporal Interaction How similar in space should temporal effects be? Constraining temporal smooths closer together to be more similar will prevent inconsistent temporal trends at locations near each other. (Unclear in advance how necessary this will prove to be.)