Likelihood Inference for Spatial Point Processes

• Introduction
• Families of Unnormalized Densities
• Examples of Families of Unnormalized Densities
  • Exponential Families
  • Conditional Families
  • Missing Data
  • Unknown Normalizing Functions and Missing Data
  • Unknown Normalizing Functions and Bayesian Inference
  • General Models Specified by Unnormalized Densities
• Markov Chain Monte Carlo
  • Updates Not `Algorithms'
  • Combination of Updates
    • Stationarity
    • Composition
    • Mixing
    • Reversibility
    • State-Dependent Mixing
  • The Metropolis-Hastings Update
  • The Metropolis Update
  • Variable-at-a-Time Metropolis-Hastings Updates
  • The Gibbs Update
  • The Metropolis-Hastings-Green Update
    • State-Dependent Mixing
  • Why it Works
• Finite Point Processes
  • Setup and Notation
  • Statistical Models
  • Strauss Processes
  • Completion of Exponential Family Models
  • Limit Models from Strauss Processes
    • Conditional Strauss Processes
    • Unconditional Strauss Processes
• Simulating Finite Point Processes
• Stability Conditions
• Markov Chain Convergence
  • -Irreducibility
  • Small Sets
  • Harris Recurrence
  • Geometric Ergodicity
  • Central Limit Theorem
  • Comment on Asymptotics
• Two New Point Processes
  • The Triplets Process
  • The Saturation Process
  • Limit Models from the Saturation and Triplets Processes
• Monte Carlo Likelihood Inference
  • Monte Carlo Likelihood
  • Monte Carlo Newton-Raphson
• Stochastic Approximation
• Reverse Logistic Regression
• Fitting the Saturation Model
  • Standard Errors
  • Choosing the Spacing
  • A Final Estimate
  • Stochastic Approximation
• Hypothesis Tests
  • Wald Test
  • Rao Test
  • Likelihood Ratio Test
• Missing Data and Edge Effects
  • Monte Carlo Likelihood with Missing Data
  • Comparison of MCL and MCEM
  • Missing Data in Point Processes
• Fitting the Triplets Process
• Comparing the Saturated and Triplets Models
• Conclusion