I'm looking for a really simple explanation of what a dynamic linear model is as I need to explain this to a non-technical audience. I have looked around for examples but they are very maths heavy.
I found this explanation below from the dlmodeler vignette:
http://www2.uaem.mx/r-mirror/web/packages/dlmodeler/dlmodeler.pdf (see pages 2 and 3)
There are still aspects of it that I think the audience won't follow so am looking for someone to provide a very basic explanation or example that illustrates broadly how dlms work (would be great if the examples were in R).
Generalized Dynamic Linear Models are a powerful approach to time-series modelling, analysis and forecasting. This framework is closely related to the families of regression models, ARIMA models, exponential smoothing, and structural time-series (also known as unobserved component models, UCM).
The origin of DLM time-series analysis has its roots in the world of engineering. In order to control dynamic physical systems, unknown quantities such as velocity and position (the state of the system) need to be estimated from noisy measurements such as readings from various sensors (the observations). The state of the system evolves from one state (e.g. position and speed at time t) to another (position and speed at time t+1) according to a known transition equation, possibly including random perturbations and intervention effects. The observations are derived from the state values by a an observation equation (e.g. observation at time t = position + noise), also possibly including random disturbances and intervention effects.
The challenge is to obtain the best estimate of the unknown state considering the set of available observations at a given point in time. Due to the presence of noise disturbances, it is generally not possible to simply use the observations directly because they lead to estimators which are too erratic. During the 1960s, the Kalman filtering and smoothing algorithm was developed and popularized to efficiently and optimally solve this estimation problem. The technique is based on an iterative procedure in which state values are successively predicted given the knowledge of the past observations, and then updated upon the reception of the next observation. Because of the predict-and-update nature of Kalman filtering, it can also be interpreted under a Bayesian perspective.
Dynamic linear models
The theory developed for the control of dynamic systems has a direct application to the general analysis of time-series. By having a good estimate of the current state and dynamics of the system, it is possible to derive assumptions about their evolution and subsequent values; and therefore to obtain a forecast for the future observations.
Dynamic Linear Models are a special case of general state-space models where the state and the observation equations are linear, and the distributions follow a normal law. They are also referred to as gaussian linear state-space models. Generalized DLMs relax the assumption of normality by allowing the distribution to be any of the exponential family of functions (which includes the Bernoulli, binomial and Poisson distributions, useful in particular for count data).
There are two constitutive operations for dynamic linear models: filtering and smoothing. In a few words, filtering is the operation consisting in estimating the state values at time t, using only observations up to (and including) t-1. On the contrary, smoothing is the operation which aims at estimating the state values using the whole set of observations.