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Table of Contents#
dismod_at-20240312: User Documentation and API
1 An Introduction To The Mathematics of Dismod_at
1.1 The Dismod_at Ordinary Differential Equation
1.2 The Censored Gaussian and Laplace Densities
1.3 The Prevalence Only ODE
2 Installing dismod_at
3 Dismod_at Getting Started Examples / Tests
3.1 Create get_started Input Tables: Example and Test
4 User Examples and Tests
4.1 Non-uniform Age Average Grid
4.2 Example Fitting With Two Levels of Random Effects
4.3 Fitting Binomial Data Example
4.4 Bounding Covariate Multipliers Absolute Data Effect
4.5 Generating Priors For Next Level Down Node Tree
4.6 Fitting Data That Has Negative Values Censored
4.7 Remove an Age or Time From a Smoothing
4.8 Using Data Interval Compression
4.9 Fitting With Non-Zero Constant Random Effects in Smoothing Grid
4.10 Constrain Omega Using const_value
4.11 Continuing a Fit From Where it Left Off
4.12 Model The Covid-19 Epidemic
4.13 csv2db_command: Example and Test
4.14 Fit With Outliers Using Data Density Command
4.15 Explanation of Simulated Data Table, data_sim
4.16 An Example Fitting Simulated Diabetes Data
4.17 Fitting with Constraints on Differences in Age and Time
4.18 Fit Fixed First Then Both
4.19 Group Measurement Noise Covariate Multipliers, Gamma
4.20 Fitting Just Random Effects
4.21 Fitting Simulated Data Example
4.22 Using Group Covariate Multipliers
4.23 Check the Hessian of the Fixed Effects Objective
4.24 Check the Hessian of the Random Effects Objective
4.25 Using hold_out in Data, Subset Data, and Option Tables
4.26 hold_out Command: Balancing Sex Covariate Values
4.27 An Ill Conditioned Example Where Re-Scaling is Helpful
4.28 Zero Rate Until a Jump at a Known Age
4.29 Using Lasso on Covariate Multiplier
4.30 Estimating Smoothing Standard Deviation Multiplies
4.31 Case with no Children; i.e., no Random Effects
4.32 Fitting One Function of Two Variables
4.33 Using Data Interval Compression
4.34 Example Plotting Log-Scaled Values w.r.t Age and Time
4.35 Example Plotting The Data and Its Fit
4.36 Example Plotting The Rates for a Fit
4.37 Predict Average Integrand Using Results of a Fit
4.38 Predict Covariate Multiplier Values
4.39 Example Using The Node Covariate Table
4.40 Case Where Re-Scaling is Useful
4.41 Weighted Residuals
4.42 Sample from Asymptotic Distribution for Model Variables
4.43 Sampling From The Asymptotic Distribution for a Simulated Data Fit
4.44 Sample Posterior Using Simulated Data
4.45 Example Fitting a Covariate with a Shock
4.46 Simulating Data with Log Transformed Distribution
4.47 A Simulate Data Speed Test
4.48 Example Fitting With Subgroup Covariate Multipliers
4.49 Sum of Residuals at Optimal Estimate
4.50 Example Using system_command_prc
4.51 Using Initialization Trace Option
4.52 Using the Trapezoidal ODE Solver
4.53 Continuing a Fit Using Ipopt Warm Start
4.54 Constrain Sum of Child Rate Effect to Zero
4.55 Constrain Sum of Subgroup Measurement Covariate Multipliers to Zero
4.56 Constrain Sum of Subgroup Rate Covariate Multipliers to Zero
5 The Dismod_at Database Tables
5.1 Tables That Are Only Used as Inputs
5.1.1 The Age Table
5.1.1.1 age_table: Example and Test
5.1.2 The avgint Table: Defines Average Integrand Cases
5.1.2.1 avgint_table: Example and Test
5.1.3 The Covariate Table
5.1.3.1 covariate_table: Example and Test
5.1.4 The Data Table
5.1.5 The Density Table
5.1.5.1 density_table: Example and Test
5.1.6 The Integrand Table
5.1.6.1 integrand_table: Example and Test
5.1.7 The mulcov Table: Covariate Multipliers
5.1.7.1 mulcov_table: Example and Test
5.1.8 The Node Table
5.1.8.1 node_table: Example and Test
5.1.9 Lists of Node Smoothing Pairs
5.1.9.1 nslist_pair_table: Example and Test
5.1.10 The Node Smoothing List Table
5.1.10.1 nslist_table: Example and Test
5.1.11 The Option Table
5.1.12 The Prior Table
5.1.12.1 prior_table: Example and Test
5.1.13 The Rate Effect Covariate Table
5.1.13.1 rate_eff_cov_table: Example and Test
5.1.14 The Rate Table
5.1.14.1 rate_table: Example and Test
5.1.15 The Smooth Grid Table
5.1.15.1 smooth_grid_table: Example and Test
5.1.16 The Smoothing Table
5.1.17 The Subgroup Table
5.1.18 The Time Table
5.1.18.1 time_table: Example and Test
5.1.19 The Weight Grid Table
5.1.19.1 weight_grid_table: Example and Test
5.1.20 The Weight Table
5.2 The Dismod_at Data Flow
5.2.1 The Age Average Table
5.2.2 The Covariate and Multiplier Bound Table
5.2.3 Simulated Measurements and Adjusted Standard Deviations
5.2.4 The Data Subset Table
5.2.5 Which Variables The Model Depends On
5.2.6 The Model and Weighted Residuals Corresponding to a Fit
5.2.7 The Optimization Results for Variables
5.2.8 Hessian of The Fixed Effect Objective Function
5.2.9 Hessian of The Random Effect Objective Function
5.2.10 The Log Table
5.2.11 The CppAD Mixed Information Table
5.2.12 The Predict Table: Average Integrand Predictions
5.2.13 Simulated Variation in Prior
5.2.14 The Sample Table: Samples of Variable Values
5.2.15 Scaling Fixed Effects Objective and Constraints
5.2.16 Starting Values Used During a Fit
5.2.17 The Fixed Effects Optimization Trace Table
5.2.18 True Values Used During Simulations
5.2.19 Identifying Model Variables
6 The Age-Time Dismod Model
6.1 The Model Variables
6.2 Model for the Average Integrand
6.3 Data Likelihood and Weighted Residuals
6.4 Prior for the Model Variables
6.4.1 The Fixed Effects Value Density Function
6.4.2 The Random Effects Value Density Function
6.4.3 Prior Density Function for Smoothing Age Difference
6.4.4 Prior Density Function for Smoothing Time Difference
6.4.5 Fixed Effects Differences Density Function
6.4.6 Random Effects Differences Density Function
6.4.7 Prior for Fixed Effect Values
6.4.8 Prior for Random Effect Values
6.5 Some Statistical Function Definitions
6.6 dismod_at Bilinear Interpolation
6.7 Simulating Posterior Distribution for Model Variables
6.8 Prevalence Does Not Depend On Other Cause Mortality
6.9 Numerical Approximation of Average Integrands
7 The dismod_at Commands
7.1 Bound The Covariate Multiplier Absolute Data Effect
7.2 Data Density Command: Change the Density for an Integrand
7.3 The Depend Command
7.3.1 depend Command: Example and Test
7.4 The Fit Command
7.4.1 fit Command: Example and Test
7.5 Hold Out Command: Randomly Sub-sample The Data
7.6 The Initialize Command
7.6.1 init Command: Example and Test
7.7 Convert an Old Database to New Format
7.7.1 old2new Command: Example and Test
7.8 The Predict Command
7.8.1 predict Command: Example and Test
7.9 The Sample Command
7.9.1 sample Command: Example and Test
7.10 Directly Setting Table Values
7.10.1 set Command: Example and Test
7.11 The Simulate Command
7.11.1 simulate Command: Example and Test
7.12 Python Program Syntax
8 Python Utilities
8.1 Compute The Average Integrand
8.1.1 Using the Python average_integrand Utility
8.2 Get File Name For a Database Connection
8.2.1 Example Using connection_file
8.3 Create a Python sqlite3 Database Connection
8.4 Create a Dismod_at Database
8.4.1 create_database: Example and Test
8.5 Create a Database Table
8.5.1 create_table and Unicode: Example and Test
8.6 Conversion of a Csv File to a Dismod_at Database
8.7 Create Csv Files that Summarize The Database
8.8 Get Column Names and Types in a Table
8.8.1 get_name_type: Example and Test
8.9 Get Data From a Table
8.9.1 get_row_list: Example and Test
8.10 Get All Data From a Table
8.10.1 get_table_dict: Example and Test
8.11 Metropolis MCMC Algorithm
8.11.1 Predict Average Integrand Using Results of a Fit
8.12 Modify a Column of an Sqlite Database
8.12.1 modify Command: Example and Test
8.13 Perturb Command: Random Change to Start or Scale Tables
8.14 Plot Log-Scaled Values With Respect To Age and Time
8.15 Plot The Data Fit By Integrand
8.16 Plot The Rates for a Fit
8.17 Replace A a Table
8.17.1 replace_table: Example and Test
8.18 Execute an SQL command
8.19 Print Run and Check a System Command
8.20 Convert an Iterable Object to a Unicode String
8.20.1 unicode_tuple: Example and Test
9 Changes and Additions to Dismod_at
9.1 Release Notes for 2024
9.2 Release Notes for 2023
9.3 Release Notes for 2022
9.4 Release Notes for 2021
9.5 Release Notes for 2020
9.6 Release Notes for 2019
9.7 Release Notes for 2018
9.8 Release Notes for 2017
9.9 Release Notes for 2016
9.10 Release Notes for 2015
10 Dismod_at Wish List